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The full text is available in the PDF provided.

Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements—the principles of relativity and light speed invariance—are used to derive the mathematical structure of Minkowski space–time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.

We examine the electronic structure of the family of ternary zinc spinel oxides ZnX₂O₄ (X=Al, Ga and In). The band gap of ZnAl₂O₄ calculated using density functional theory (DFT) is 4.25 eV and is overestimated compared with the experimental value of 3.8–3.9 eV. The DFT band gap of ZnGa₂O₄ is 2.82 eV and is underestimated compared with the experimental value of 4.4–5.0 eV. Since DFT typically underestimates the band gap in the oxide system, the experimental measurements for ZnAl₂O₄ probably require a correction. We use two first-principles techniques capable of describing accurately the excited states of semiconductors, namely the GW approximation and the modified Becke–Johnson (MBJ) potential approximation, to calculate the band gap of ZnX₂O₄. The GW and MBJ band gaps are in good agreement with each other. In the case of ZnAl₂O₄, the predicted band gap values are >6 eV, i.e. ∼2 eV larger than the only reported experimental value. We expect future experimental work to confirm our results. Our calculations of the electron effective masses and the second band gap indicate that these compounds are very good candidates to act as transparent conducting host materials.

We study the quantum Hall liquid and the metal–insulator transition in a high-mobility two-dimensional electron gas, by means of photoluminescence and magnetotransport measurements. In the integer and fractional regime at ν>1/3, by analyzing the emission energy dispersion we probe the magneto-Coulomb screening and the hidden symmetry of the electron liquid. In the fractional regime above ν=1/3, the system undergoes metal-to-insulator transition, and in the insulating phase the dispersion becomes linear with evidence of an increased renormalized mass.

We present the results of a global neutrino oscillation data analysis within the three-flavour framework. We include the latest results from the MINOS long-baseline experiment (including electron neutrino appearance and anti-neutrino data), updating all relevant solar (Super-Kamiokande (SK) II+III), atmospheric (SK I+II+III) and reactor (KamLAND) data. Furthermore, we include a recent re-calculation of the anti-neutrino fluxes emitted from nuclear reactors. These results have important consequences for the analysis of reactor experiments and in particular for the status of the mixing angle θ₁₃. In our recommended default analysis, we find from the global fit that the hint for nonzero θ₁₃ remains weak, at 1.8σ for both neutrino mass hierarchy schemes. However, we discuss in detail the dependence of these results on assumptions regarding the reactor neutrino analysis.

Two-dimensional photonic crystal can be exploited as the top part of a light source in order to increase its extraction efficiency. Here, we report on the room-temperature intrinsic photoluminescence (PL) behavior of a nanocrystalline diamond (NCD) layer with diamond columns prepared on the top and periodically ordered into the lattice with square symmetry. Angle-resolved far-field measurements in the Γ–X crystal direction of broadband visible PL revealed up to six-fold enhancement of extraction efficiency as compared to a smooth NCD layer. A photonic band diagram above the lightcone derived from these measurements is in agreement with the diagram obtained from transmission measurements and simulation, suggesting that the enhancement is primarily due to light's coupling to leaky modes.

The rapid formation of large molecules and the subsequent production of solid-state dust particles in a low-pressure discharge is unlikely, because of the low rates of the polymerization reactions and short lifetimes of the species. Here, we suggest that C dust particles can form in atypically low (10^{− 3} mbar)-pressure hydrocarbon plasmas if the dust charging time is much shorter than the gas residence time in the device; we present supporting experimental evidence for this. Such a condition can be obtained by the production of high-density plasmas. The results show that dust formation from the gaseous phase can occur in a much wider parameter range than is commonly assumed.

The effects of intense electromagnetic fields on the decay of quasistationary states are investigated theoretically. We focus on the parameter regime of strong laser fields and nonlinear effects where an essentially nonperturbative description is required. Our approach is based on the imaginary time method previously introduced in the theory of strong-field ionization. Spectra and total decay rates are presented for a test case and the results are compared with exact numerical calculations. The potential of this method is confirmed by good quantitative agreement with numerical results.

We have investigated the impact of out-of-plane ferromagnetic (FM) anisotropy (which can be coincident with the direction of unidirectional anisotropy), where antiferromagnetic (AF) anisotropy is along the film plane. This provides a platform for non-collinear exchange coupling in an archetypal exchange coupled system in an unconventional way. We probe the in-plane magnetization by the depth-sensitive vector magnetometry technique. The experimental findings reveal a magnetization reversal (i) that is symmetric for both the branches of the hysteresis loop, (ii) that is characterized by vertically correlated domains associated with a strong transverse component of magnetization and (iii) that remains untrained (suppression of trained state) with field cycling. This scenario has been compared with in-plane magnetization reversal for a conventionalin-plane unidirectional anisotropic case in the same system that shows usual asymmetric reversal and training for vertically uncorrelated domains. We explain the above observations for the out-of-plane case in terms of inhomogeneous magnetic states due to competing perpendicular anisotropies that result in non-collinear FM–AF coupling. This study provides direct evidence for the vertical correlation of domains mediated by out-of-plane exchange coupling.

We study the formation and dynamics of the bound pair (BP) in a strongly correlated extended Hubbard model for both the Bose and the Fermi system. The bound triple (BT) for the Bose system is also investigated. We find that the bandwidths of the BP and BT gain significantly when the on-site and nearest-neighbor interaction strengths reach the corresponding resonant points. This allows fast transfer and efficient coherent separation of the BP and BT. The exact result shows that the success probability of the coherent separation is unity in the optimal system. In the Fermi system, this finding can be applied to create distant entanglement without the need for temporal control and the measurement process.

Using few-cycle laser pulses generated by optical parametric chirped pulse amplification, sub-cycle light-wave control of electrons was achieved at a carrier wavelength of 2.1 μm. We demonstrate the sub-cycle light-wave control in the case of strong field ionization of xenon atoms. Angle-resolved spectra of electrons emitted in the photoionization process were recorded as a function of the carrier-envelope phase (CEP) using an electron imaging technique. We observed a clear CEP-dependent asymmetry in the electron momentum distribution.

Point projection microscopy (PPM) is used to image suspended graphene by using low-energy electrons (100–205 eV). Because of the low energies used, the graphene is neither damaged nor contaminated by the electron beam for doses of the order of 10⁷ electrons per nm². The transparency of graphene is measured to be 74%, equivalent to electron transmission through a sheet twice as thick as the covalent radius of sp²-bonded carbon. Also observed is rippling in the structure of the suspended graphene, with a wavelength of approximately 26 nm. The interference of the electron beam due to diffraction off the edge of a graphene knife edge is observed and is used to calculate a virtual source size of 4.7±0.6 Å for the electron emitter. It is demonstrated that graphene can serve as both the anode and the substrate in PPM, thereby avoiding distortions due to strong field gradients around nanoscale objects. Graphene can be used to image objects suspended on the sheet using PPM and, in the future, electron holography.

A new scheme for mode locking a free-electron laser (FEL) amplifier is proposed based on electron beam current modulation. It is found that certain properties of the original concept (Thompson and McNeil 2008 Phys. Rev. Lett.100 203901), based on the energy modulation of electrons, are improved, including the spectral brightness of the source and the purity of the series of short pulses. Numerical comparisons are made between the new and old schemes and between a mode-locked FEL and a self-amplified spontaneous emission FEL. Illustrative examples using a hypothetical mode-locked FEL amplifier are provided. The ability to generate intense coherent radiation with a large bandwidth is demonstrated.

This paper aims to explore the inherent connection between Heisenberg groups, quantum Fourier transform (QFT) and (quasi-probability) distribution functions. Distribution functions for continuous and finite quantum systems are examined from three perspectives and all of them lead to Weyl–Gabor–Heisenberg groups. The QFT appears as the intertwining operator of two equivalent representations arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of the Wigner function from the marginal distributions via inverse Radon transform giving explicit formulae. We consider some applications of our approach to quantum information processing and quantum process tomography.

We present the experimental realization of a theoretical effect discovered by Olivares and Paris (2009 Phys. Rev. A 80 032329), in which a pair of entangled optical beams undergoing independent losses can see nonlocal correlations restored by the use of a nonlocal resource correlating the losses. Twin optical beams created in an entangled, Einstein–Podolsky–Rosen (EPR) state by an optical parametric oscillator above threshold were subjected to 50% loss from beamsplitters in their paths. The resulting severe degradation of the amplitude-quadrature correlations between the two beams was then suppressed when another, independent EPR state impinged upon the other input ports of the beamsplitters, effectively entangling the losses inflicted to the initial EPR state. The additional EPR beam pair was classically coherent with the primary one but had no quantum correlations with it. This result may find applications as a 'quantum tap' for entanglement.

In the microscopic world, multipartite entanglement has been achieved with various types of nanometer-sized two-level systems such as trapped ions, atoms and photons. On the macroscopic scale ranging from micrometers to millimeters, recent experiments have demonstrated bipartite and tripartite entanglement for electronic quantum circuits with superconducting Josephson junctions. It remains challenging to bridge these largely different length scales by constructing hybrid quantum systems. Doing so may allow us to manipulate the entanglement of individual microscopic objects separated by macroscopically large distances in a quantum circuit. Here we report on the experimental demonstration of induced coherent interaction between two intrinsic two-level states (TLSs) formed by atomic-scale defects in a solid via a superconducting phase qubit. The tunable superconducting circuit serves as a shuttle communicating quantum information between the two microscopic TLSs. We present a detailed comparison between experiment and theory and find excellent agreement over a wide range of parameters. We then use the theoretical model to study the creation and movement of entanglement between the three components of the quantum system.

An air–silica photonic crystal fibre with a gold nanowire at core centre is shown to support a low-loss azimuthally polarized mode. Since all the other modes have very high attenuation, the fibre effectively supports only this mode, acting as a single-polarization fibre with an extinction ratio >20 dB cm⁻¹ over a broad range of wavelengths (550–1650 nm in the device reported). It can be used as an effective azimuthal mode filter.

We investigated the magnetic properties of hydrogen-plasma-treated ZnO single crystals by using superconducting quantum interferometer device magnetometry. In agreement with the expected hydrogen penetration depth, we found that ferromagnetic behavior is present in the first 20 nm of the H-treated surface of ZnO with magnetization at saturation up to 6 emu g⁻¹ at 300 K and a Curie temperature of T_c≳400 K. In the ferromagnetic samples, a hydrogen concentration of a few atomic per cent in the first 20 nm of the surface layer was determined by nuclear reaction analysis. The saturation magnetization of H-treated ZnO increases with the concentration of hydrogen.

We have investigated single layer, bilayer and few-layer graphene exfoliated on SiO₂ and on single crystal surfaces of SrTiO₃, Al₂O₃ and TiO₂ using Raman spectroscopy. The typical 'fingerprint' 2D peak turns out to be indicative of the number of graphene layers independent of the substrate material. The morphological quality of the graphene is as good as on SiO₂ substrates for all the materials. We find evidence for substrate-induced changes due to doping. With most substrates, hole doping is observed, but with SrTiO₃ we have identified a dielectric substrate with which electron accumulation in graphene can be achieved.

In this paper, we report original measurements of total cross-sections (TCSs) for positron scattering from an important biomolecule, α-tetrahydrofurfuryl alcohol (THFA). The energy range of these measurements was 0.15–50.15 eV, whereas the energy resolution was ∼260 meV. In addition, we report theoretical results, calculated within the independent-screened additivity rule (IAM-SCAR) formalism, on the corresponding electron impact total cross-sections. In this case, the energy range is 1–10 000 eV. With the advent of new particle track simulation codes, which incorporate accurate atomic and molecular data in order to provide interaction details at the nanoscale, interest in positron and electron TCSs has enjoyed something of a recent renaissance as they specify the mean free path between collisions in such codes. Because the present data are, to the best of our knowledge, the first TCSs to be reported for positron scattering from THFA, they fill an important void in the knowledge available to us from the literature.

For chaotic cavities with scattering leads attached, transport properties can be approximated in terms of the classical trajectories that enter and exit the system. With a semiclassical treatment involving fine correlations between such trajectories, we develop a diagrammatic technique to calculate the moments of various transport quantities. Namely, we find the moments of the transmission and reflection eigenvalues for systems with and without time-reversal symmetry. We also derive related quantities involving an energy dependence: the moments of the Wigner delay times and the density of states of chaotic Andreev billiards, where we find that the gap in the density persists when subleading corrections are included. Finally, we show how to adapt our techniques to nonlinear statistics by calculating the correlation between transport moments. In each setting, the answer for the nth moment is obtained for arbitrary n (in the form of a moment generating function) and for up to three leading orders in terms of the inverse channel number. Our results suggest patterns that should hold for further corrections, and by matching with the lower-order moments available from random matrix theory, we derive the likely higher-order generating functions.

In this paper, we investigate the network of ownership relationships among European firms and its embedding in the geographical space. We carry out a detailed analysis of geographical distances between pairs of nodes, connected by edges or by shortest paths of varying length. In particular, we study the relation between geographical distance and network distance in comparison with a random spatial network model. While the distribution of geographical distance can be fairly well reproduced, important deviations appear in the network distance and in the size of the largest strongly connected component. Our results show that geographical factors allow us to capture several features of the network, while the deviations quantify the effect of additional economic factors at work in shaping the topology. The analysis is relevant to other types of geographically embedded networks and sheds light on the link formation process in the presence of spatial constraints.

Gaining insights into the mechanisms of how order and broken symmetry emerges from many-particle interactions is a major challenge in solid state physics. Most experimental techniques—such as angle-resolved photoemission spectroscopy (ARPES)—probe the single-particle excitation spectrum and extract information about the ordering mechanism and collective effects, often indirectly through theory. Time-resolved ARPES (tr-ARPES) makes collective dynamics of a system after optical excitation directly visible through their influence on the quasi-particle band structure. Using this technique, we present a systematic study of TbTe₃, a metal that exhibits a charge-density wave (CDW) transition. We discuss time-resolved data taken at different positions in the Brillouin zone (BZ) and at different temperatures. The transient change in the band structure due to the excitation is qualitatively different between the region gapped by the CDW order vector and an ungapped but otherwise equivalent region. Also, we discovered two distinct collective modes at roughly 3.5 and 2.5 THz, the latter of which only occurs in the CDW band near the gapped region, demonstrating the strength of tr-ARPES in discerning the origin of the modes from the way in which they couple to the quasi-particle bands. In addition, a systematic pump fluence dependence in the gapped region documents the crossover from a weakly perturbed to a strongly perturbed regime, which can be related to a crossover from a regime where mainly the amplitude mode gets excited to a regime where the CDW gap closes at least partially.

The direct laser cooling of neutral diatomic molecules in molecular beams suggests that trapped molecular ions can also be laser cooled. The long storage time and spatial localization of trapped molecular ions provides an opportunity for multi-step cooling strategies, but also requires careful consideration of rare molecular transitions. We briefly summarize the requirements that a diatomic molecule must meet for laser cooling, and we identify a few potential molecular ion candidates. We then carry out a detailed computational study of the candidates BH⁺ and AlH⁺, including improved ab initio calculations of the electronic state potential energy surfaces and transition rates for rare dissociation events. On the basis of an analysis of the population dynamics, we determine which transitions must be addressed for laser cooling, and compare experimental schemes using continuous-wave and pulsed lasers.

The outcomes of measurements on entangled quantum systems can be nonlocally correlated. However, while it is easy to write down toy theories allowing arbitrary nonlocal correlations, those allowed in quantum mechanics are limited. Quantum correlations cannot, for example, violate a principle known as macroscopic locality, which implies that they cannot violate Tsirelson's bound. This paper shows that there is a connection between the strength of nonlocal correlations in a physical theory and the structure of the state spaces of individual systems. This is illustrated by a family of models in which local state spaces are regular polygons, where a natural analogue of a maximally entangled state of two systems exists. We characterize the nonlocal correlations obtainable from such states. The family allows us to study the transition between classical, quantum and super-quantum correlations by varying only the local state space. We show that the strength of nonlocal correlations—in particular whether the maximally entangled state violates Tsirelson's bound or not—depends crucially on a simple geometric property of the local state space, known as strong self-duality. This result is seen to be a special case of a general theorem, which states that a broad class of entangled states in probabilistic theories—including, by extension, all bipartite classical and quantum states—cannot violate macroscopic locality. Finally, our results show that models exist that are locally almost indistinguishable from quantum mechanics, but can nevertheless generate maximally nonlocal correlations.

A method is presented for the implementation of edge local complementation (ELC) in graph states, based on the application of two Hadamard operations and a single controlled-phase (CZ) gate. As an application, we demonstrate an efficient scheme for constructing a one-dimensional logical cluster state based on the five-qubit quantum error-correcting code, using a sequence of ELCs. A single physical CZ operation, together with local operations, is sufficient to create a logical CZ operation between two logical qubits. This approach in concatenation may allow one to create a hierarchical quantum network for quantum information tasks.

The canonical quantization of macroscopic electromagnetism was recently presented in (Philbin 2010 New J. Phys.12 123008). This theory is used here to derive the Casimir effect, by considering the special case of thermal and zero-point fields. The stress-energy-momentum tensor of the canonical theory follows from Noether's theorem, and its electromagnetic part in thermal equilibrium gives the Casimir energy density and stress tensor. The results hold for arbitrary inhomogeneous magnetodielectrics and are obtained from a rigorous quantization of electromagnetism in dispersive, dissipative media. Continuing doubts about the status of the standard Lifshitz theory as a proper quantum treatment of Casimir forces do not apply to the derivation given here. Moreover, the correct expressions for the Casimir energy density and stress tensor inside media follow automatically from the simple restriction to thermal equilibrium, without the need for complicated thermodynamical or mechanical arguments.

A standard assumption in quantum chaology is the absence of correlation between spectra pertaining to different symmetries. Doubts were raised about this statement for several reasons, in particular because in semiclassics the spectra of different symmetries are expressed in terms of the same set of periodic orbits. We re-examine this question and notice the absence of correlations in the universal regime. In the case of continuous symmetry, the problem is reduced to parametric correlation, and we expect correlations to be present up to a certain time which is essentially classical but larger than the ballistic time.

It is experimentally verified that a two-dimensional planar focusing antenna based on gradient-index metamaterials has a similar performance as that of its parabolic counterpart. The antenna is designed using quasi-conformal transformation optics, and is realized with non-resonant I-shaped metamaterial unit cells. It is shown that the antenna has a broad bandwidth and very low loss. Near-field distributions of the antenna are measured and far-field radiation patterns are calculated from the measured data, which have good agreement with the full-wave simulations. Using all-dielectric metamaterials, the design can be scaled down to find applications at optical frequencies.

We investigate field enhancements by one-dimensional periodic arrays of tapered slits fabricated to a high quality (nm precision) using focused ion beam milling in a 180 nm-thick gold film. Tapering of periodic slits in metal was recently shown to boost the extraordinary optical transmission (EOT) exhibited by similar, but non-tapered, plasmonic structures. Here, both simulated and experimental reflection spectra, along with high-resolution two-photon luminescence (TPL) scanning optical images and simulated electric field plots of the metal slits, are compared, revealing good correspondence between spectral dependences and field intensity enhancements (FEs) estimated via the local TPL. Experimentally investigated structures had a fixed taper angle α=20.5° for two different widths, w=80 and 130 nm, having gaps g=25 and 65 nm, respectively, both fabricated at two different periods, Λ=500  and 700 nm. We attributed the obtained FE reaching ∼110 to nanofocusing and resonant interference of counter-propagating plasmons by the periodic tapered gaps. As both simulated and experimentally achieved FEs depend on taper angle, gold film thickness, period and gap of the slit arrays, the resonances can actually be tuned in the wavelength range from visible to infrared, making this configuration promising for a wide range of practical applications, e.g. within surface-enhanced spectroscopies.

The structural dynamics of graphite and graphene are unique, because of the selective coupling between electron and lattice motions and hence the limit on electric and electro-optic properties. Here, we report on the femtosecond probing of graphite films (1–3 nm) using ultrafast electron crystallography in the transmission mode. Two time scales are observed for the dynamics: a 700 fs initial decrease in diffraction intensity due to lattice phonons in optically dark regions of the Brillouin zone, followed by a 12 ps decrease due to phonon thermalization near the Γ and K regions. These results indicate the non-equilibrium distortion of the unit cells at early time and the subsequent role of long-wavelength atomic motions in the thermalization process. Theory and experiment are now in agreement regarding the nature of nuclear motions, but the results suggest that potential change plays a role in the lateral dynamics of the lattice.

The experimental verification of quantum features, such as entanglement, at large scales is extremely challenging because of environment-induced decoherence. Indeed, measurement techniques for demonstrating the quantumness of multiparticle systems in the presence of losses are difficult to define, and if they are not sufficiently accurate they can provide wrong conclusions. We present a Bell test where one photon of an entangled pair is amplified and then detected by threshold detectors, whose signals undergo postselection. The amplification is performed by a classical machine, which produces a fully separable micro–macro state. However, by adopting such a technique one can surprisingly observe a violation of the Clauser–Horne–Shimony–Holt inequality. This is due to the fact that ignoring the detection loophole opened by the postselection and the system losses can lead to misinterpretations, such as claiming micro–macro entanglement in a setup where evidently it is not present. By using threshold detectors and postselection, one can only infer the entanglement of the initial pair of photons, and so micro–micro entanglement, as is further confirmed by the violation of a nonseparability criterion for bipartite systems. How to detect photonic micro–macro entanglement in the presence of losses with the currently available technology remains an open question.

Magnetic monopoles have stimulated a great amount of theoretical and experimental interest since their prediction by Dirac in 1931. To date, their presence has evaded detection in high energy experiments despite intensive efforts. Recently, entities that mimic magnetic monopoles have been observed in bulk and planar frustrated materials known as spin-ice materials, and artificial spin-ice materials, respectively. In this paper we discuss the formation of these so-called monopole defects within a cobalt honeycomb artificial spin-ice lattice. Experimental results and micromagnetic simulations show that monopole defects of opposite sign are created at the boundaries of the lattice, and move in opposing directions. Discrepancies between simulations and experimental results demonstrate the importance of quenched disorder. Furthermore, we show that controlled edge nucleated monopole defect formation can be realized with the use of soft magnetic injection pads, which is a very promising development for technological applications based upon magnetic charge.

We investigate simple open few-body systems, the spectra of which exhibit fluctuating patterns, and review the conditions for the existence of an Ericson regime in deterministic, open quantum systems. A widely used criterion, the Lorentzian shape of the autocorrelation function of the spectrum, is shown to be insufficient for the occurrence of Ericson fluctuations: integrable systems or open systems that are not in the Ericson regime might display such an autocorrelation function. We also investigate the sensitivity of Ericson fluctuations on simplified models of realistic systems. In particular, we show that a simplified hydrogenic model for alkali atoms in crossed magnetic and electric fields does not yield Ericson fluctuations for a choice of the energy and field parameters where the realistic system is in the Ericson regime.

We report on vibrating reed measurements combined with density functional theory-based calculations to assess the elastic and damping properties of Fe–Pd ferromagnetic shape memory alloy splats. While the austenite–martensite phase transformation is generally accompanied by lattice softening, a severe modulus defect and elevated damping behavior are characteristic of the martensitic state. We interpret the latter in terms of twin boundary motion between pinning defects via partial 'twinning' dislocations. Energy dissipation is governed by twin boundary drag, primarily due to lattice imperfections, as concluded from the temperature dependence of damping and related activation enthalpies.

We examine a quantum memory scheme based on controlled de- and rephasing of atomic coherence of a nonresonant, inhomogeneously broadened Raman transition. We show that it generalizes the physical conditions for time-reversible interaction between light and atomic ensembles in the case of strong fields and nonlinear interactions. Furthermore, assuming weak input fields, we develop a unified framework for realizations exploiting either controlled reversible inhomogeneous broadening or atomic frequency combs, and discuss new aspects of the storage and manipulation of quantum states.

We made use of supersymmetric (SUSY) quantum mechanics to find the condition under which the Stark effect problem for a polar and polarizable closed-shell diatomic molecule subjected to collinear electrostatic and nonresonant radiative fields becomes exactly solvable. The condition connects values of the dimensionless parameters ω and Δω that characterize the strengths of the permanent and induced dipole interactions of the molecule with the respective fields. The exact solutions are obtained for the family of 'stretched' states. The field-free and strong-field limits of the combined-fields problem were found to exhibit supersymmetry and shape invariance, which is indeed the reason why they are analytically solvable. By making use of the analytic form of the wavefunctions, we obtained simple formulae for the expectation values of the space-fixed electric dipole moment, the alignment cosine and the angular momentum squared, and derived a 'sum rule' that combines the above expectation values into a formula for the eigenenergy. The analytic expressions for the characteristics of the strongly oriented and aligned states provide direct access to the values of the interaction parameters required for creating such states in the laboratory.

Several kinds of bent-shaped molecules with different lengths of the terminal chain are doped in chiral nematic liquid crystals (LCs), respectively, to induce the blue phase. The effects of the terminal chain length on the blue phase range are studied. The mechanisms of the phenomena are investigated through molecular dynamics, and the results indicate that molecules with a long terminal chain decrease the interfacial energy between the LCs and defects, whereas they also disturb the alignment of LCs near the interface and make an evident impact on the bent angle of molecules, which is not helpful in forming a stable blue phase. This work provides some useful insights into the molecular design of suitable bent-shaped dopants in order to obtain a wide range of LC blue phases.

A novel multilayer material system consisting of lanthanum and molybdenum nano-layers for both broadband and highly reflecting multilayer mirrors in the energy range between 80 and 130 eV is presented. The simulation and design of these multilayers were based on an improved set of optical constants, which were recorded by extreme ultraviolet (XUV)/soft-x-ray absorption measurements on freestanding lanthanum nano-films between 30 eV and 1.3 keV. Lanthanum–molybdenum (La/Mo) multilayer mirrors were produced by ion-beam sputtering and characterized through both x-ray and XUV reflectivity measurements. We demonstrate the ability to precisely simulate and realize aperiodic stacks. Their stability against ambient air conditions is demonstrated. Finally, the La/Mo mirrors were used in the generation of single attosecond pulses from high-harmonic cut-off spectra above 100 eV. Isolated 200 attosecond-long pulses were measured by XUV-pump/IR-probe streaking experiments and characterized using frequency-resolved optical gating for complete reconstruction of attosecond bursts (FROG/CRAB) analyses.

Information encoded on individual quanta will play an important role in our future lives, much as classically encoded digital information does today. Combining quantum information carried by single photons with classical signals encoded on strong laser pulses in modern fibre-to-the-home (FTTH) networks is a significant challenge, the solution to which will facilitate the global distribution of quantum information to the home and with it a quantum internet [1]. In real-world networks, spontaneous Raman scattering in the optical fibre would induce crosstalk between the high-power classical channels and a single-photon quantum channel, such that the latter is unable to operate. Here, we show that the integration of quantum and classical information on an FTTH network is possible by performing quantum key distribution (QKD) on a network while simultaneously transferring realistic levels of classical data. Our novel scheme involves synchronously interleaving a channel of quantum data with the Raman scattered photons from a classical channel, exploiting the periodic minima in the instantaneous crosstalk and thereby enabling secure QKD to be performed.

We determine the real-time quantum dynamics of a biomolecular donor–acceptor system in order to describe excitonic energy transfer in the presence of slow environmental Gaussian fluctuations. For this, we compare two different approaches. On the one hand, we use the numerically exact iterative quasi-adiabatic propagator path-integral scheme that incorporates all non-Markovian contributions. On the other, we apply the second-order cumulant time-nonlocal quantum master equation that includes non-Markovian effects. We show that both approaches yield coinciding results in the relevant crossover regime from weak to strong electronic couplings, displaying coherent as well as incoherent transitions.

Rigorous, closed form expressions are derived for non-paraxial imaging of sources of multipole radiation from which conservation of angular momentum (AM) flux is established. Coupling of spin and orbital optical AM flux is also quantitatively investigated, highlighting the importance of spin–orbit interactions in high numerical aperture imaging.

Raman amplification in plasma has been proposed to be a promising method of amplifying short radiation pulses. Here, we investigate chirped pulse Raman amplification (CPRA) where the pump pulse is chirped and leads to spatiotemporal distributed gain, which exhibits superradiant scaling in the linear regime, usually associated with the nonlinear pump depletion and Compton amplification regimes. CPRA has the potential to serve as a high-efficiency high-fidelity amplifier/compressor stage.

Nonlinear interaction between kinetic Alfvén waves (KAWs) and the electrostatic and magnetostatic convective cells in plasmas is considered here. It is shown that the KAWs in the kinetic regime can excite only magnetostatic convective cells, but those in the inertial regime can excite only electrostatic convective cells. Moreover, there is a preferred spatial scale for the instability-generated electrostatic cells, but not for the magnetostatic cells. The significance of the present results for space plasmas is discussed.

Wave propagation in disordered media can be strongly modified by multiple scattering and wave interference. Ultimately, the so-called Anderson-localized regime is reached when the waves become strongly confined in space. So far, Anderson localization of light has been probed in transmission experiments by measuring the intensity of an external light source after propagation through a disordered medium. However, discriminating between Anderson localization and losses in these experiments remains a major challenge. In this paper, we present an alternative approach where we use quantum emitters embedded in disordered photonic crystal waveguides as light sources. Anderson-localized modes are efficiently excited and the analysis of the photoluminescence spectra allows us to explore their statistical properties, for example the localization length and average loss length. With increasing the amount of disorder induced in the photonic crystal, we observe a pronounced increase in the localization length that is attributed to changes in the local density of states, a behavior that is in stark contrast to entirely random systems. The analysis may pave the way for accurate models and the control of Anderson localization in disordered photonic crystals.

We propose a new criterion for judging zero quantum discord for arbitrary bipartite states. A bipartite quantum state has zero quantum discord if and only if all the blocks of its density matrix are normal matrices and commute with each other. Given a bipartite state with zero quantum discord, the question of how to find the set of local projectors that do not disturb the whole state after being imposed on one subsystem is also presented. A class of two-qubit X-state is used to test the criterion, and an experimental scheme is proposed for realizing it. Consequently, we prove that the positive operator-valued measurement cannot extinguish the quantum correlation of a bipartite state with nonzero quantum discord.

We have investigated the conduction over a wide range of temperatures of λ DNA molecules deposited across slits etched through a few-nanometers-thick platinum film. The slits were insulating before DNA deposition but contained metallic Ga nanoparticles, a result of focused ion beam etching. When these nanoparticles were superconducting, we found that they can induce superconductivity through the DNA molecules, even though the main electrodes are nonsuperconducting. These results indicate that minute metallic particles can easily transfer charge carriers to attached DNA molecules and provide a possible reconciliation between apparently contradictory previous experimental results concerning the length over which DNA molecules can conduct electricity.

First-principles calculations have been utilized to investigate the biaxial strain-dependent electronic properties of fully hydrogenated bilayer graphene. It has been found that after complete hydrogenation, bilayer graphene exhibits semiconducting characteristics with a wide direct band gap. The band gap can be tuned continuously by the biaxial strain. Furthermore, compressive strain can induce the semiconductor-to-metal transition of this hydrogenated system. The origin of the strain-tunable band gap is discussed. The present study suggests the possibility of tuning the band gap of fully hydrogenated bilayer graphene by using mechanical strain and may provide a promising approach for the fabrication of electromechanical devices based on bilayer graphene.

We study double-barrier interfaces separating regions of asymptotically subsonic and supersonic flow of Bose-condensed atoms. These setups contain at least one black hole sonic horizon from which the analogue of Hawking radiation should be generated and emitted against the flow in the subsonic region. Multiple coherent scattering by the double-barrier structure strongly modulates the transmission probability of phonons, rendering it very sensitive to their frequency. As a result, resonant tunneling occurs with high probability within a few narrow frequency intervals. This gives rise to highly non-thermal spectra with sharp peaks. We find that these peaks are mostly associated with decaying resonances and only occasionally with dynamical instabilities. Even at achievable non-zero temperatures, the radiation peaks can be dominated by spontaneous emission, i.e. enhanced zero-point fluctuations, and not, as is often the case in analogue models, by stimulated emission.

A group of barchans, crescent sand dunes, exhibit a characteristic flying-geese pattern in deserts on Earth and Mars. This pattern implies that an indirect interaction between barchans, mediated by an inter-dune sand stream, which is released from one barchan's horns and caught by another barchan, plays an important role in the dynamics of barchan fields. We used numerical simulations of a recently proposed cell model to investigate the effects of inter-dune sand streams on barchan fields. We found that a sand stream from a point source moves a downstream barchan laterally until the head of the barchan is finally situated behind the stream. This final configuration was shown to be stable by a linear stability analysis. These results indicate that flying-geese patterns are formed by the lateral motion of barchans mediated by inter-dune sand streams. By using simulations we also found a barchan mono-corridor generation effect, which is another effect of sand streams from point sources.

Lattice Hamiltonians (e.g. Levin and Wen 2005 Phys. Rev. B 71 045110) can be constructed that have a low energy description, that is a doubled Chern–Simons (CS) theory—two independent opposite chirality topological sectors. We show that the partition function of these theories is an expectation of Wilson loops that form a link in 2+1 dimensional spacetime known in the mathematical literature as chain–mail. This geometric construction establishes a concrete connection between the lattice models and continuum Chern–Simons theories, allowing us to use well-established results on the latter to obtain a physical interpretation of the lattice model Hilbert space and Hamiltonian, its topological invariance, exactness under coarse-graining and how two opposite chirality sectors of the doubled theory arise. These features of the lattice models can thus be situated in the broader context of topological invariants obtained from CS theories.

We consider the bosonic fractional quantum Hall (FQH) effect in the presence of a non-Abelian gauge field in addition to the usual Abelian magnetic field. The non-Abelian field breaks the twofold internal state degeneracy, but preserves the Landau level degeneracy. Using exact diagonalization, we find that for moderate non-Abelian field strengths the system's behaviour resembles a single internal state quantum Hall system, while for stronger fields there is a phase transition to either two internal state behaviour or the complete absence of FQH plateaus. Usually the energy gap is reduced by the presence of a non-Abelian field, but some non-Abelian fields appear to slightly increase the gap of the ν=1 and ν=3/2 Read–Rezayi states.

The detailed features of solitons in holographic superfluids are discussed. Using solitons as probes, we study the behavior of holographic superfluids by varying the scaling dimension of the condensing operator and make a comparison to the Bose–Einstein condensate–Bardeen–Cooper–Schrieffer comparison phenomena. Further evidence of this analogy is provided by the behavior of the solitons' length scales as well as by the superfluid critical velocity.

Topologically non-trivial superconductivity has been predicted to occur in superconductors with a sizable spin–orbit (SO) coupling in the presence of an external Zeeman splitting. Two such systems have been proposed: (a) s-wave superconductor pair potential is proximity induced on a semiconductor and (b) pair potential naturally arises from an intrinsic s-wave pairing interaction. As it is now well known, such systems in the form of a two-dimensional (2D) film or 1D nano-wires in a wire network can be used in topological quantum computation. When the external Zeeman splitting Γ crosses a critical value Γ_c, the system passes from a regular superconducting phase to a non-Abelian topological superconducting phase. In both cases (a) and (b) that we consider in this paper, the pair potential Δ is strictly s-wave in both the ordinary and the topological superconducting phases, which are separated by a topological quantum critical point at , where μ (≫Δ) is the chemical potential. On the other hand, since Γ_c≫Δ, the Zeeman splitting required for the topological phase (Γ>Γ_c) far exceeds the value (Γ∼Δ) above which an s-wave pair potential is expected to vanish (and the system to become non-superconducting) in the absence of SO coupling. We are thus led to the situation that the topological superconducting phase appears to set in a parameter regime at which the system is actually non-superconducting in the absence of SO coupling. In this paper, we address the question of how a pure s-wave pair potential can survive a strong Zeeman field to give rise to a topological superconducting phase. We show that the SO coupling is the crucial parameter for the quantum transition into and the robustness of the topologically non-trivial superconducting phase realized for Γ≫Δ.

We performed a Hong–Ou–Mandel interference experiment with 1.5 μm band photon pairs generated through spontaneous four-wave mixing (SFWM) in two independent silicon wire waveguides (SWWs). To maintain the long-term stability of the coupling between the SWWs and optical fibers without a fiber alignment system, we employed fiber module SWWs installed in a rigid metallic case with fiber array interfaces. In addition, those signal photons that passed through a beam splitter (BS) were detected by high-speed single-photon detectors that used InGaAs avalanche photodiodes operated in a gated mode with a high gate frequency of 500 MHz. With these novel technologies, we successfully observed a quantum interference with a visibility of 73% without subtracting accidental coincidence counts in the fourfold coincidence measurement.

Collisions between nuclei at ultrarelativistic energies produce a colour-deconfined plasma that expands explosively and rapidly reverts to the colour-confined (hadronic) state. In non-central collisions, the zone of hot matter is transversely anisotropic and may be 'tilted' relative to the direction of the incoming beams. As the matter cools and expands into the vacuum, the evolution of the system shape depends sensitively on the dynamical response of the plasma under extreme conditions. Two-pion intensity interferometry performed relative to the impact parameter can be used to measure the approximate final shape of the system when pions decouple from the system. We use several transport models to illustrate the dependence of the final shape on the QCD equation of state and late-stage hadronic rescattering. The dependence of the final shape on collision energy may reveal non-trivial structures in the QCD phase diagram. Indeed, the few measurements published to date show an intriguing behaviour in an energy region under intense experimental and theoretical scrutiny, as signatures of a first-order phase transition may appear there. We discuss strong parallels between shape studies in heavy-ion collisions and those in two other strongly coupled systems.

When inverting nuclear magnetic resonance relaxation data in order to obtain quasi-continuous distributions of relaxation times for fluids in porous media, it is common practice to impose a non-negative (NN) constraint on the distributions. While this approach can be useful in reducing the effects of data distortion and/or preventing wild oscillations in the distributions, it may give misleading results in the presence of real negative amplitude components. Here, some examples of valid negative components for articular cartilage and hydrated collagen are given. Articular cartilage is a connective tissue, consisting mainly of collagen, proteoglycans and water, which can be considered, in many aspects, as a porous medium. Separate T₁ relaxation data are obtained for low-mobility ('solid') macromolecular ¹H and for higher-mobility ('liquid') ¹H by the separation of these components in free induction decays, with α denoting the solid/liquid ¹H ratio. When quasi-continuous distributions of relaxation times (T₁) of the solid and liquid signal components of cartilage or collagen are computed from experimental relaxation data without imposing the usual NN constraint, valid negative peaks may appear. The features of the distributions, in particular negative peaks, and the fact that peaks at longer times for macromolecular and water protons are at essentially the same T₁, are interpreted as the result of a magnetization exchange between these two spin pools. For the only-slightly-hydrated collagen samples, with α>1, the exchange leads to small negative peaks at short T₁ times for the macromolecular component. However, for the cartilage, with substantial hydration or for a strongly hydrated collagen sample, both with α≪1, the behavior is reversed, with a negative peak for water at short times. The validity of a negative peak may be accepted (dismissed) by a high (low) cost of NN in error of fit. Computed distributions for simulated data using observed signal-to-noise ratios also verify the need for some negative components. Observed relaxation times and signal ratios can be fitted formally by a simple two-site exchange model that gives the exchange times and the uncoupled relaxation times of the liquid and solid components, with significant trends of these parameters with increasing ¹H ratio, α. The solid-to-liquid exchange times are found to be in the range from 10 ms to a few tens of ms at all hydration levels. The results may be of interest for the application of magnetization exchange contrast in the imaging of articular cartilage to determine changes associated with pathologies and ageing. Other important porous media exist where exchange phenomena and negative relaxation components cannot be disregarded.

Dynamin is a protein that plays a key role in the transport and recycling of membrane tubes and vesicles within a living cell. This protein adsorbs from solution to PIP₂-containing membranes, and on these tubes it forms curved oligomers that condense into tight helical domains of uniform radius. The dynamics of this process is treated here in terms of the linear stability of a continuum model, whereby membrane-mediated interactions are shown to drive the spontaneous nucleation of condensed dynamin domains. We furthermore show that the deformation of the membrane outside the dynamin domains induces an energy barrier that can hinder the full coalescence of neighboring growing domains. We compare these calculations to experimental observations on dynamin dynamics in vitro.

In this paper, we study the tailoring of photon spectral properties generated by four-wave mixing in a birefringent photonic crystal fibre (PCF). The aim is to produce intrinsically narrow-band photons and hence to achieve high non-classical interference visibility and generate high-fidelity entanglement without any requirement for spectral filtering, leading to high effective detection efficiencies. We show unfiltered Hong–Ou–Mandel interference visibilities of 77% between photons from the same PCF and 80% between separate sources. We compare results from modelling the PCF to these experiments and analyse photon purities.

In this paper, we prove, extend and review possible mappings between the two-dimensional (2D) cluster state, Wen's model, the 2D Ising chain and Kitaev's toric code model. We introduce a 2D duality transformation to map the 2D lattice cluster state into the topologically ordered Wen model. Then, we investigate how this mapping could be achieved physically, which allows us to discuss the rate at which a topologically ordered system can be achieved. Next, using a lattice fermionization method, Wen's model is mapped into a series of 1D Ising interactions. Considering the boundary terms with this mapping then reveals how the Ising chains interact with one another. The duality of these models can be taken as a starting point to address questions as to how their gate operations in different quantum computational models can be related to each other.

A degenerate three-component Fermi gas of atoms with identical attractive interactions is expected to exhibit superfluidity and magnetic order at low temperature and, for sufficiently strong pairwise interactions, become a Fermi liquid of weakly interacting trimers. The phase diagram of this system is analogous to that of quark matter at low temperature, motivating strong interest in its investigation. We describe how a three-component gas below the superfluid critical temperature can be prepared in an optical lattice. To realize an SU(3)-symmetric system, we show how pairwise interactions in the three-component atomic system can be made equal by applying radiofrequency and microwave radiation. Finally, motivated by the aim to make more accurate models of quark matter, which have color, flavor and spin degrees of freedom, we discuss how an atomic system with SU(2)⊗SU(3) symmetry can be achieved by confining a three-component Fermi gas in the p-orbital band of an optical lattice potential.

Spinor ultracold gases in one dimension (1D) represent an interesting example of strongly correlated quantum fluids. They have a rich phase diagram and exhibit a variety of quantum phase transitions. We consider a 1D spinor gas of bosons with a large spin S. A particular example is the gas of chromium atoms (S=3), where the dipolar collisions efficiently change the magnetization and make the system sensitive to the linear Zeeman effect. We argue that in 1D the most interesting effects come from the pairing interaction. If this interaction is negative, it gives rise to a (quasi)condensate of singlet bosonic pairs with an algebraic order at zero temperature, and for (2S+1)≫1 the saddle point approximation leads to physically transparent results. Since in 1D one needs a finite energy to destroy a pair, the spectrum of spin excitations has a gap. Hence, in the absence of a magnetic field, there is only one gapless mode corresponding to phase fluctuations of the pair quasicondensate. Once the magnetic field exceeds the gap, another condensate emerges, namely the quasicondensate of unpaired bosons with spins aligned along the magnetic field. The spectrum then contains two gapless modes corresponding to the singlet-paired and spin-aligned unpaired Bose condensed particles, respectively. At T=0, the corresponding phase transition is of the commensurate–incommensurate type.

Adhesion micro-domains (ADs) formed during encounters of lymphocytes with antigen-presenting cells (APC) mediate the genetic expression of quanta of cytokines interleukin-2 (IL-2). The IL-2-induced activation of IL-2 receptors promotes the stepwise progression of the T-cells through the cell cycle, hence their name, immunological synapses. The ADs form short-lived reaction centres controlling the recruitment of activators of the biochemical pathway (the kinases Lck and ZAP) while preventing the access of inhibitors (phosphatase CD45) through steric repulsion forces. CD45 acts as the generator of adhesion domains and, through its role as a spacer protein, also as the promoter of the reaction. In a second phase of T-cell–APC encounters, long-lived global reaction spaces (called supramolecular activation complexes (SMAC)) form by talin-mediated binding of the T-cell integrin (LFA-1) to the counter-receptor ICAM-1, resulting in the formation of ring-like tight adhesion zones (peripheral SMAC). The ADs move to the centre of the intercellular adhesion zone forming the central SMAC, which serve in the recycling of the AD. We propose that cell stimulation is triggered by integrating the effect evoked by the short-lived adhesion domains. Similar global reaction platforms are formed by killer cells to destruct APC. We present a testable mechanical model showing that global reaction spaces (SMAC or dome-like contacts between cytotoxic cells and APC) form by self-organization through delayed activation of the integrin-binding affinity and stabilization of the adhesion zones by F-actin recruitment. The mechanical stability and the polarization of the adhering T-cells are mediated by microtubule–actin cross-talk.

We survey the use of spectroscopic imaging scanning tunneling microscopy (SI-STM) to probe the electronic structure of underdoped cuprates. Two distinct classes of electronic states are observed in both the d-wave superconducting (dSC) and the pseudogap (PG) phases. The first class consists of the dispersive Bogoliubov quasiparticle excitations of a homogeneous d-wave superconductor, existing below a lower energy scale E=Δ₀. We find that the Bogoliubov quasiparticle interference (QPI) signatures of delocalized Cooper pairing are restricted to a k-space arc, which terminates near the lines connecting k=±(π/a₀,0) to k=±(0,π/a₀). This arc shrinks continuously with decreasing hole density such that Luttinger's theorem could be satisfied if it represents the front side of a hole-pocket that is bounded behind by the lines between k=±(π/a₀,0) and k=±(0,π/a₀). In both phases, the only broken symmetries detected for the |E|<Δ₀ states are those of a d-wave superconductor. The second class of states occurs proximate to the PG energy scale E=Δ₁. Here the non-dispersive electronic structure breaks the expected 90°-rotational symmetry of electronic structure within each unit cell, at least down to 180°-rotational symmetry. This electronic symmetry breaking was first detected as an electronic inequivalence at the two oxygen sites within each unit cell by using a measure of nematic (C₂) symmetry. Incommensurate non-dispersive conductance modulations, locally breaking both rotational and translational symmetries, coexist with this intra-unit-cell electronic symmetry breaking at E=Δ₁. Their characteristic wavevector Q is determined by the k-space points where Bogoliubov QPI terminates and therefore changes continuously with doping. The distinct broken electronic symmetry states (intra-unit-cell and finite Q) coexisting at E∼Δ₁ are found to be indistinguishable in the dSC and PG phases. The next challenge for SI-STM studies is to determine the relationship of the E∼Δ₁ broken symmetry electronic states with the PG phase, and with the E<Δ₀ states associated with Cooper pairing.

We study in detail the flux properties of a radiofrequency (rf) outcoupled horizontally guided atom laser by following the scheme demonstrated by Guerin W et al (2006 Phys. Rev. Lett.97 200402). Both the outcoupling spectrum (flux of the atom laser versus rf frequency of the outcoupler) and the flux limitations imposed on operating in the quasi-continuous regime are investigated. These aspects are studied using a quasi-one-dimensional model, whose predictions are shown to be in fair agreement with the experimental observations. This work allows us to identify the operating range of the guided atom laser and to confirm its promises with regard to studying quantum transport phenomena.

Matter–wave interferometry has been used extensively over the last few years to demonstrate the quantum-mechanical wave nature of increasingly larger and more massive particles. We have recently suggested the use of the historical Poisson spot setup to test the diffraction properties of larger objects. In this paper, we present the results of a classical particle van der Waals (vdW) force model for a Poisson spot experimental setup and compare these to Fresnel diffraction calculations with a vdW phase term. We include the effect of disc-edge roughness in both models. Calculations are performed with D₂ and with C₇₀ using realistic parameters. We find that the sensitivity of the on-axis interference/focus spot to disc-edge roughness is very different in the two cases. We conclude that by measuring the intensity on the optical axis as a function of disc-edge roughness, it can be determined whether the objects behave as de Broglie waves or classical particles. The scaling of the Poisson spot experiment to larger molecular masses is, however, not as favorable as in the case of near-field light-grating-based interferometers. Instead, we discuss the possibility of studying the Casimir–Polder potential using the Poisson spot setup.

We report on emerging beam resonances appearing in diffraction patterns of a helium atom beam reflected at grazing incidence from a grating. The plane ruled grating is mounted in an out-of-plane diffraction configuration. We present the measured angular diffraction patterns as a function of the atom's energy change along the grating normal. This presentation allows us to readily trace back the peak positions and widths to the geometry of the out-of-plane diffraction configuration. In the diffraction patterns, an interference effect due to emerging beam resonances is found to progress side by side with a new emerging diffraction beam.

In the Stern–Gerlach experiment, silver atoms were separated according to their spin state (Gerlach and Stern 1922 Z. Phys.9 353–355). This experiment demonstrates the quantization of spin and relies on the classical description of motion. However, so far, no design has led to a functional Stern–Gerlach magnet for free electrons. Bohr and Pauli showed in the 1930 Solvay conference that Stern–Gerlach magnets for electrons cannot work, at least if the design is based on classical trajectories (Pauli W 1932 Proc. of the 6th Solvay Conf. 2 (1930) (Brussels: Gauthier-Villars) pp 183–86, 217–20, 275–80; Pauli W 1964 Collected Scientific Papers ed R Kronig and V F Weiskopf, vol 2 (New York: Wiley)). Here, we present ideas for the realization of a Stern–Gerlach magnet for electrons in which spin and motion are treated fully quantum mechanically. We show that a magnetic phase grating composed of a regular array of microscopic current loops can separate electron diffraction peaks according to their spin states. The experimental feasibility of a diffractive approach is compared to that of an interferometric approach. We show that an interferometric arrangement with magnetic phase control is the functional equivalent of an electron Stern–Gerlach magnet.

We present a filtered backprojection algorithm for reconstructing the Wigner function of a system of large angular momentum j from Stern–Gerlach-type measurements. Our method is advantageous over the full determination of the density matrix in that it is insensitive to experimental fluctuations in j, and allows for a natural elimination of high-frequency noise in the Wigner function by taking into account the experimental uncertainties in the determination of j, its projection m and the quantization axis orientation. No data binning and no arbitrary smoothing parameters are necessary in this reconstruction. Using recently published data (Riedel et al 2010 Nature464 1170), we reconstruct the Wigner function of a spin-squeezed state of a Bose–Einstein condensate of about 1250 atoms, demonstrating that measurements along quantization axes lying in a single plane are sufficient for performing this tomographic reconstruction. Our method does not guarantee positivity of the reconstructed density matrix in the presence of experimental noise, which is a general limitation of backprojection algorithms.

We present a Ramsey-type atom interferometer operating with an optically trapped sample of 10⁶ Bose-condensed ⁸⁷Rb atoms. We investigate this interferometer experimentally and theoretically with an eye to the construction of future high precision atomic sensors. Our results indicate that, with further experimental refinements, it will be possible to produce and measure the output of a sub-shot-noise-limited, large atom number BEC-based interferometer. The optical trap allows us to couple the |F=1,  m_F=0⟩→|F=2,  m_F=0⟩ clock states using a single photon 6.8 GHz microwave transition, while state selective readout is achieved with absorption imaging. We analyse the process of absorption imaging and show that it is possible to observe atom number variance directly, with a signal-to-noise ratio ten times better than the atomic projection noise limit on 10⁶ condensate atoms. We discuss the technical and fundamental noise sources that limit our current system, and present theoretical and experimental results on interferometer contrast, de-phasing and miscibility.

We report on a novel experiment to generate non-classical atomic states via quantum non-demolition (QND) measurements on cold atomic samples prepared in a high-finesse ring cavity. The heterodyne technique developed for QND detection exhibits an optical shot-noise limited behavior for local oscillator optical power of a few hundred μW, and a detection bandwidth of several GHz. This detection tool is used in a single pass to follow non-destructively the internal state evolution of an atomic sample when subjected to Rabi oscillations or a spin-echo interferometric sequence.

We report on the realization of a sodium Bose–Einstein condensate (BEC) in a combined red-detuned optical dipole trap formed by two beams crossing in a horizontal plane and a third, tightly focused dimple trap (dT) propagating vertically. We produce a BEC in three main steps: loading of the crossed dipole trap from laser-cooled atoms, an intermediate evaporative cooling stage that results in efficient loading of the auxiliary dT, and a final evaporative cooling stage in the dT. Our protocol is implemented in a compact setup and allows us to reach quantum degeneracy even with relatively modest initial atom numbers and available laser power.

We study the measurement of the positions of atoms as a means of estimating the relative phase between two Bose–Einstein condensates. We consider N bosonic atoms released from a double-well trap, which form an interference pattern; we show that the measurement of the position of N atoms has a sensitivity that saturates the bound set by the quantum Fisher information, and allows for estimation at the Heisenberg limit of precision. Phase estimation through the measurement of the center of mass of the interference pattern can also provide sub-shot-noise sensitivity. Finally, we study the effect of an overlap of the two clouds on the estimation precision when Mach–Zehnder interferometry is performed in a double well. We find that a nonzero overlap of the clouds strongly reduces the phase sensitivity.

We develop a unified theory for clocks and gravimeters using the interferences of multiple atomic waves put in levitation by traveling light pulses. Inspired by optical methods, we identify a propagation invariant, which enables us to analytically derive the wave function of the sample scattering on the light pulse sequence. A complete characterization of the device sensitivity with respect to frequency or acceleration measurements is obtained. These results agree with previous numerical simulations and confirm the conjecture of sensitivity improvement through multiple atomic wave interferences. A realistic experimental implementation for such a clock architecture is discussed.

Limits on the long-term stability and accuracy of a second generation cold atom gravimeter are investigated. We demonstrate a measurement protocol based on four interleaved measurement configurations, which allows rejection of most of the systematic effects, but not those related to Coriolis acceleration and wave-front distortions. Both are related to the transverse motion of the atomic cloud. Carrying out measurements with opposite orientations with respect to the Earth's rotation vector direction allows us to separate the effects and correct for the Coriolis shift. Finally, measurements at different atomic temperatures are presented and analyzed. In particular, we show the difficulty of extrapolating these measurements to zero temperature, which is required in order to correct for the bias due to wave-front distortions.

We analyze the emergence of Shapiro resonances in tunnel-coupled Bose–Einstein condensates, realizing a bosonic Josephson junction. Our analysis is based on an experimentally relevant implementation using magnetic double-well potentials on an atomchip. In this configuration, the potential bias (implementing the junction voltage) and the potential barrier (realizing the Josephson link) are intrinsically coupled. We show that the dynamically driven system exhibits significantly enhanced Shapiro resonances which will facilitate experimental observation. To describe the system's response to the dynamic drive, we compare a single-mode Gross–Pitaevskii (GP) description, an improved two-mode (TM) model and the self-consistent multi-configurational time-dependent Hartree equations for bosons (MCTDHB) method. We show that in the case of significant atom–atom interactions, the spatial dynamics of the involved modes has to be taken into account and only the MCTDHB method allows reliable predictions.

We have observed the interference between two Bose–Einstein condensates of weakly bound Feshbach molecules of fermionic ⁶Li atoms. Two condensates are prepared in a double-well trap and, after release from this trap, overlap in expansion. We detect a clear interference pattern that unambiguously demonstrates the de Broglie wavelength of molecules. We verify that only the condensate fraction shows interference. With increasing interaction strength, the pattern vanishes because elastic collisions during overlap remove particles from the condensate wave function. For strong interaction, the condensates do not penetrate each other as they collide hydrodynamically.

We explore the salient features of the 'Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z₂ symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce and employ a new topological invariant for explicitly determining the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder and, in particular, the post-quench dynamics governed by tuning through a quantum critical point.

Full control over the spatiotemporal structure of quantum states of light is an important goal in quantum optics, to generate, for instance, single-mode quantum pulses or to encode information on multiple modes, enhancing channel capacities. Quantum light pulses feature an inherent, rich spectral broadband-mode structure. In recent years, exploring the use of integrated optics as well as source engineering has led to a deep understanding of the pulse-mode structure of guided quantum states of light. In addition, several groups have started to investigate the manipulation of quantum states by means of single-photon frequency conversion. In this paper, we explore new routes towards complete control of the inherent pulse-modes of ultrafast pulsed quantum states by employing specifically designed nonlinear waveguides with adapted dispersion properties. Starting from our recently proposed quantum pulse gate (QPG), we further generalize the concept of spatiospectral engineering for arbitrary χ⁽²⁾-based quantum processes. We analyse the sum-frequency generation-based QPG and introduce the difference-frequency generation-based quantum pulse shaper (QPS). Together, these versatile and robust integrated optical devices allow for arbitrary manipulations of the pulse-mode structure of ultrafast pulsed quantum states. The QPG can be utilized to select an arbitrary pulse mode from a multimode input state, whereas the QPS enables the generation of specific pulse modes from an input wavepacket with a Gaussian-shaped spectrum.

We examine how best to design qubits for use in topological quantum computation. These qubits are topological Hilbert spaces associated with small groups of anyons. Operations are performed on these by exchanging the anyons. One might argue that in order to have as many simple single-qubit operations as possible, the number of anyons per group should be maximized. However, we show that there is a maximal number of particles per qubit, namely 4, and more generally a maximal number of particles for qudits of dimension d. We also look at the possibility of having topological qubits for which one can perform two-qubit gates without leakage into non-computational states. It turns out that the requirement that all two-qubit gates are leakage free is very restrictive and this property can only be realized for two-qubit systems related to Ising-like anyon models, which do not allow for universal quantum computation by braiding. Our results follow directly from the representation theory of braid groups, which implies that they are valid for all anyon models. We also make some remarks about generalizations to other exchange groups.

A quantum chromodynamics (QCD) phase diagram is usually plotted as the temperature (T) versus the chemical potential associated with the conserved baryon number (μ_B). Two fundamental properties of QCD, related to confinement and chiral symmetry, allow for two corresponding phase transitions when T and μ_B are varied. Theoretically, the phase diagram is explored through non-perturbative QCD calculations on a lattice. The energy scale for the phase diagram (Λ_QCD ∼200 MeV) is such that it can be explored experimentally by colliding nuclei at varying beam energies in the laboratory. In this paper, we review some aspects of the QCD phase structure as explored through experimental studies using high-energy nuclear collisions. Specifically, we discuss three observations related to the formation of a strongly coupled plasma of quarks and gluons in the collisions, the experimental search for the QCD critical point on the phase diagram and the freeze-out properties of the hadronic phase.

Philbin and Leonhardt (2009 New J. Phys.11 033035; 2009 arXiv:0904.2148v3 [quant-ph]) recently presented a new theory of van der Waals friction. Contrary to previous theories, they claimed that there is no 'quantum friction' at zero temperature. We argue that this theory is incorrect.

We reply to the comment on our paper made by Volokitin and Persson (2011 New J. Phys. 13 068001).