Table of contents

An essential feature of weak measurements on quantum systems is the reduction of measurement back-action to negligible levels. To observe the non-classical features of weak measurements, it is therefore more important to avoid additional back-action errors than it is to avoid errors in the actual measurement outcome. In this paper, it is shown how an optical weak measurement of diagonal (PM) polarization can be realized by path interference between the horizontal (H) and vertical (V) polarization components of the input beam. The measurement strength can then be controlled by rotating the H and V polarizations towards each other. This well-controlled operation effectively generates the back-action without additional decoherence, while the visibility of the interference between the two beams only limits the measurement resolution. As the experimental results confirm, we can obtain extremely high weak values, even at rather low visibilities. Our method therefore provides a realization of weak measurements that is extremely robust against experimental imperfections.

Electronic transport and magnetization measurements were carried out on La_0.7Ca_0.3MnO₃/YBa₂Cu₃O_7−δ (LCMO/YBCO) bilayers below the superconducting transition temperature in order to study the interaction between magnetism and superconductivity. This study shows that a substantial number of weakly pinned vortices are induced in the YBCO layer by the large out-of-plane stray field in the domain walls. Their motion gives rise to large dissipation peaks at the coercive field. The angular dependent magnetoresistance (MR) data reveal the interaction between the stripe domain structure present in the LCMO layer and the vortices and anti-vortices induced in the YBCO layer by the out-of-plane stray field. In addition, this study shows that a superconducting surface spin valve effect is present in these bilayers as a result of the relative orientation between the magnetization at the LCMO/YBCO interface and the magnetization in the interior of the LCMO layer that can be tuned by the rotation of a small H. This latter finding will facilitate the development of superconductive magnetoresistive memory devices. These low-magnetic-field MR data, furthermore, suggest that triplet superconductivity is induced in the LCMO layer, which is consistent with recent reports on triplet superconductivity in LCMO/YBCO/LCMO trilayers and LCMO/YBCO bilayers.

We study the sedimentation of buoyant giant lipid vesicles in a quiescent fluid at velocities ranging from 5 to 20 μm s⁻¹. Floppy vesicles are deformed by the flow. Their bottom (upstream) part remains spherical, while their top (downstream) part narrows down and elongates along the direction of motion, resulting in pear-like shapes or in the reversible formation of a micron-size tube at the vesicle top. The sedimentation velocity of a vesicle is very similar to that of a rigid sphere. Using a thermodynamic approach, we show that the hydrodynamic force acting at the top of a floppy vesicle can exceed the critical force needed to draw a membrane tube. We predict that the tube radius scales as the power 1/3 of the ratio of the bending energy to the typical hydrodynamic stress, ηU/R, where η is the fluid viscosity, U the sedimentation velocity and R the vesicle radius. This result is consistent with the previously reported experimental data. The tensions of vesicles exhibiting a tube and of pear-like shape are deduced from the thermodynamic approach.

We find that universal three-body physics extends beyond the threshold regime to non-zero energies. For ultracold atomic gases with a negative two-body s-wave scattering length near a Feshbach resonance, we show that the resonant peaks characteristic of Efimov physics persist in three-body recombination to higher collision energies. For this and other inelastic processes, we use the adiabatic hyperspherical representation to derive universal analytical expressions for their dependence on the scattering length, the collision energy and—for narrow resonances—the effective range. These expressions are supported by full numerical solutions of the Schrödinger equation and display log-periodic dependence on energy characteristic of Efimov physics. This dependence is robust and might be used to experimentally observe several Efimov features.

A huge variety of optical colour centres can be found in diamond, emitting in its whole wide transparency range. Although several of these centres have been demonstrated as single-photon emitters, none of them meets all of the requirements of an ideal single-photon source. In this view, we discuss the properties of prominent optical centres, such as the nitrogen vacancy, the silicon vacancy or the so-called NE8 centre, as well as recently found centres ascribed to defects containing Ni, Si, Cr and Xe. Besides suitable intrinsic properties, it is necessary for practical applications that optical centres can be created artificially on demand. Of all known methods, only ion implantation allows for the most controlled creation of such defect centres. In this paper, we discuss how nanoscalability, that is, the nanometre placement and the deterministic creation of optical centres, can, could or cannot be achieved by the available ion implantation techniques. A fine analysis of individual optical centres is now possible, thanks to the recently developed subdiffraction optical microscopy methods.

We study graphene with an adsorbed spin texture, where the localized spins create a periodic magnetic flux. The latter produces gaps in the graphene spectrum and breaks the valley symmetry. The resulting effective electronic model, which is similar to Haldane's periodic flux model, allows us to tune the gap of one valley independently from that of the other valley. This leads to the formation of two Hall plateaux and a quantum Hall transition. We discuss the density of states, optical longitudinal and Hall conductivities for nonzero frequencies and nonzero temperatures. A robust logarithmic singularity appears in the Hall conductivity when the frequency of the external field agrees with the width of the gap.

Recent studies have shown that the total magnetic moment in off-stoichiometric Ni–Mn–Ga alloys depends not only on electronic concentration but also on the degree of chemical order in the alloy. We have performed neutron diffraction experiments and magnetization measurements for determining the preferential atomic order and saturation moment in off-stoichiometric compounds (44–52 at.% Ni), having excess Mn and deficient in Ga. These alloys include isoelectronic alloys with different magnetic moments and were chosen in an effort to study the impact of chemical order on the magnetic moment distribution. In this work, we present an improved model of magnetic interaction between Mn atoms, which carry most of the localized magnetic moment of the alloys. The Mn atoms at Ga sites, which are nearest neighbors to properly sited Mn, couple antiferromagnetically to the dominant moment. In contrast, Mn atoms at Ga sites, which are nearest neighbors to Mn at Ni sites, couple ferromagnetically. Mn at Ni sites is always antiferromagnetic (AF). The new model is supported by the exchange variation with the Mn–Mn distance and demonstrates excellent agreement between experimental and calculated magnetic moments. The proposed model is shown to better explain the observed experimental results as compared to the rigid band model and previous localized moment models that assumed AF coupling for all off-site Mn atoms.

Brownian motion plays an important role in the separation of small particles and molecules, but generally leads to undirected motion or intermixing by diffusion. Matthias and Müller (2003 Nature 424 53–7) reported on the experimental realization of a drift ratchet, a microfluidic particle transport mechanism that utilizes random fluctuations instead, i.e. a Brownian motor. Here, we offer a new interpretation of this previously published work on the drift ratchet. New experiments, which allow us to distinguish between particles of different sizes, as well as a re-examination of the original work, lead to the conclusion that the measured particle transport does not result from a ratchet effect. We demonstrate that the transport is caused by convection instead. While our result challenges one specific type of experiment, we do not assess the feasibility of a drift ratchet in principle. Instead, we identify the experimental conditions that need to be fulfilled for the successful separation of particles.

The dynamics of the survival probability of quantum walkers on a one-dimensional lattice with random distribution of absorbing immobile traps is investigated. The survival probability of quantum walkers is compared with that of classical walkers. It is shown that the time dependence of the survival probability of quantum walkers has a piecewise stretched exponential character depending on the density of traps in numerical and analytical observations. The crossover between the quantum analogues of the Rosenstock and Donsker–Varadhan behavior is identified.

The coherence of electron spins can be enhanced significantly by preparing the nuclear spin polarizations to generate an Overhauser field with small fluctuations. We propose a theoretical model for calculating the long time dynamics of the prepared Overhauser field under nuclear spin diffusion in a quantum dot. We obtained a simplified diffusion equation that can be numerically solved, and we show quantitatively how the Knight shift and the electron-mediated nuclear spin flip-flops affect the nuclear spin diffusion. The results explain several recent experimental observations, where the measured decay time of the Overhauser field is dependent on the external magnetic field, electron spin state in double quantum dots and initial nuclear spin polarization rate.

The relaxation kinetics of cell sorting are studied with the cellular Potts model. In contrast to previous reports, the increase in domain size is found to obey a power law (R(t)∝tⁿ). The growth exponent turns out to be n=1/3 for an even mixture of two cell types, where the domains for each cell type are interconnected and the kinetics are dominated by smoothing of the domain boundary. The exponent is n=1/4 for uneven mixtures where cell sorting proceeds via the diffusion–coalescence of circular cell domains. The exponent is explained by the decrease in motility of a cell cluster as a function of its size according to D(R)∝R⁻². Our results provide a theoretical framework for elucidating how cell populations migrate within tissue.

In this paper, we present first results of in situ characterization of nitrogen vacancy (NV)-center formation in single-crystal diamonds after implantation of low-energy nitrogen ions (7.7 keV), co-implantation of hydrogen, helium and carbon ions and in situ annealing. Diamond samples were implanted either at room temperature or at 780 °C. We found that dynamic annealing during co-implantation enhances NV-center formation by up to 25%.

We demonstrate the fabrication of reduced graphene oxide (RGO) Schottky diodes via dielectrophoretic (DEP) assembly of RGO between two dissimilar metal contacts. Titanium (Ti) was used to make a Schottky contact, while palladium (Pd) was used to make an Ohmic contact. From the current–voltage characteristics, we obtain rectifying behavior with a rectification ratio of up to 600. The ideality factor was high (4.9), possibly due to the presence of a large number of defects in the RGO sheets. The forward biased turn-on voltage was 1 V, whereas the reverse biased breakdown voltage was −3.1 V, which improved further upon mild annealing at 200 °C and can be attributed to an increase in the work function of RGO due to annealing.

We study the scaling behavior in the tunneling amplitude when quasiparticles tunnel along a straight path between the two edges of a fractional quantum Hall annulus. Such scaling behavior originates from the propagation and tunneling of charged quasielectrons and quasiholes in an effective field analysis. In the limit when the annulus deforms continuously into a quasi-one-dimensional (1D) ring, we conjecture the exact functional form of the tunneling amplitude for several cases, which reproduces the numerical results in finite systems exactly. The results for Abelian quasiparticle tunneling is consistent with the scaling analysis; this allows for the extraction of the conformal dimensions of the quasiparticles. We analyze the scaling behavior of both Abelian and non-Abelian quasiparticles in the Read–Rezayi -parafermion states. Interestingly, the non-Abelian quasiparticle tunneling amplitudes exhibit non-trivial k-dependent corrections to the scaling exponent.

A celebrated important result due to Freedman et al (2002 Commun. Math. Phys.227 605–22) states that providing additive approximations of the Jones polynomial at the kth root of unity, for constant k=5 and k⩾7, is BQP-hard. Together with the algorithmic results of Aharonov et al (2005) and Freedman et al (2002 Commun. Math. Phys.227 587–603), this gives perhaps the most natural BQP-complete problem known today and motivates further study of the topic. In this paper, we focus on the universality proof; we extend the result of Freedman et al (2002) to ks that grow polynomially with the number of strands and crossings in the link, thus extending the BQP-hardness of Jones polynomial approximations to all values to which the AJL algorithm applies (Aharonov et al 2005), proving that for all those values, the problems are BQP-complete. As a side benefit, we derive a fairly elementary proof of the Freedman et al density result, without referring to advanced results from Lie algebra representation theory, making this important result accessible to a wider audience in the computer science research community. We make use of two general lemmas we prove, the bridge lemma and the decoupling lemma, which provide tools for establishing the density of subgroups in SU(n). Those tools seem to be of independent interest in more general contexts of proving the quantum universality. Our result also implies a completely classical statement, that the multiplicative approximations of the Jones polynomial, at exactly the same values, are #P-hard, via a recent result due to Kuperberg (2009 arXiv:0908.0512). Since the first publication of those results in their preliminary form (Aharonov and Arad 2006 arXiv:quant-ph/0605181), the methods we present here have been used in several other contexts (Aharonov and Arad 2007 arXiv:quant-ph/0702008; Peter and Stephen 2008 Quantum Inf. Comput.8 681). The present paper is an improved and extended version of the results presented by Aharonov and Arad (2006) and includes discussions of the developments since then.

Molecular exchange properties and diffusion of n-hexane embedded in a bimodal pore structure with characteristic length scales in the order of nano and micrometres, respectively, formed by packing of zeolite particles, are studied. Two-dimensional (2D) nuclear magnetic resonance (NMR) diffusion correlation experiments together with relaxation–diffusion correlation experiments are performed at low magnetic field using a single-sided NMR scanner. The exchange time covers a range from 10⁻³ to 10⁻¹ s. The molecular exchange properties are modulated by transport inside the zeolite particles. Different exchange regimes are observed for molecules starting from different positions inside the porous sample. The influence of the spin–lattice relaxation properties of the fluid molecules inside the zeolite particles on the signal intensity is also studied. A Monte Carlo simulation of the exchange process is performed and is used to support the analysis of the experimental data.

The results of a ¹H double-quantum-filtered (DQF) nuclear magnetic resonance (NMR) study of water in cement pastes are reported. It is shown that the DQF signal increases with curing time and in sympathy with the loss of mobile single-quantum signal, suggesting strongly that a signal from ¹H in chemically combined and strongly confined water is selectively observed. The DQF signal in white cement comprises at least two components: the first is assigned to portlandite (Ca(OH)₂); the second is assigned to water in the planar, nanometre-wide, calcium–silicate–hydrate (C–S–H) gel pores. The pore water signal is significantly broader than that expected for bound water. The width is interpreted in terms of the water undergoing a two-dimensional walk in the vicinity of Fe³⁺ impurities. A simple model is presented and found to be consistent with experiment and the known Fe³⁺ concentration. In grey cements, a third component is identified and associated with Fe-rich phases. The analysis places a lower bound on the lateral extent of planar C–S–H pores. The change in DQF signal components upon drying a sample mirrors the loss of the single-quantum components observed in a parallel study.

Nuclear magnetic relaxation is useful for probing physical and chemical properties of liquids in porous media. Examples are given on high surface area porous materials including calibrated porous silica glasses, granular packings, plaster pastes, cement-based materials and natural porous materials, such as sandstone and carbonate rocks. Here, we outline our recent NMR relaxation work for these very different porous materials. For instance, low field NMR relaxation of water in calibrated granular packings leads to striking different pore-size dependencies of the relaxation times T₁ and T₂ when changing the amount of surface paramagnetic impurities. This allows separation of the diffusion and surface limited regimes of relaxation in these macroporous media. The magnetic field dependence of the nuclear spin–lattice relaxation rate 1/T₁(ω₀) is also a rich source of dynamical information for characterizing the molecular dynamics of liquids in porous media. This allows a continuous characterization of the evolving microstructure of various cementitious materials. Our recent applications of two-dimensional (2D) T₁–T₂ and T₂-z-store-T₂ correlation experiments have evidenced the water exchange in connected micropores of cement pastes. The direct probing of water adsorption time on a solid surface gives access to an original characterization of the surface nano-wettability of porous plaster pastes. We show that such a parameter depends directly on the physical chemistry of the pore surfaces. Lastly, we outline our recent measurements of wettability in oil/brine/reservoir carbonate rocks.

A regular step, a dislocation slip step and a step formed by the emergence of a split edge dislocation (SED) to the surface influence the local density of states close to the onset of the surface state as investigated by scanning tunnelling spectroscopy at low temperature. The onset of the surface state shifts close to the regular step and the dislocation slip step by approximately 15 meV towards the Fermi energy. Additional maxima above the onset are only observed if a second step leads to confinement. In both cases, the conductivity decreases close to the step. However, an increase in conductance above the surface state onset is observed close to the SED step. Furthermore, a variety of additional states are discernable. Thus, different types of steps lead to markedly different changes in the local electronic structure on surfaces.

We report on the quantification of entanglement by means of entanglement measures on a four- and a six-qubit cluster state realized by using photons entangled both in polarization and linear momentum. This paper also addresses the question of the scaling of entanglement bounds from incomplete tomographic information on the density matrix under realistic experimental conditions.

We study the tunneling of a small ensemble of strongly repulsive bosons in a one-dimensional (1D) triple-well potential. The usual treatment within the single-band approximation suggests a suppression of tunneling in the strong-interaction regime. However, we show that several windows of enhanced tunneling are opened in this regime. This enhanced tunneling results from higher band contributions, and has the character of interband tunneling. It can give rise to various tunneling processes, such as single-boson tunneling and two-boson correlated tunneling of the ensemble of bosons, and is robust against deformations of the triple-well potential. We introduce a basis of generalized number states, including all contributing bands, to explain the interband tunneling, and demonstrate various processes of interband tunneling and its robustness by numerically exact calculation.

We demonstrate the control of electron tunneling in the high-order harmonic generation process and subsequent positive-energy wavepacket propagation until recollision with the unprecedented precision of about 10 attoseconds. This is accomplished with waveforms synthesized from a few-cycle near-infrared pulse and its second harmonic. The presented attosecond control of few-cycle-driven high harmonics permits the generation of tunable isolated attosecond pulses, opening the prospects for a new class of attosecond pump–probe experiments.

The magnetism of small (only a few nanometers in diameter) Co nanoparticles (NPs) grown on Au(111) was investigated by means of spin-dependent scanning tunneling microscopy and spectroscopy in a broad energy range. Direct evidence is provided for the existence of localized d-states of minority and majority character that govern the spin polarization of the NPs below the Fermi level. On the other hand, the discrete electronic states resulting from the spatially confined sp-like Co surface state electrons above the Fermi level are found to be of majority character. This confirms the theoretically predicted spin-polarized character of the delocalized surface state electrons of Co NPs on Au(111).

Quantum walks on a line with a single particle possess a classical analogue. Involving more walkers opens up the possibility of studying collective quantum effects, such as many-particle correlations. In this context, entangled initial states and the indistinguishability of the particles play a role. We consider the directional correlations between two particles performing a quantum walk on a line. For non-interacting particles, we find analytic asymptotic expressions and give the limits of directional correlations. We show that by introducing δ-interaction between the particles, one can exceed the limits for non-interacting particles.

We studied the low-energy spin excitations of zigzag graphene nanoribbons of varying width. We found their energy dispersion at small wave vectors to be dominated by antiferromagnetic correlations between the ribbon's edges, in accordance with previous calculations. We point out that spin wave lifetimes are very long owing to the semi-conducting nature of electrically neutral nanoribbons. However, the application of very modest gate voltages causes a discontinuous transition to a regime of finite spin wave lifetimes. On further increasing doping, the ferromagnetic alignments along the edge become unstable against transverse spin fluctuations. This makes the experimental detection of ferromagnetism in this class of systems very delicate and poses a difficult challenge to the possible use of these nanoribbons as the basis for spintronic devices.

Broadband multimode squeezers constitute a powerful quantum resource with promising potential for different applications in quantum information technologies such as information coding in quantum communication networks or quantum simulations in higher-dimensional systems. However, the characterization of a large array of squeezers that coexist in a single spatial mode is challenging. In this paper, we address this problem and propose a straightforward method for determining the number of squeezers and their respective squeezing strengths by using broadband multimode correlation function measurements. These measurements employ the large detection windows of the state of the art avalanche photodiodes in order to simultaneously probe the full Hilbert space of the generated state, which enables us to benchmark the squeezed states. Moreover, due to the structure of correlation functions, our measurements are not affected by losses. This is a significant advantage, since detectors with low efficiencies are sufficient. Our approach is less costly than tomographic methods relying on multimode homodyne detection, which is based on much more demanding measurement and analysis tools and appear to be impractical for large Hilbert spaces.

We derive a dynamic closed-form dispersion relation for the analysis of the entire spectrum of guided wave propagation along coupled parallel linear arrays of plasmonic nanoparticles, operating as optical 'two-line' waveguides. Compared to linear arrays of nanoparticles, our results suggest that these waveguides may support more confined beams with comparable or even longer propagation lengths, operating analogously to transmission-line segments at lower frequencies. Our formulation fully takes into account the entire dynamic interaction among the infinite number of nanoparticles composing the parallel arrays, considering also the realistic presence of losses and the frequency dispersion of the involved plasmonic materials, providing physical insights into the guidance properties that characterize this geometry.

An electronic diode is a nonlinear semiconductor circuit component that allows conduction of electrical current in one direction only. A component with similar functionality for electromagnetic waves, an electromagnetic isolator, is based on the Faraday effect of rotation of the polarization state and is also a key component in optical and microwave systems. Here we demonstrate a chiral electromagnetic diode, which is a direct analogue of an electronic diode: its functionality is underpinned by an extraordinarily strong nonlinear wave propagation effect in the same way as the electronic diode function is provided by the nonlinear current characteristic of a semiconductor junction. The effect exploited in this new electromagnetic diode is an intensity-dependent polarization change in an artificial chiral metamolecule. This microwave effect exceeds a similar optical effect previously observed in natural crystals by more than 12 orders of magnitude and a direction-dependent transmission that differs by a factor of 65.

We demonstrate that a one-dimensional periodically corrugated metal film can be used to create planar terahertz (THz) waveguides. The periodic corrugation is in the form of rectangular blind holes (i.e. holes that do not completely perforate the metal film) that are fabricated using a multilayer construction. The approach allows for the creation of structures in which the hole depth can be more than four times the hole width. This is necessary to achieve tightly confined THz guided-wave modes. We find that the modes can be modeled using an effective cavity resonance model and that the mode properties depend sensitively on the depth of corrugation. We use numerical simulations to validate the experimental results. We also highlight the differences between simulations that incorporate idealized input parameters and our experimental measurements. Using these data, we fabricate and characterize a Y-splitter to demonstrate the utility of this approach.

Epitaxial bilayers of ferromagnetic (FM) La_2/3Ca_1/3MnO₃ (LCMO) and superconducting YBa₂Cu₃O_7−δ (YBCO) have been grown on single-crystalline SrTiO₃ (STO) substrates by pulsed laser deposition. The manganese magnetization profile across the FM layer has been determined with high spatial resolution at low temperatures by x-ray resonant magnetic reflectivity (XRMR) performed at the BESSY II synchrotron light source of the Helmholtz Zentrum Berlin. It is found that not only the adjacent superconductor but also the substrate underneath influences the magnetization of the LCMO film at the interface at low temperatures. Both effects can be investigated individually by XRMR.

We study two species of attractively interacting fermion confined to a quasi-one-dimensional geometry, in the presence of a strong scattering potential that can couple, selectively, to one or both species. We show that the fermion density distribution in the presence of such a spin-selective scattering potential reflects the pairing spin gap of the fermions.

We compute the viscosity spectral function of the dilute Fermi gas for different values of the s-wave scattering length a, including the unitarity limit a→∞. We perform the calculation in kinetic theory by studying the response to a non-trivial background metric. We find the expected structure consisting of a diffusive peak in the transverse shear channel and a sound peak in the longitudinal channel. At zero momentum the width of the diffusive peak is ω₀≃(2ε)/(3η) where ε is the energy density and η is the shear viscosity. At finite momentum the spectral function approaches the collisionless limit and the width is of the order of ω₀∼k(T/m)^1/2.

We study the phase diagram of an SU(3)-symmetric mixture of three-component ultracold fermions with attractive interactions in an optical lattice, including the additional effect on the mixture of an effective three-body constraint induced by three-body losses. We address the properties of the system in D⩾2 by using dynamical mean-field theory and variational Monte Carlo techniques. The phase diagram of the model shows a strong interplay between magnetism and superfluidity. In the absence of the three-body constraint (no losses), the system undergoes a phase transition from a color superfluid (c-SF) phase to a trionic phase, which shows additional particle density modulations at half-filling. Away from the particle–hole symmetric point the c-SF phase is always spontaneously magnetized, leading to the formation of different c-SF domains in systems where the total number of particles of each species is conserved. This can be seen as the SU(3) symmetric realization of a more general tendency for phase separation in three-component Fermi mixtures. The three-body constraint strongly disfavors the trionic phase, stabilizing a (fully magnetized) c-SF also at strong coupling. With increasing temperature we observe a transition to a non-magnetized SU(3) Fermi liquid phase.

Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semicircle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the dc ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero dc conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semicircle transitions between them. The model can be regarded as a strongly coupled analogue of the old 'composite boson' picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model. In particular, the model indicates the value for low-temperature scaling exponents for transitions among quantum Hall plateaux, in agreement with the measured value 0.42±0.01.

In this paper, we study how quantum fluctuations modify the quantum evolution of an initially classical field theory. We consider a scalar ϕ⁴ theory coupled to an external source as a toy model for the color glass condensate description of the early time dynamics of heavy-ion collisions. We demonstrate that quantum fluctuations considerably modify the time evolution driving the system to evolve in accordance with ideal hydrodynamics. We attempt to understand the mechanism behind this relaxation to ideal hydrodynamics by using modified initial spectra and studying the particle content of the theory.

The Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover problem is solved for stationary gray solitons via the Boguliubov–de Gennes equations at zero temperature. These crossover solitons exhibit a localized notch in the gap and a characteristic phase difference across the notch for all interaction strengths, from BEC to BCS regimes. However, they do not follow the well-known Josephson-like sinusoidal relationship between velocity and phase difference except in the far BEC limit: at unitarity, the velocity has a nearly linear dependence on phase difference over an extended range. For a fixed phase difference, the soliton is of nearly constant depth from the BEC limit to unitarity and then grows progressively shallower into the BCS limit, and on the BCS side, Friedel oscillations are apparent in both gap amplitude and phase. The crossover soliton appears fundamentally in the gap; we show, however, that the density closely follows the gap, and the soliton is therefore observable. We develop an approximate power-law relationship to express this fact: the density of gray crossover solitons varies as the square of the gap amplitude in the BEC limit and as a power of about 1.5 at unitarity.

In a clean Fermi liquid, due to spin up/spin down symmetry, the dc spin current driven by a magnetic field gradient is finite even in the absence of impurities. Hence, the spin conductivity σ_s assumes a well-defined collision-dominated value in the disorder-free limit, providing a direct measure of the inverse strength of electron–electron interactions. In neutral graphene, with Fermi energy at the Dirac point, the Coulomb interactions remain unusually strong, such that the inelastic scattering rate comes close to a conjectured upper bound τ_inel⁻¹≲k_BT/ℏ, similar to the case of strongly coupled quantum critical systems. The strong scattering is reflected by a minimum of spin conductivity at the Dirac point, where it reaches at weak Coulomb coupling α, μ_s≈μ_B being the magnetic moment of the electronic spins. Up to the replacement of quantum units, e²/ℏ→μ_s²/ℏ, this result equals the collision-dominated electrical conductivity obtained previously. This accidental symmetry is, however, broken to higher orders in the interaction strength. For gated graphene and two-dimensional metals in general, we show that the transport time is parametrically smaller than the collision time. We exploit this fact to compute the collision-limited σ_s analytically as , with for weak Coulomb coupling α.

In the high-temperature phase of QCD, the heavy-quark momentum diffusion constant determines, via a fluctuation–dissipation relation, how fast a heavy quark kinetically equilibrates. This transport coefficient can be extracted from thermal correlators via a Kubo formula. We present a lattice calculation of the relevant Euclidean correlators in the gluon plasma, based on a recent formulation of the problem in heavy-quark effective field theory (HQET). We find a ≈20% enhancement of the Euclidean correlator at maximal time separation as the temperature is lowered from 6T_c to 2T_c, pointing to stronger interactions at lower temperatures. At the same time, the correlator becomes flatter from 6T_c down to 2T_c, indicating a relative shift of the spectral weight to lower frequencies. A recent next-to-leading order perturbative calculation of the correlator agrees with the time dependence of the lattice data at the few-per cent level. We estimate how much additional contribution from the ω≲T region of the perturbative spectral function would be required to bring it in agreement with the lattice data at 3.1T_c.

The recently discovered universal thermodynamic behavior of dilute, strongly interacting Fermi gases also implies a universal structure in the many-body pair-correlation function at short distances, as quantified by the contact . Here, we theoretically calculate the temperature dependence of this universal contact for a Fermi gas in free space and in a harmonic trap. At high temperatures above the Fermi degeneracy temperature, T≳T_F, we obtain a reliable non-perturbative quantum virial expansion up to third order. At low temperatures, we compare different approximate strong-coupling theories. These make different predictions, which need to be tested either by future experiments or by advanced quantum Monte Carlo simulations. We conjecture that in the universal unitarity limit, the contact or correlation decreases monotonically with increasing temperature, unless the temperature is significantly lower than the critical temperature, T≪T_c∼0.2T_F. We also discuss briefly how to measure the universal contact in either homogeneous or harmonically trapped Fermi gases.

We propose a new and simple method of estimating the radiation due to an accelerated quark in a strongly coupled medium, within the framework of the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. In particular, we offer a heuristic explanation of the collimated nature of synchrotron radiation produced by a circling quark, which was recently studied by Athanasiou et al (2010 Phys. Rev. D 81 26001). The gravitational dual of such a quark is a coiling string in AdS, whose backreaction on the spacetime geometry remains tightly confined, as if 'beamed' towards the boundary. While this appears to contradict conventional expectations from the scale/radius duality, we resolve the issue by observing that the backreaction of a relativistic string is reproduced by a superposition of gravitational shock waves. We further demonstrate that this proposal allows us to reduce the problem of computing the boundary stress tensor to merely calculating geodesics in AdS, as opposed to solving linearized Einstein's equations.

We examine spin diffusion in a two-component homogeneous Fermi gas in the normal phase. Using a variational approach, analytical results are presented for the spin diffusion coefficient and the related spin relaxation time as a function of temperature and interaction strength. For low temperatures, strong correlation effects are included through the Landau parameters, which we extract from Monte Carlo results. We show that the spin diffusion coefficient has a minimum for a temperature somewhat below the Fermi temperature with a value that approaches the quantum limit ∼ℏ/m in the unitarity regime, where m is the particle mass. Finally, we derive a value for the low-temperature shear viscosity in the normal phase from the Landau parameters.

We abstract the essential features of holographic dimer models, and develop several new applications of these models. Firstly, semi-holographically coupling free band fermions to holographic dimers, we uncover novel phase transitions between conventional Fermi liquids and non-Fermi liquids, accompanied by a change in the structure of the Fermi surface. Secondly, we make dimer vibrations propagate through the whole crystal by way of double trace deformations, obtaining nontrivial band structure. In a simple toy model, the topology of the band structure experiences an interesting reorganization as we vary the strength of the double trace deformations. Finally, we develop tools that would allow one to build, in a bottom-up fashion, a holographic avatar of the Hubbard model.

We report on the observation of a quenched moment of inertia resulting from superfluidity in a strongly interacting Fermi gas. Our method is based on setting the hydrodynamic gas in slow rotation and determining its angular momentum by detecting the precession of a radial quadrupole excitation. The measurements distinguish between the superfluid and collisional origins of hydrodynamic behavior, and show the phase transition.

We study the disorder effect on the excitonic gap generation caused by strong Coulomb interaction in graphene. By solving the self-consistently coupled equations of dynamical fermion gap m and disorder scattering rate Γ, we have found a critical line on the plane of interaction strength λ and disorder strength g. The phase diagram is divided into two regions: in the region with large λ and small g, m≠0 and Γ=0; in the other region, m=0 and Γ≠0 for nonzero g. In particular, there is no coexistence of finite fermion gap and finite scattering rate. These results imply a strong competition between excitonic gap generation and disorder scattering. This conclusion does not change when an additional contact four-fermion interaction is included. For sufficiently large λ, the growing disorder may drive a quantum phase transition from an excitonic insulator to a metal.

The (001)-oriented surface of epitaxial off-stoichiometric Ni–Mn–Ga ferromagnetic shape memory alloys was studied in both austenitic and martensitic phases. Scanning tunneling microscopy (STM) imaging of the austenitic surface reveals a well-ordered and reconstruction-free surface exhibiting predominantly Mn–Ga termination. We found that only one of the two atomic species (Ga or Mn) is visible in STM, which is attributed to a pronounced geometric corrugation of the surface layer. After a transformation of the sample from the initial austenitic phase to the martensitic phase upon a high-temperature annealing step, a thorough investigation of the martensitic surface was conducted. On a larger scale, pronounced corrugation lines arise from the macroscopically twinned surface. A second corrugation feature is found on a distinctly smaller scale and is shown to originate from the modulated nature of the martensitic film structure. The irregularly spaced corrugation lines support the model of adaptive martensites.

In this paper, we report the synthesis of iron-based superconductors CaFe_2−xRh_xAs₂ using a one-step solid state reaction method that crystallizes in the ThCr₂Si₂-type structure with a space group I4/mmm. The systematic evolution of the lattice constants demonstrates that the Fe ions are successfully replaced by the Rh. By increasing the doping content of Rh, the spin–density–wave (SDW) transition in the parent compound is suppressed and superconductivity emerges. The maximum superconducting transition temperature is found at 18.5 K with a doping level of x=0.15. The temperature dependence of dc magnetization confirms superconducting transitions at around 15 K. The general phase diagram was obtained and found to be similar to the case of the Rh-doping Sr122 system. Our results explicitly demonstrate the feasibility of inducing superconductivity in Ca122 compounds by higher d-orbital electron doping; however, different Rh-doping effects between FeAs122 compounds and FeAs1111 systems still remains an open question.

The spectrum of temporal fluctuations of total magnetic energy for several dynamo models is different from white noise at frequencies smaller than the inverse of the turnover time of the underlying turbulent velocity field. Examples of this phenomenon are known from previous work, and we add in this paper simulations of the G O Roberts dynamo and of convectively driven dynamos in rotating spherical shells. The appearance of colored noise in the magnetic energy is explained by simple phenomenological models. The Kolmogorov theory of turbulence is used to predict the spectrum of kinetic and magnetic energy fluctuations in the inertial range.

A Monte Carlo model has been developed for investigating the electron behavior in a dual-magnetron sputter deposition system. To describe the three-dimensional (3D) geometry, different reference frames, i.e. a local and a global coordinate system, were used. In this study, the influence of both closed and mirror magnetic field configurations on the plasma properties is investigated. In the case of a closed magnetic field configuration, the calculated electron trajectories show that if an electron is emitted in (or near) the center of the cathode, where the influence of the magnetic field is low, it is able to travel from one magnetron to the other. On the other hand, when an electron is created at the race track area, it is more or less trapped in the strong magnetic field and cannot easily escape to the second magnetron region. In the case of a mirror magnetic field configuration, irrespective of where the electron is emitted from the cathode, it cannot travel from one magnetron to the other because the magnetic field lines guide the electron to the substrate. Moreover, the electron density and electron impact ionization rate have been calculated and studied in detail for both configurations.

Betatron x-ray radiation in laser–plasma accelerators is produced when electrons are accelerated and wiggled in the laser-wakefield cavity. This femtosecond source, producing intense x-ray beams in the multi-kiloelectronvolt (keV) range, has been observed at different interaction regimes using a high-power laser from 10 to 100 TW. However, none of the spectral measurements carried out were at sufficient resolution, bandwidth and signal-to-noise ratio to precisely determine the shape of spectra with a single laser shot in order to avoid shot-to-shot fluctuations. In this paper, the Betatron radiation produced using a 80 TW laser is characterized by using a single photon counting method. We measure in a single shot spectra from 8 to 21 keV with a resolution better than 350 eV. The results obtained are in excellent agreement with theoretical predictions and demonstrate the synchrotron-type nature of this radiation mechanism. The critical energy is found to be E_c=5.6±1 keV for our experimental conditions. In addition, the features of the source at this energy range open up novel opportunities for applications in time-resolved x-ray science.

The resolution of lenses is normally limited by the wave nature of light. Imaging with perfect resolution was believed to rely on negative refraction, but here we present experimental evidence for subwavelength imaging with positive refraction.

The magnetic interlayer coupling of Fe₁₉Ni₈₁/Cu/Co trilayered microstructures has been studied by means of x-ray magnetic circular dichroism in combination with photoelectron emission microscopy (XMCD-PEEM). We find that a parallel coupling between magnetic domains coexists with a non-parallel coupling between magnetic domain walls (DWs) of each ferromagnetic layer. We attribute the non-parallel coupling of the two magnetic layers to local magnetic stray fields arising at DWs in the magnetically harder Co layer. In the magnetically softer FeNi layer, non-ordinary DWs, such as 270° and 90° DWs with overshoot of the magnetization either inwards or outwards relative to the turning direction of the Co magnetization, are identified. Micromagnetic simulations reveal that in the absence of magnetic anisotropy, both types of overshooting DWs are energetically equivalent. However, if a uniaxial in-plane anisotropy is present, the relative orientation of the DWs with respect to the anisotropy axis determines which of these DWs is energetically favorable.

We report on the occupation of the lower exciton–polariton branch in a ZnO-based microcavity as a function of the detuning between the exciton and the uncoupled cavity-photon mode and on the optical excitation density. We emphasize the difference in the dispersion and occupation of the lower polariton branch as a function of the linear polarization of the emitted light. For the negative detuning regime, we found an energy splitting between the transverse electric (TE)- and transverse magnetic (TM)-polarized states at in-plane wave vectors between 0.4×10⁷ m⁻¹ and 1.2×10⁷ m⁻¹, which is caused by the polarization dependence of the dispersion of the uncoupled cavity-photon mode. The maximum energy splitting of about 6 meV was observed for a detuning of about Δ=−70 meV. From the integrated photoluminescence peak, we deduce the occupation of the lower polariton branch as well as the scattering rates of exciton–polaritons into the lower polariton branch. We found that the energy splitting causes an enhanced scattering of exciton–polaritons into the lower polariton branch for the TM-polarized light compared with that of the TE-polarized light. By varying the excitation density, we observe a superlinear growth of the lower polariton branch occupation for negative and intermediate detuning regimes. For an accumulation of exciton–polaritons in the ground state at low temperatures (T=10 K), we found an intermediate detuning regime (−20 meV<Δ<+20 meV) as the optimum. With increasing temperature, this optimum detuning range shifts to larger negative values.

We present a novel design method capable of finding the magnetization densities that generate prescribed magnetic fields. The method is based on the solution to a simple variational inequality and the resulting designs have simple piecewise-constant magnetization densities. By this method, we obtain new designs of magnets that generate commonly used magnetic fields: uniform magnetic fields, self-shielding fields, quadrupole fields and sextupole fields. Further, it is worth noting that this method is not limited to the presented examples, and in particular, three-dimensional designs can be constructed in a similar manner. In conclusion, this novel design method is anticipated to have broad applications where specific magnetic fields are important for the performance of the devices.

We present a study of binary mixtures of Bose–Einstein condensates confined in a double-well potential within the framework of the mean field Gross–Pitaevskii (GP) equation. We re-examine both the single component and the binary mixture cases for such a potential, and we investigate what are the situations in which a simpler two-mode approach leads to an accurate description of their dynamics. We also estimate the validity of the most usual dimensionality reductions used to solve the GP equations. To this end, we compare both the semi-analytical two-mode approaches and the numerical simulations of the one-dimensional (1D) reductions with the full 3D numerical solutions of the GP equation. Our analysis provides a guide to clarify the validity of several simplified models that describe mean-field nonlinear dynamics, using an experimentally feasible binary mixture of an F = 1 spinor condensate with two of its Zeeman manifolds populated, m = ±1.

In this paper, we analyze how transformation optics recipes can be applied to control the flow of surface plasmons on metal–dielectric interfaces. We study in detail five different examples: a cylindrical cloak, a beam shifter, a right-angle bend, a lens and a ground-plane cloak. First, we demonstrate that only the modification of the electric permittivity and magnetic permeability in the dielectric side can lead to almost perfect functionalities for surface plasmons. We also show that, thanks to the quasi two-dimensional (2D) character of surface plasmons and their inherent polarization, applying conformal and quasiconformal mapping techniques allows one to design plasmonic devices in which only the isotropic refractive index of the dielectric film needs to be engineered.

A perturbation method was used to solve optical Bloch equations (OBEs) for the transition F_g=1→F_e=2, in order to describe the role of ground-level Zeeman coherences in the formation of electromagnetically induced absorption (EIA). A narrow Lorentzian peak, centered at zero value of the scanning magnetic field, appears in the analytical expression of the second-order correction of a density-matrix element for ground-level Zeeman coherences, (ρ_{g−1, g+1})_x2. Through analytical expressions for lower-order corrections of density-matrix elements, we were able to establish clear relations between the narrow Lorentzian in (ρ_{g− 1, g+1})_x2 and higher-order corrections of optical coherences, i.e. EIA. We see from analytical expressions that these two resonances have opposite signs and that EIA becomes electromagnetically induced transparency (EIT) in the limit of low efficiency of spontaneous transfer of coherences from excited-level to ground-level Zeeman sublevels. The transient behavior of EIA follows the time evolution of (ρ_{g− 1, g+1})_x2. After the coupling laser is turned on, both the Lorentzian peak in (ρ_{g− 1, g+1})_x2 and EIA reach steady state via over-damped oscillations.

We present a laser cooling scheme for trapped ions and atoms using a combination of laser couplings and a magnetic gradient field. In a Schrieffer–Wolff transformed picture, this setup cancels the carrier and blue sideband terms completely (up to first order in the Lamb–Dicke parameter), resulting in an improved cooling behaviour compared to standard cooling schemes in the Lamb–Dicke regime (e.g. sideband cooling) and allowing cooling to the vibrational ground state. A condition for optimal cooling rates is presented and the cooling behaviour for different Lamb–Dicke parameters and spontaneous decay rates is discussed. Cooling rates of one order of magnitude less than the trapping frequency are achieved using the new cooling method. Furthermore, the scheme exhibits fast rates and low final populations, even for significant deviations from the optimal parameters, and provides good cooling rates also in the multi-particle case.

We have performed high hydrostatic pressure resistivity measurements (up to 1.7 GPa) on the newly discovered superconductor A_xFe₂Se₂ (A = K and Cs) single crystals. Two batches of single crystals K_xFe₂Se₂ with different transition temperatures (T_c) were used to study the effect of pressure. The T_c of the first one gradually decreases with increasing pressure from 32.6 K at ambient pressure. While a dome-like behavior was observed for the crystal with T_c = 31.1 K, T_c reaches its maximum value of 32.7 K at the pressure of 0.48 GPa. This indicates that there exists an optimal doping with maximum T_c of 32.7 K in the K_xFe₂Se₂ system. The behavior of T_c versus pressure for Cs_xFe₂Se₂ also shows a dome-like behavior, and T_c reaches its maximum value of 31.1 K at a pressure of 0.82 GPa. The hump observed in the temperature dependence of resistivity for all of the samples tends to shift to high temperature with increasing pressure. The resistivity hump could arise from the vacancy of Fe or Se.

One approach for analyzing the dynamics of two languages in competition is to fit historical data for the number of speakers of each with a mathematical model in which the parameters are interpreted as the similarity between those languages and their relative status. Within this approach, on the basis of a detailed analysis and extensive calculations, we show the outcomes that can emerge for given values of these parameters. In contrast to previous results, it is possible that in the long term both languages may coexist and survive. This happens only where there is a stable bilingual group, and this is possible only if the competing languages are sufficiently similar, in which case its occurrence is favoured by both similarity and status symmetry.

Coherent x-ray diffraction imaging has been used to study a single ZnO nanorod in a confined illuminating condition. The focused beam size is smaller than the length of the nanorod, and the diffraction intensity is strongly dependent on the illumination position. The density maps show that the nanorod width in the radial direction is around 210 nm and has a length of 1.5 μm, in agreement with the scanning electron microscope measurement. Reconstructed phase maps show a maximum phase change of 0.8 radians. The reconstructed direct space structures reveal the exit wavefront profile, which includes that of the focused x-ray beam. The beam profile presents in reconstructions some 'hill and valley' surface features with a typical size of a few tens of nanometres and are attributed to the noise due to the slow variation of the focused beam intensity along the boundary. A single ZnO tetrapod has been investigated with the same method to recover the beam profile in the horizontal direction.

Superconducting properties of SrFe_1.85Co_0.15As₂ single crystals and their parent material, SrFe₂As₂, were investigated by scanning tunneling microscopy and spectroscopy (STM/S). In the parent material, we modeled surface conditions on the in situ cleaved single crystals, based on the observation of 2×1 stripe patterns and square-lattice patterns in the atomic-resolution topography images and with the help of local density of states measurements. In the STM/S studies on SrFe_1.85Co_0.15As₂, a robust superconducting gap (2Δ_large=17.3 meV) was observed in the conductance spectra measured along a line on the SrFe_1.85Co_0.15As₂ surface. Moreover, an additional small gap-like (2Δ_small=2.9 meV) structure was simultaneously observed. Our observation corroborates the two-gap structures in iron-based superconductors.

Dualities yield considerable insight into field theories by relating the weak coupling regime of one theory to the strong coupling regime of another. A prominent example is the 'vortex–boson' (or 'Abelian-Higgs', 'XY') duality in 2+1 dimensions demonstrating that the quantum disordered superfluid is equivalent to an ordered superconductor and the other way around. Such a duality structure should be ubiquitous, but despite the simplicity of the complex scalar field theory in 3+1 (and higher) dimensions, a precise formulation of the duality is lacking. In 2+1 dimensions the construction rests on the fact that the topological excitations of the superfluid (vortices) are particle-like and the dual superconductor corresponds just to a conventional Bose condensate of vortices. Departing from the superfluid, the vortices in 3+1d are Nielsen–Olesen strings and the difficulty is in the construction of string field theory. We demonstrate that an earlier attempt [1] to construct the dual theory is subtly flawed. Relying on the understanding of the physics of the disordered superfluid in higher dimensions, as well as a gauge invariant formulation of the Higgs mechanism at work in this context, we derive the effective action for the dual string superconductor in 3+1d. This turns out to be a very simple affair: the string condensate just supports a massive compressional mode, while it gives mass to the 2-form transversal photon that represents the remnant of the zero sound mode of the superfluid. We conclude with the observation that the 2+1d superfluid–superconductor duality actually persists in all D+1 dimensions with D ⩾ 2: the condensates are formed from D − 2-branes interacting via D − 1-form gauge fields but the form of the effective theory of the dual superconductor is eventually independent of dimensionality. Finally, we demonstrate that Bose–Mott insulators support topological defects that are string-like in 3+1d. This surprising implication of duality may be seen in cold atom experiments.

We argue that the Fermi–Hubbard Hamiltonian describing the physics of ultracold atoms on optical lattices in the presence of artificial non-Abelian gauge fields is exactly equivalent to the gauge theory Hamiltonian describing Dirac fermions in the lattice. We show that it is possible to couple the Dirac fermions to an 'artificial' gravitational field, i.e. to consider the Dirac physics in a curved spacetime. We identify the special class of spacetime metrics that admit a simple realization in terms of a Fermi–Hubbard model subjected to an artificial SU(2) field, corresponding to position-dependent hopping matrices. As an example, we discuss in more detail the physics of the 2+1D Rindler metric and its possible experimental realization and detection.

Magnetic resonance (MR) techniques are increasingly used to improve our understanding of the multi-component, multi-phase processes encountered in chemical engineering. This review brings together many of the MR techniques used, and often developed specifically, to study chemical engineering systems and, in particular, processes occurring within porous media. Pulse sequences for relaxometry, pulsed field gradient measurements of diffusion, imaging and velocimetry measurements are described. Recent applications of these MR pulse sequences to microporous, mesoporous and macroporous structures are then reviewed. Considering the microporous and mesoporous systems, we focus attention on studies of rock cores, manufactured materials such as cement and gypsum plaster, and catalysts. When considering macroporous structures, the transport through packed beds of particles typical of fixed-bed catalytic reactors is reviewed; a brief overview of the increasing research interest in gas–solid fluidized beds is also presented. We highlight the field of sparse k-space sampling as an area that is in its infancy and suggest that, combined with Bayesian methods, it will offer new opportunities in both extending the application of high-field MR techniques to chemical engineering and increasing the range of measurements that can be carried out using low-field hardware.

We explore the phase transitions of the ideal relativistic neutral Bose gas confined in a cubic box, without assuming the thermodynamic limit nor continuous approximation. While the corresponding non-relativistic canonical partition function is essentially a one-variable function depending on a particular combination of temperature and volume, the relativistic canonical partition function is genuinely a two-variable function of them. Based on an exact expression for the canonical partition function, we performed numerical computations for up to 10⁵ particles. We report that if the number of particles is equal to or greater than a critical value, which amounts to 7616, the ideal relativistic neutral Bose gas features a spinodal curve with a critical point. This enables us to depict the phase diagram of the ideal Bose gas. The consequent phase transition is first order below the critical pressure or second order at the critical pressure. The exponents corresponding to the singularities are 1/2 and 2/3, respectively. We also verify the recently observed 'Widom line' in the supercritical region.

We show that high harmonic generation driven by an intense near-infrared (IR) laser can be temporally controlled when an attosecond pulse train (APT) is used to ionize the generation medium, thereby replacing tunnel ionization as the first step in the well-known three-step model. New harmonics are formed when the ionization occurs at a well-defined time within the optical cycle of the IR field. The use of APT-created electron wave packets affords new avenues for the study and application of harmonic generation. In the present experiment, this makes it possible to study harmonic generation at IR intensities where tunnel ionization does not give a measurable signal.

We introduce a novel technique for measuring spatially resolved photoionization yields of gas-phase ions created in an intense-laser focus. Overcoming the limitations of traditional experiments where the ionization yield is integrated over the entire focal volume, the technique provides precise information on the ionization dynamics over a wide range of intensities between the appearance intensity of the lowest charge state up to relativistic intensities. The new method provides insights into the ionization process beyond the saturation intensity and, at the same time, a precise way for noninvasive, in situ focus diagnostics. We demonstrate these advances for the case of strong-field ionization of argon. The data are analyzed using the Ammosov–Delone–Krainov (ADK) formula (Ammosov et al 1986 Zh. Éksp. Teor. Fiz.91 2008).