Table of contents

Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights.

Focus on quantum information and many-body theory Contents

TENSOR NETWORKS

Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio

Concatenated tensor network states R Hübener, V Nebendahl and W Dür

Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal

Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou

Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac

Matrix product operator representations B Pirvu, V Murg, J I Cirac and F Verstraete

SIMULATION AND DYNAMICS

A quantum differentiation of k-SAT instances B Tamir and G Ortiz

Classical Ising model test for quantum circuits Joseph Geraci and Daniel A Lidar

Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain S R Clark, J Prior, M J Hartmann, D Jaksch and M B Plenio

Exact solution of Markovian master equations for quadratic Fermi systems: thermal baths, open XY spin chains and non-equilibrium phase transition Tomaž Prosen and Bojan Žunkovič

Quantum kinetic Ising models R Augusiak, F M Cucchietti, F Haake and M Lewenstein

ENTANGLEMENT AND SPECTRAL PROPERTIES

Ground states of unfrustrated spin Hamiltonians satisfy an area law Niel de Beaudrap, Tobias J Osborne and Jens Eisert

Correlation density matrices for one-dimensional quantum chains based on the density matrix renormalization group W Münder, A Weichselbaum, A Holzner, Jan von Delft and C L Henley

The invariant-comb approach and its relation to the balancedness of multipartite entangled states Andreas Osterloh and Jens Siewert

Entanglement scaling of fractional quantum Hall states through geometric deformations Andreas M Läuchli, Emil J Bergholtz and Masudul Haque

Entanglement versus gap for one-dimensional spin systems Daniel Gottesman and M B Hastings

Entanglement spectra of critical and near-critical systems in one dimension F Pollmann and J E Moore

Macroscopic bound entanglement in thermal graph states D Cavalcanti, L Aolita, A Ferraro, A García-Saez and A Acín

Entanglement at the quantum phase transition in a harmonic lattice Elisabeth Rieper, Janet Anders and Vlatko Vedral

Multipartite entanglement and frustration P Facchi, G Florio, U Marzolino, G Parisi and S Pascazio

Entropic uncertainty relations—a survey Stephanie Wehner and Andreas Winter

Entanglement in a spin system with inverse square statistical interaction D Giuliano, A Sindona, G Falcone, F Plastina and L Amico

APPLICATIONS

Time-dependent currents of one-dimensional bosons in an optical lattice J Schachenmayer, G Pupillo and A J Daley

Implementing quantum gates using the ferromagnetic spin-J XXZ chain with kink boundary conditions Tom Michoel, Jaideep Mulherkar and Bruno Nachtergaele

Long-distance entanglement in many-body atomic and optical systems Salvatore M Giampaolo and Fabrizio Illuminati

QUANTUM MEMORIES AND TOPOLOGICAL ORDER

Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes Stefano Chesi, Daniel Loss, Sergey Bravyi and Barbara M Terhal

Topological color codes and two-body quantum lattice Hamiltonians M Kargarian, H Bombin and M A Martin-Delgado

RENORMALIZATION

Local renormalization method for random systems O Gittsovich, R Hübener, E Rico and H J Briegel

We investigate the entanglement content of the ground state of a system characterized by effective elementary degrees of freedom with fractional statistics. To this end, we explicitly construct the ground state for a chain of N spins with inverse square interaction (the Haldane–Shastry model) in the presence of an external uniform magnetic field. For such a system at zero temperature, we evaluate the entanglement in the ground state both at finite size and in the thermodynamic limit. We relate the behavior of the quantum correlations with the spinon condensation phenomenon occurring at the saturation field.

In this paper, we introduce a quantum generalization of classical kinetic Ising models (KIM), described by a certain class of quantum many-body master equations. Similarly to KIMs with detailed balance that are equivalent to certain Hamiltonian systems, our models reduce to a set of Hamiltonian systems determining the dynamics of the elements of the many-body density matrix. The ground states of these Hamiltonians are well described by the matrix product, or pair entangled projected states. We discuss critical properties of such Hamiltonians, as well as entanglement properties of their low-energy states.

In this paper, we introduce a real-space renormalization transformation for random spin systems on two-dimensional (2D) lattices. The general method is formulated for random systems and results by merging two well-known real-space renormalization techniques, namely the strong disorder renormalization technique and the contractor renormalization technique. We analyze the performance of the method on the 2D random transverse field Ising model.

We discuss the phenomenon of long-distance entanglement (LDE) in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body systems of ultracold atoms in optical lattices and in arrays of coupled optical cavities. We investigate XX quantum spin models on one-dimensional lattices with open ends and different patterns of site-dependent interaction couplings, singling out two general settings: patterns that allow for perfect LDE in the ground state of the system, namely such that the end-to-end entanglement remains finite in the thermodynamic limit, and patterns of quasi-long-distance entanglement (QLDE) in the ground state of the system, namely such that the end-to-end entanglement vanishes with a very slow power-law decay as the length of the spin chain is increased. We discuss physical realizations of these models in ensembles of ultracold bosonic atoms loaded in optical lattices. We show how, using either suitably engineered super-lattice structures or exploiting the presence of edge impurities in lattices with single periodicity, it is possible to realize models endowed with nonvanishing LDE or QLDE. We then study how to realize models that optimize the robustness of QLDE at finite temperature and in the presence of imperfections using suitably engineered arrays of coupled optical cavities. For both cases the numerical estimates of the end-to-end entanglement in the actual physical systems are thoroughly compared with the analytical results obtained for the spin model systems. We finally introduce LDE-based schemes of long-distance quantum teleportation in linear arrays of coupled cavities, and show that they allow for high-fidelity and high success rates even at moderately high temperatures.

Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z₂×Z₂ of the color code could already be realized by identifying three distinct plaquette operators on the ruby lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other. This gives rise to exact topological degeneracy of the model. A connection to 2-colexes can be established via the coloring of the strings. We discuss it at the non-perturbative level. The particular structure of the two-body Hamiltonian provides a fruitful interpretation in terms of mapping onto bosons coupled to effective spins. We show that high-energy excitations of the model have fermionic statistics. They form three families of high-energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. The emergence of invisible charges is related to the string-net structure of the model. The emerging fermions are coupled to nontrivial gauge fields. We show that for particular 2-colexes, the fermions can see the background fluxes in the ground state. Also, we use the Jordan–Wigner transformation in order to test the integrability of the model via introducing Majorana fermions. The four-valent structure of the lattice prevents the fermionized Hamiltonian from being reduced to a quadratic form owing to interacting gauge fields. We also propose another construction for the two-body Hamiltonian based on the connection between color codes and cluster states. The corresponding two-body Hamiltonian encodes a cluster state defined on a bipartite lattice as its low-energy spectrum, and subsequent selective measurements give rise to the color code model. We discuss this latter approach along with the construction based on the ruby lattice.

The entanglement properties of phase transition in a two-dimensional harmonic lattice, similar to the one observed in recent ion trap experiments, are discussed for both finite number of particles and thermodynamical limit. We show that for the ground state at the critical value of the trapping potential, two entanglement measures, the negativity between two neighbouring sites and the block entropy for blocks of size 1, 2 and 3, change abruptly. Entanglement thus indicates quantum phase transitions in general, not only in the finite-dimensional case considered in Wu et al (2004 Phys. Rev. Lett.93250404). Finally, we consider the thermal state and compare its exact entanglement with a temperature entanglement witness introduced in Anders (2008 Phys. Rev. A 77 062102).

We generalize the method of third quantization to a unified exact treatment of Redfield and Lindblad master equations for open quadratic systems of n fermions in terms of diagonalization of a 4n×4n matrix. Non-equilibrium thermal driving in terms of the Redfield equation is analyzed in detail. We explain how one can compute all the physically relevant quantities, such as non-equilibrium expectation values of local observables, various entropies or information measures, or time evolution and properties of relaxation. We also discuss how to exactly treat explicitly time-dependent problems. The general formalism is then applied to study a thermally driven open XY spin 1/2 chain. We find that the recently proposed non-equilibrium quantum phase transition in the open XY chain survives the thermal driving within the Redfield model. In particular, the phase of long-range magnetic correlations can be characterized by hypersensitivity of the non-equilibrium steady state to external (bath or bulk) parameters. Studying the heat transport, we find negative differential thermal conductance for sufficiently strong thermal driving as well as non-monotonic dependence of the heat current on the strength of the bath coupling.

Some features of the global entanglement of a composed quantum system can be quantified in terms of the purity of a balanced bipartition, made up of half of its subsystems. For the given bipartition, purity can always be minimized by taking a suitable (pure) state. When many bipartitions are considered, the requirement that purity be minimal for all bipartitions can engender conflicts and frustration will arise. This unearths an interesting link between frustration and multipartite entanglement, defined as the average purity over all (balanced) bipartitions.

We analyse the time dependence of currents in a one-dimensional (1D) Bose gas in an optical lattice. For a 1D system, the stability of currents induced by accelerating the lattice exhibits a broad crossover as a function of the magnitude of the acceleration, and the strength of the inter-particle interactions. This differs markedly from mean-field results in higher dimensions. Using the infinite time evolving block decimation algorithm, we characterize this crossover by making quantitative predictions for the time-dependent behaviour of the currents and their decay rate. We also compute the time dependence of quasi-condensate fractions which can be measured directly in experiments. We compare our results to calculations based on phase-slip methods, finding agreement with the scaling as the particle density increases, but with significant deviations near unit filling.

We discuss several thermodynamic criteria that have been introduced to characterize the thermal stability of a self-correcting quantum memory. We first examine the use of symmetry-breaking fields in analyzing the properties of self-correcting quantum memories in the thermodynamic limit; we show that the thermal expectation values of all logical operators vanish for any stabilizer and any subsystem code in any spatial dimension. On the positive side, we generalize the results of Alicki et al to obtain a general upper bound on the relaxation rate of a quantum memory at nonzero temperature, assuming that the quantum memory interacts via a Markovian master equation with a thermal bath. This upper bound is applicable to quantum memories based on either stabilizer or subsystem codes.

We show how to construct relevant families of matrix product operators (MPOs) in one and higher dimensions. These form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In particular, we construct translationally invariant MPOs suitable for time evolution, and show how such descriptions are possible for Hamiltonians with long-range interactions. We show how these tools can be exploited for constructing new algorithms for simulating quantum spin systems.

We address the presence of bound entanglement in strongly interacting spin systems at thermal equilibrium. In particular, we consider thermal graph states composed of an arbitrary number of particles. We show that for a certain range of temperatures no entanglement can be extracted by means of local operations and classical communication, even though the system is still entangled. This is found by harnessing the independence of the entanglement in some bipartitions of such states with the system's size. Specific examples for one- and two-dimensional systems are given. Our results thus prove the existence of thermal bound entanglement in an arbitrary large spin system with finite-range local interactions.

We show that two different tensors defining the same translational invariant injective projected entangled pair state (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any local or spatial symmetry in the state. As an application of these results we prove that a SU(2) invariant PEPS with half-integer spin cannot be injective, which can be seen as a Lieb–Shultz–Mattis theorem in this context. We also give the natural generalization for U(1) symmetry in the spirit of Oshikawa–Yamanaka–Affleck, and show that a PEPS with Wilson loops cannot be injective.

Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum cryptographic protocols. Yet, little is known about entropic uncertainty relations with more than two measurement settings. In the present survey, we review known results and open questions.

The global geometric entanglement (GE) is studied in the context of newly developed tensor network algorithms for finite systems. For one-dimensional quantum spin systems it is found that, at criticality, the leading finite-size correction to the global GE per site behaves as b/n, where n is the size of the system and b a given coefficient. Our conclusion is based on the computation of the GE per spin for the quantum Ising model in a transverse magnetic field and for the spin-1/2 XXZ model. We also discuss the possibility of coefficient b being universal.

The ability of entanglement renormalization (ER) to generate a proper real-space renormalization group (RG) flow in extended quantum systems is analyzed in the setting of harmonic lattice systems in D=1 and 2 spatial dimensions. A conceptual overview of the steps involved in momentum-space RG is provided and contrasted against the equivalent steps in the real-space setting. The real-space RG flow, as generated by ER, is compared against the exact results from momentum-space RG, including an investigation of a critical fixed point and the effect of relevant and irrelevant perturbations.

The entanglement spectrum of a pure state of a bipartite system is the full set of eigenvalues of the reduced density matrix obtained from tracing out one part. Such spectra are known in several cases to contain important information beyond that in the entanglement entropy. This paper studies the entanglement spectrum for a variety of critical and near-critical quantum lattice models in one dimension, chiefly by the infinite time evolving block decimation (iTEBD) numerical method, which enables both integrable and non-integrable models to be studied. We find that the distribution of eigenvalues in the entanglement spectra agrees with an approximate result derived by Calabrese and Lefevre to an accuracy of a few per cent for all models studied. This result applies whether the correlation length is intrinsic or generated by the finite matrix size accessible in iTEBD. For the transverse Ising model, the known exact results from Peschel and Eisler for the entanglement spectrum are used to confirm the validity of the iTEBD approach. For more general models, no exact result is available but the iTEBD results directly test the hypothesis that all moments of the reduced density matrix are determined by a single parameter.

In recent work, Hartmann et al (2009 Phys. Rev. Lett. 102 057202) demonstrated that the classical simulation of the dynamics of open 1D quantum systems with matrix product algorithms can often be dramatically improved by performing time evolution in the Heisenberg picture. For a closed system this was exemplified by an exact matrix product operator (MPO) solution of the time-evolved creation operator of a quadratic fermi chain with a matrix dimension of just two. In this work, we show that this exact solution can be significantly generalized to include the case of an open quadratic fermi chain subjected to master equation evolution with Lindblad operators that are linear in the fermionic operators. Remarkably even in this open system the time evolution of operators continues to be described by MPOs with the same fixed dimension as that required by the solution of a coherent quadratic fermi chain for all times. Through the use of matrix product algorithms the dynamical behaviour of operators in this non-equilibrium open quantum system can be computed with a cost that is linear in the system size. We present some simple numerical examples that highlight how useful this might be for the more detailed study of open system dynamics. Given that Heisenberg picture simulations have been demonstrated to offer significant accuracy improvements for other open systems that are not exactly solvable, our work also provides further insight into how and why this advantage arises.

We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise entanglement and long-ranged correlations. We illustrate the approach for the enhancement of matrix product states, i.e. one-dimensional (1D) tensor networks, where we replace each of the matrices of the original matrix product state with another 1D tensor network. This procedure yields a 2D tensor network, which includes—already for tensor dimension 2—all states that can be prepared by circuits of polynomially many (possibly non-unitary) two-qubit quantum operations, as well as states resulting from time evolution with respect to Hamiltonians with short-ranged interactions. We investigate the possibility of efficiently extracting information from these states, which serves as the basic step in a variational optimization procedure. To this aim, we utilize the known exact and approximate methods for 2D tensor networks and demonstrate some improvements thereof, which are also applicable e.g. in the context of 2D projected entangled pair states. We generalize the approach to higher dimensional and tree tensor networks.

We demonstrate an implementation scheme for constructing quantum gates using unitary evolutions of the one-dimensional spin-J ferromagnetic XXZ chain. We present numerical results based on simulations of the chain using the time-dependent density matrix renormalization group method and techniques from optimal control theory. Using only a few control parameters, we find that it is possible to implement one- and two-qubit gates on a system of spin- XXZ chains, such as Not, Hadamard, Pi-8, Phase and C-Not, with fidelity levels exceeding 99%.

We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension (1D). The area law for a 1D system states that for the ground state, the entanglement of any interval is upper bounded by a constant independent of the size of the interval. However, the possible dependence of the upper bound on the spectral gap Δ is not known, as the best known general upper bound is asymptotically much larger than the largest possible entropy of any model system previously constructed for small Δ. To help resolve this asymptotic behavior, we construct a family of 1D local systems for which some intervals have entanglement entropy, which is polynomial in 1/Δ, whereas previously studied systems, such as free fermion systems or systems described by conformal field theory, had the entropy of all intervals bounded by a constant time log(1/Δ).

An approach is presented for converting a two-atom singlet state into a three-atom singlet state based on the quantum Zeno dynamics induced by continuous coupling. The scheme can be achieved within one step through appropriately regulating the Rabi frequencies of the classical fields. The effects of decoherence such as atomic spontaneous emission and the loss of cavity are also considered in virtue of the master equation. The numerical simulation result shows that this proposal is especially robust against the cavity decay, since no cavity-photon population is involved during the whole process because of the quantum Zeno dynamics. Furthermore, if a multilevel atom and a multi-mode cavity are applicable, the N-atom singlet state could be derived directly from the (N−1)-atom singlet state with the same principle, which provides a scalable way for the preparation of |S_N⟩ in theory.

We present an analysis of magnetic traps for ultracold atoms based on current-carrying wires with sub-micron dimensions. We analyze the physical limitations of these conducting wires as well as how such miniaturized magnetic traps are affected by the nearby surface due to tunneling to the surface, surface thermal noise, electron scattering within the wire and the Casimir–Polder force. We show that wires with cross sections as small as a few tens of nanometers should enable robust operating conditions for coherent atom optics (e.g. tunneling barriers for interferometry). In particular, trap sizes of the order of the de Broglie wavelength become accessible, based solely on static magnetic fields, thereby bringing the atomchip a step closer to fulfilling its promise of a compact device for complex and accurate quantum optics with ultracold atoms.

We present approximate methods for calculating the three-dimensional electric potentials of finite surface electrodes including gaps between electrodes, and estimate the effects of finite electrode thickness and an underlying dielectric substrate. As an example, we optimize a radio-frequency surface-electrode ring ion trap, and find that each of these factors reduces the trapping secular frequencies by less than 5% in realistic situations. This small magnitude validates the usual assumption of neglecting the influences of gaps between electrodes and the finite electrode extent.

By means of particle-in-cell (PIC) simulations, we found that when the focus size of a laser pulse is much larger than the plasma wavelength and when the laser power is hundreds of times larger than the critical power required for relativistic self-focusing, a large complex bubble is formed. The transversal size of the bubble depends on the laser spot size. Owing to the large bubble size, a bunch of electrons with the total charge in the range of a few tens of nano-Coulombs is trapped and accelerated in the bubble. When the plasma density is 2×10¹⁹ cm⁻³, the charge of the energetic electron bunch with energy above 5 MeV exceeds 45 nC with a laser spot size of 60 μm. Electrons continuously self-injected into such a complex bubble serve as an effective source of high-charge electron bunches.

In the Aharonov–Albert–Vaidman (AAV) weak measurement, it is assumed that the measuring device or the pointer is in a quantum mechanical pure state. In reality, however, it is often not the case. In this paper, we generalize the AAV weak measurement scheme to include more generalized situations in which the measuring device is in a mixed state. We also report an optical implementation of the weak value measurement in which the incoherent pointer is realized with the pseudo-thermal light. The theoretical and experimental results show that the measuring device under the influence of partial decoherence could still be used for amplified detection of minute physical changes and is applicable for implementing the weak value measurement for massive particles.

In this work, we studied polyvinylidene fluoride (PVDF)-based ferroelectric copolymer and terpolymer films grown, by the Langmuir–Blodgett (LB) technique, on polyimide substrates. The LB technique is believed to improve the film quality, i.e. to confer better crystallinity and less parasitic amorphous phase. As a consequence, a reversible adiabatic temperature change ΔT up to 21 K is demonstrated. The large electrocaloric effects of LB films close to room temperature suggest the potential for applying LB films in cooling systems.

A method for fabricating multiple free-standing structures on the same sheet of graphene is demonstrated. Mechanically exfoliated mono- and bilayer graphene sheets were sandwiched between two layers of polymethyl-methacrylate. Suspended areas were defined by e-beam exposure allowing precise control over their shape and position. Mechanical characterization of suspended graphene sheets was performed by nanoindentation with an atomic force microscopy tip. The obtained built-in tensions of 12 nN are significantly lower than those in suspended graphene exfoliated on an SiO₂ substrate, and therefore permit access to the intrinsic properties of this material system.

To gain a better understanding of recent experiments on the turbulence-induced melting of a periodic array of vortices in a thin fluid film, we perform a direct numerical simulation of the two-dimensional Navier–Stokes equations forced such that, at low Reynolds numbers, the steady state of the film is a square lattice of vortices. We find that as we increase the Reynolds number, this lattice undergoes a series of nonequilibrium phase transitions, first to a crystal with a different reciprocal lattice and then to a sequence of crystals that oscillate in time. Initially, the temporal oscillations are periodic; this periodic behaviour becoming more and more complicated with increasing Reynolds number until the film enters a spatially disordered nonequilibrium statistical steady state that is turbulent. We study this sequence of transitions using fluid-dynamics measures, such as the Okubo–Weiss parameter that distinguishes between vortical and extensional regions in the flow, ideas from nonlinear dynamics, e.g. Poincaré maps, and theoretical methods that have been developed to study the melting of an equilibrium crystal or the freezing of a liquid and that lead to a natural set of order parameters for the crystalline phases and spatial autocorrelation functions that characterize short- and long-range order in the turbulent and crystalline phases, respectively.

We studied the superfluidity of strongly repulsive fermionic atoms in optical lattices. Atoms are paired through a correlated tunneling mechanism, which induces superfluidity when repulsive nearest-neighbor interactions are included in the Hubbard model. This paired superfluid is a metastable state, which persists for a long time as the pair-broken process is severely suppressed. The mean-field phase diagram and low-energy excitations are investigated in a square lattice system. Intriguingly, spontaneous superflows may appear in the ground state of a triangular optical lattice system due to antiferromagnetic frustration.

We calculate the adiabatic potentials and adiabatic wavefunctions of Rydberg atoms in a one-dimensional ponderomotive optical lattice. All lattice-induced couplings between the degenerate high-angular-momentum Rydberg states are taken into account. To obtain insight into the underlying physics, we analyze the numerical results in terms of effective electric and magnetic fields produced by the lattice. Near the inflection points of the lattice potential and for sufficiently low principal quantum numbers (n≲35 in the cases studied), the adiabatic level structure resembles that of the dc Stark effect, and an effective electric-field model can be used to model the lattice-induced perturbation. Near the nodes and anti-nodes of the lattice field, the adiabatic level structure exhibits a combination of adjacent rotational and vibrational energy level sequences. Here, an analogy between the ponderomotive optical lattice and the diamagnetic problem works well to interpret the lattice-induced perturbation in terms of an effective magnetic field.

Using path integrals and the theory of polarizable fluids, we develop a model treating non-degenerate interacting Fröhlich polarons at low densities and temperatures. Starting from the dilute regime, we show that at strong electron–phonon coupling, the collective properties of polarons are mainly governed by the London dispersion forces, i.e. induced dipole–dipole van der Waals interactions. At a critical density, these forces provoke a non-metal-to-metal transition by means of a polarization catastrophe and a mechanical instability, which results in a polaron dissociation.

We report a strategy for achieving ultrahigh-contrast all-optical diodes by using tunable surface plasmon polaritons (SPPs) in a silver grating coated with poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene], a nonlinear organic material. According to the nonlinear optical Kerr effect, the coupling of SPPs on both sides of the silver grating varied with the pump intensity of incident light, which results in a shift of resonant frequencies of extraordinary transmission modes. The asymmetric configuration and the optical nonlinearity ensure unidirectional transmission properties. An ultrahigh contrast ratio of 2166 is achieved theoretically.

Image potential states (IPSs) are electronic states localized in front of a surface in a potential well, formed by the surface projected bulk band gap on one side and the image potential barrier on the other. In the limit of a two-dimensional solid, a double Rydberg series of IPSs has been predicted, which is in contrast to a single series present in three-dimensional solids. Here, we confirm this prediction experimentally for mono- and bilayer graphene. The IPSs of epitaxial graphene on SiC are measured by scanning tunneling spectroscopy and the results are compared with ab-initio band structure calculations. Despite the presence of the substrate, both calculations and experimental measurements show that the first pair of the double series of IPSs survives and eventually evolves into a single series for graphite. Thus, IPSs provide an elegant quantum probe of the interfacial coupling in graphene systems.

We demonstrate experimentally a simple method for preparing non-diffractive vectorial optical beams that can display wave-front helicity. This method is based on space-variant modifications of the polarization of an optical beam transmitted through subwavelength annular rings perforating opaque metal films. We show how the description of the optical properties of such structures must account for the vectorial character of the polarization and how, in turn, these properties can be controlled by straightforward sequences of preparation and analysis of polarization states.

From small-angle neutron scattering studies of the flux line lattice (FLL) in CeCoIn₅, with magnetic field applied parallel to the crystal c-axis, we obtain the field and temperature dependence of the FLL form factor (FF), which is a measure of the spatial variation of the field in the mixed state. We extend our earlier work (Bianchi et al 2008 Science 319 177) to temperatures up to 1250 mK. Over the entire temperature range, paramagnetism in the flux line cores results in an increase of the FF with field. Near H_c2 the FF decreases again, and our results indicate that this fall-off extends outside the proposed Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) region. Instead, we attribute the decrease to a paramagnetic suppression of Cooper pairing. At higher temperatures, a gradual crossover toward more conventional mixed state behavior is observed.

We demonstrate efficient and reversible mapping of a light field on to a thulium-doped crystal using an atomic frequency comb (AFC). Owing to an accurate spectral preparation of the sample, we reach an efficiency of nine per cent. Our interpretation of the data is based on an original spectral analysis of the AFC. By independently measuring the absorption spectrum, we show that the efficiency is limited by both the available optical thickness and the preparation procedure at large absorption depth for a given bandwidth. The experiment is repeated with less than one photon per pulse and single-photon counting detectors. We clearly observe that the AFC protocol is compatible with the noise level required for weak quantum field storage.

We present a passive approach to the security analysis of quantum key distribution (QKD) with an untrusted source. A complete proof of its unconditional security is also presented. This scheme has significant advantages in real-life implementations as it does not require fast optical switching or a quantum random number generator. The essential idea is to use a beam splitter to split each input pulse. We show that we can characterize the source using a cross-estimate technique without active routing of each pulse. We have derived analytical expressions for the passive estimation scheme. Moreover, using simulations, we have considered four real-life imperfections: additional loss introduced by the 'plug&play' structure, inefficiency of the intensity monitor noise of the intensity monitor, and statistical fluctuation introduced by finite data size. Our simulation results show that the passive estimate of an untrusted source remains useful in practice, despite these four imperfections. Also, we have performed preliminary experiments, confirming the utility of our proposal in real-life applications. Our proposal makes it possible to implement the 'plug&play' QKD with the security guaranteed, while keeping the implementation practical.

Palladium (Pd) films have been grown and characterized in situ by low-energy electron diffraction (LEED) and microscopy in two different regimes: ultrathin films 2–6 monolayers (ML) thick on Ru(0001), and ∼20 ML thick films on both Ru(0001) and W(110). The thinner films are grown at elevated temperature (750 K) and are lattice matched to the Ru(0001) substrate. The thicker films, deposited at room temperature and annealed to 880 K, have a relaxed in-plane lattice spacing. All the films present an fcc stacking sequence as determined by LEED intensity versus energy analysis. In all the films, there is hardly any expansion in the surface-layer interlayer spacing. Two types of twin-related stacking sequences of the Pd layers are found on each substrate. On W(110) the two fcc twin types can occur on a single substrate terrace. On Ru(0001) each substrate terrace has a single twin type and the twin boundaries replicate the substrate steps.

Charge transport through a short DNA oligomer (Dickerson dodecamer (DD)) in the presence of structural fluctuations is investigated using a hybrid computational methodology based on a combination of quantum mechanical electronic structure calculations and classical molecular dynamics (MD) simulations with a model Hamiltonian approach. Based on a fragment orbital description, the DNA electronic structure can be coarse-grained in a very efficient way. The influence of dynamical fluctuations, arising either from the solvent fluctuations or from base-pair vibrational modes, can be taken into account in a straightforward way through the time series of the effective DNA electronic parameters, evaluated at snapshots along the MD trajectory. We show that charge transport can be promoted through the coupling to solvent fluctuations, which gate the on-site energies along the DNA wire.

We investigate the Lagrangian mechanism of the kinematic 'fluctuation' magnetic dynamo in a turbulent plasma flow at small magnetic Prandtl numbers. The combined effect of turbulent advection and plasma resistivity is to carry infinitely many field lines to each space point, with the resultant magnetic field at that point given by the average over all the individual line vectors. As a consequence of the roughness of the advecting velocity, this remains true even in the limit of zero resistivity. We show that the presence of the dynamo effect requires sufficient angular correlation of the passive line vectors that arrive simultaneously at the same space point. We illustrate this in detail for the Kazantsev–Kraichnan model of the kinematic dynamo with a Gaussian advecting velocity that is spatially rough and white noise in time. In the regime where dynamo action fails, we also obtain the precise rate of decay of the magnetic energy. These exact results for the model are obtained by a generalization of the 'slow-mode expansion' of Bernard, Gawȩdzki and Kupiainen to non-Hermitian evolution. Much of our analysis applies also to magnetohydrodynamic turbulence.

The rapid ionization of D₂ in a short and intense laser pulse generates a rotational–vibrational (RV) nuclear wave packet in D₂⁺. By solving the time-dependent Schrödinger equation in full dimensionality, we simulate the coherent evolution of such wave packets and discuss their ro-vibrational dynamics. Within a harmonic time-series analysis of the evolving nuclear probability density, we characterize the RV dynamics in D₂⁺ in an external intense linearly polarized infrared laser field in terms of quantum-beat (QB) spectra in which both internuclear distance and molecular orientation relative to the linearly polarized laser field are resolved. Based on numerical examples for the nuclear dynamics without and under the influence of pulsed and continuum-wave (cw) laser light, we discuss and quantify the signature of RV couplings in QB spectra and the extent to which the QB analysis of measured time-dependent fragment kinetic energy release spectra is expected to image the laser-dressed RV structure of D₂⁺.

In this paper, we present the operation of an electron shuttle realized as a nanomechanical diode for phase-coherent frequency conversion. The mechanical response of the balanced resonator displays a hierarchy of frequency-locked resonances. We are able to achieve phase control via intrinsic frequency locking of the commensurate oscillations. By selecting the appropriate winding numbers, we can apply this nanomechanical resonator for radio-frequency conversion and rectification. The results also indicate that correlated electron shuttling and dividers for frequency combs can be realized with nanomechanical resonators.

Using an annular phased array of eight loudspeakers, we generate sound beams that simultaneously contain phase singularities at a number of different frequencies. These frequencies correspond to different musical notes and the singularities can be set to overlap along the beam axis, creating a polyphonic acoustic vortex. Perturbing the drive amplitudes of the speakers means that the singularities no longer overlap, each note being nulled at a slightly different lateral position, where the volume of the other notes is now nonzero. The remaining notes form a tri-note chord. We contrast this acoustic phenomenon to the optical case where the perturbation of a white light vortex leads to a spectral spatial distribution.

The concurrent existence of ferroelectricity and magnetism within a single crystalline system characterizes the multiferroic materials discovered in recent years. To understand and develop the multiferroic phenomenon, we need to investigate the unusual coupling between spin and lattice degrees of freedom. Spins in multiferroics are expected to be elastically coupled to phonons. Therefore, the time-dependent study can be a crucial factor in understanding the coupled dynamics. Here, we report the observations of strong dynamic spin–lattice coupling in multiferroic LuMnO₃. A coherent optical phonon of 3.6 THz and its temperature dependence is measured for the first time from our femtosecond IR pump and probe spectroscopy. Also, we observed a coherent acoustic phonon of 47 GHz similar to a previous report (Lim et al 2003 Appl. Phys. Lett.83 4800). Temperature-dependent measurements show that both optical and acoustic phonons become significantly underdamped as temperature decreases to T_N, and they disappear below T_N. These observations reveal that phonons are coupled to spins by magneto-elastic coupling, and the disappearance of phonon modes at T_N is consistent with the isostructural coupling scheme suggested by Lee et al (2008 Nature451 805).

It was recently found that the heterogeneity of complex networks can enhance transport properties such as epidemic spreading, electric energy transfer, etc. A trivial deduction would be that the presence of hubs in complex networks can also accelerate the heat transfer although no concrete research has been done so far. In the present study, we have studied this problem and have found a surprising answer: the heterogeneity does not favor but prevents the heat transfer. We present a model to study heat conduction in complex networks and find that the network topology greatly affects the heat flux. The heat conduction decreases with the increase of heterogeneity of the network caused by both degree distribution and the clustering coefficient. Its underlying mechanism can be understood by using random matrix theory. Moreover, we also study the rectification effect and find that it is related to the degree difference of the network, and the distance between the source and the sink. These findings may have potential applications in real networks, such as nanotube/nanowire networks and biological networks.

It is commonly believed that epidemic spreading on scale-free networks is difficult to control and that the disease can spread even with a low infection rate, lacking an epidemic threshold. In this paper, we study epidemic spreading on complex networks under the framework of game theory, in which a voluntary vaccination strategy is incorporated. In particular, individuals face the 'dilemma' of vaccination: they have to decide whether or not to vaccinate according to the trade-off between the risk and the side effects or cost of vaccination. Remarkably and quite excitingly, we find that disease outbreak can be more effectively inhibited on scale-free networks than on random networks. This is because the hub nodes of scale-free networks are more inclined to take self-vaccination after balancing the pros and cons. This result is encouraging as it indicates that real-world networks, which are often claimed to be scale free, can be favorably and easily controlled under voluntary vaccination. Our work provides a way of understanding how to prevent the outbreak of diseases under voluntary vaccination, and is expected to provide valuable information on effective disease control and appropriate decision-making.

The charge spreading of the ground and excited states of Klein–Gordon particles moving in a Coulomb potential is quantitatively analysed by means of ordinary moments and the Heisenberg measure as well as by using the most relevant information-theoretic measures of global (Shannon entropic power) and local (Fisher information) types. The dependence of these complementary quantities on the nuclear charge Z and the quantum numbers characterizing the physical states is carefully discussed. The comparison of relativistic Klein–Gordon and non-relativistic Schrödinger values is made. Non-relativistic limits at large principal quantum number n and for small values of Z are also reached.

In this paper we report on the gravity-driven transport of rigid spheres of various sizes through the fluid–fluid interface of a demixed colloid–polymer mixture. Three consecutive stages can be distinguished: (i) the sphere approaches the interface by sedimenting through the polymer-rich phase, (ii) it is subsequently transported to the colloid-rich phase and (iii) it moves away from the interface. The spheres are covered by a thin wetting film of the colloid-rich phase, to which they are eventually transported. The ultralow interfacial tension in these phase-separating mixtures results in very small capillary forces so that the process takes place in the low Reynolds regime. Moreover, it enables the investigation of the role of capillary waves in the process. Depending on the Bond number, the ratio between gravitational force and capillary force acting on the sphere, different transport configurations are observed. At low Bond numbers, the drainage transport configuration, with a dominant capillary force, is encountered. At high Bond numbers, spheres are transported through the tailing configuration, with a dominant gravitational force. By varying the sphere diameter, we observe both transport configurations as well as a crossover regime in a single experimental system.

In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely complementarity, measurement simulability, and global gauge invariance. When these features are appropriately formalized within an information geometric framework, and combined with a novel information-theoretic principle, the central features of the finite-dimensional quantum formalism can be reconstructed.

We present an ab initio description of charge transport in organic semiconductors based on a recently developed theory that goes beyond small-polaron and/or narrow-band models. The mobility expression is evaluated with parameters from density functional theory, and application to naphthalene crystals demonstrates substantial progress in the simulated temperature dependence and relative magnitudes for all transport directions. The scattering by phonons is described in a manner that goes beyond the Holstein model for small polarons and, consequently, significantly improves the temperature dependence and anisotropy of carrier mobility with respect to the previous narrow-band theory. The contributions of coherent and incoherent scattering processes are analyzed. Special emphasis is placed on the origin and understanding of the transition from band transport at low temperatures to hopping at high temperatures, both of which are fully included in the theory. Additionally, in contrast to earlier narrow-band theories, the unphysical divergence at zero temperatures is removed.

We explore precision in a measurement process incorporating pure probe states, unitary dynamics and complete measurements via a simple formalism. The concept of 'information complement' is introduced. It undermines measurement precision and its minimization reveals the optimal system properties. Maximally precise measurements can exhibit independence from the true value of the estimated parameter, but demanding this severely restricts the type of viable probe and dynamics, including the requirement that the Hamiltonian be block diagonal in a basis of preferred measurements. The curvature of the information complement near a globally optimal point provides a new quantification of measurement stability.

We study precipitation patterns occurring in diffusion-limited reactions, focusing on Liesegang bands. Naturally, these patterns are non-equidistantly spaced, and thus less useful for bottom-up material design. However, we show how a continuous large-scale modification of the inhomogeneity of the substrate and/or the nucleation threshold can be used to obtain equidistantly spaced bands on small length scales. We confirm our suggestions by lattice-gas simulations and propose an iterative experimental procedure not requiring a priori knowledge of parameters. We discuss the feasibility for glass substrates modified by irradiation with femtosecond laser pulses.

Manganese-doped ZnO dielectric films sandwiched between Cu and Pt electrodes were prepared and investigated for nonvolatile resistive memory applications. These structures exhibit promising bipolar resistive switching (RS) behavior with a large ON/OFF ratio (∼10³), suitable threshold voltages (1.4 and −0.7 V for SET and RESET, respectively), long retention (>10⁴ s at 85 °C) and low write current (10 μA). A study on the ZnO:Mn thickness dependence of threshold voltages reveals that RS should be an interfacial effect rather than bulk behavior. By elevating current compliance during the SET process, an anomalous transition from bistable memory switching to monostable threshold switching was observed, which is attributed to the instability of conductive filaments induced by Joule heating effects. Apart from this, fast voltage sweep cycles without efficient heat dissipation were also found to accelerate the hard dielectric breakdown of the device, reflecting the impact of accumulative Joule heating. These results reveal the possible influences of Joule heating effects on bipolar resistance switching and thus the necessity of avoiding them in future high-density memory applications. Conceivable solutions are considered to be reducing the operating currents and improving the heat dissipation of memory devices based on our experiments.

We report the growth and low-temperature photoluminescent characteristics of well-aligned Ni-doped ZnO nanoneedles and V-doped ZnO nanostructured thin film grown by a modified pulsed laser deposition technique. Low-temperature photoluminescence spectra of the as-grown films show the presence of free excitonic as well as bound excitonic transitions, whose relative intensity changes with increasing temperature. Ni-doped ZnO films show a characteristic fine structure in the visible range (2.6–2.9 meV) attributed to either exciton–polariton longitudinal–transverse splitting or the splitting caused by electron–hole exchange interaction. The excitonic and visible region emission can be clearly seen as can the phonon replicas produced from longitudinal optical phonons. Different possible attributions of the various peaks in the emission band at low temperature have been discussed. The as-grown nanostructures of Ni- and V-doped ZnO thin films also clearly show the effect of doping on the microstructure of ZnO.

In this paper, we report the field and temperature dependence of low-temperature specific heat down to 400 mK and in magnetic fields up to 9 T of the electron-doped Ba(Fe_0.92Co_0.08)₂As₂ superconductor. Using the phonon specific heat obtained from pure BaFe₂As₂, we found a normal state Sommerfeld coefficient of 18 mJ mol⁻¹ K^-2 and a condensation energy of 1.27 J mol⁻¹. The temperature dependence of electronic specific heat clearly indicates the presence of low-energy excitations in the system. The magnetic field variation of field-induced specific heat cannot be described by single clean s- or d-wave models. Rather, the data require an anisotropic gap scenario that may or may not have nodes. We discuss the implications of these results.

Ac susceptibility measurements have been carried out on superconducting LaO_1−xF_xFeAs for x=0.07 and 0.14 under He-gas pressures to ∼0.8 GPa. Not only do the measured values of dT_c/dP differ substantially from those obtained in previous studies using other pressure media, but also the T_c(P) dependences observed depend on the detailed pressure/temperature history of the sample. A sizeable sensitivity of T_c(P) to shear stresses provides a possible explanation.

Much progress has been made recently in the study of the effects of electron–phonon (el–ph) coupling in doped insulators using angle-resolved photoemission (ARPES), yielding evidence for the dominant role of el–ph interactions in underdoped cuprates. As these studies have been limited to doped Mott insulators, the important question arises as to how this compares with doped band insulators where similar el–ph couplings should be at work. The archetypical case is that of perovskite SrTiO₃ (STO), well known for its giant dielectric constant of 10 000 at low temperatures, exceeding that of La₂CuO₄ by a factor of 500. Based on this fact, it has been suggested that doped STO should be the archetypical bipolaron superconductor. Here we report an ARPES study from high-quality surfaces of lightly doped STO. In comparison to lightly doped Mott insulators, we find the signatures of only moderate el–ph coupling; a dispersion anomaly associated with the low-frequency optical phonon with a λ ' ∼0.3 and an overall bandwidth renormalization suggesting an overall λ ' ∼0.7 coming from the higher frequency phonons. Furthermore, we find no clear signatures of the large pseudogap or small-polaron phenomena. These findings demonstrate that a large dielectric constant itself is not a good indicator of el–ph coupling and highlight the unusually strong effects of the el–ph coupling in doped Mott insulators.

We develop a simple theoretical framework for the evolution of weighted networks that is consistent with a number of stylized features of real-world data. In our framework, the Barabási–Albert model of network evolution is extended by assuming that link weights evolve according to a geometric Brownian motion. Our model is verified by means of simulations and real-world trade data. We show that the model correctly predicts the intensity and growth distribution of links, the size–variance relationship of the growth of link weights, the relationship between the degree and strength of nodes, and the scale-free structure of the network.

It is shown how one can implement quantum feedback and probabilistic error correction in an open quantum system consisting of a single atom, with ground- and excited-state Zeeman structure, in a driven two-mode optical cavity. The ground-state superposition is manipulated and controlled through conditional measurements and external fields, which shield the coherence and correct quantum errors. Modeling an experimentally realistic situation demonstrates the robustness of the proposal for realization in the laboratory.

The impact of free surfaces on the mobility and conformational fluctuations of model polymer chains is investigated with the help of classical molecular dynamics simulations over a broad temperature range. Below a critical temperature, T^*, similar to the critical temperature of the mode coupling theory, the center-of-mass displacements and temporal fluctuations of the radius of gyration of individual chains—as a fingerprint of structural reconfigurations—reveal a strong enhancement close to surfaces, while this effect diminishes with increasing temperature and observation time. Interpreting conformational fluctuations as a random walk in conformational space, identical activation enthalpies for structural reconfigurations and diffusion are obtained within the error bars in the bulk and at the surfaces, thus indicating a coupling of diffusive and conformational dynamics.