We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our criteria are simple functions of the given quantum state and detect genuine multipartite entanglement that had not been identified so far. They are experimentally accessible without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed.

Particles in a perfect lattice potential perform Bloch oscillations when subject to a constant force, leading to localization and preventing conductivity. For a weakly interacting Bose-Einstein condensate of Cs atoms, we observe giant center-of-mass oscillations in position space with a displacement across hundreds of lattice sites when we add a periodic modulation to the force near the Bloch frequency. We study the dependence of these “super” Bloch oscillations on lattice depth, modulation amplitude, and modulation frequency and show that they provide a means to induce linear transport in a dissipation-free lattice.

We analyze the coherent quantum evolution of a many-particle system after slowly sweeping a power-law confining potential. The amplitude of the confining potential is varied in time along a power-law ramp such that the many-particle system finally reaches or crosses a critical point. Under this protocol we derive general scaling laws for the density of excitations created during the nonadiabatic sweep of the confining potential. It is found that the mean excitation density follows an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential. We confirm our scaling laws by first order adiabatic calculation and exact results on the Ising quantum chain with a varying transverse field.

We demonstrate that a transmission electron microscope fitted with two spherical-aberration correctors can be operated as an energy-filtered scanning confocal electron microscope. A method for establishing this mode is described and initial results showing 3D chemical mapping with nanoscale sensitivity to height and thickness changes in a carbon film are presented. Importantly, uncorrected chromatic aberration does not limit the depth resolution of this technique and moreover performs an energy-filtering role, which is explained in terms of a combined depth and energy-loss response function.

We describe a novel approach to directly measure the energy of the narrow, low-lying isomeric state in ${}^{229}\mathrm{Th}$. Since nuclear transitions are far less sensitive to environmental conditions than atomic transitions, we argue that the ${}^{229}\mathrm{Th}$ optical nuclear transition may be driven inside a host crystal with a high transition $Q$. This technique might also allow for the construction of a solid-state optical frequency reference that surpasses the short-term stability of current optical clocks, as well as improved limits on the variability of fundamental constants. Based on analysis of the crystal lattice environment, we argue that a precision (short-term stability) of $3\times {10}^{-17}<\Delta f/f<1\times {10}^{-15}$ after 1 s of photon collection may be achieved with a systematic-limited accuracy (long-term stability) of $\Delta f/f\sim 2\times {10}^{-16}$. Improvement by ${10}^2-{10}^3$ of the constraints on the variability of several important fundamental constants also appears possible.

We show that the chirality of triangular antiferromagnetic clusters can be used as a qubit even if it is entirely decoupled from the total spin of the cluster. In particular, we estimate the orbital moment associated with the chirality, and we show that it can be large enough to allow a direct measurement of the chirality with a field perpendicular to the cluster. Consequences for molecular magnets are discussed, and an alternative implementation with Cu atoms on a surface is proposed, for which one- and two-qubit gates are worked out in detail. Decoherence effects are also discussed.

We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times $t<\overline{t}$. In this initial time interval classical correlations decay. For $t>\overline{t}$, on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time $\overline{t}$ the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.

We demonstrate atomic four-wave mixing of two-component matter waves in a collinear geometry. Starting from a single-species Bose–Einstein condensate, seed and pump modes are prepared through microwave state transfer and state-selective Kapitza–Dirac diffraction. Four-wave mixing then populates the initially empty output modes. Simulations based on a coupled-mode expansion of the Gross–Pitaevskii equation are in very good agreement with the experimental data. We show that four-wave mixing can play an important role in studies of bosonic mixtures in optical lattices. Moreover, our system should be of interest in the context of quantum atom optics.

Molecular nanostructures may constitute the fabric of future quantum technologies, if their degrees of freedom can be fully harnessed. Ideally one might use nuclear spins as low-decoherence qubits and optical excitations for fast controllable interactions. Here, we present a method for entangling two nuclear spins through their mutual coupling to a transient optically excited electron spin, and investigate its feasibility through density-functional theory and experiments on a test molecule. From our calculations we identify the specific molecular properties that permit high entangling power gates under simple optical and microwave pulses; synthesis of such molecules is possible with established techniques.

We consider a gas of two species of fermions with population imbalance. Using the renormalization group in $d=1+ϵ$ spatial dimensions, we show that for spinless fermions and $2>ϵ>0$ a fixed point appears at finite attractive coupling where the quasiparticle residue vanishes, and identify this with the transition to Larkin-Ovchinnikov-Fulde-Ferrell order (inhomogeneous superconductivity). When the two species of fermions also carry spin degrees of freedom we find a fixed point indicating a transition to spin density wave order.

The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of special importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion and give examples of the obtained solutions that describe propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium and free electromagnetic oscillations in a cylindrical cavity resonator filled with such a medium.

We define matrix product states in the continuum limit, without any reference to an underlying lattice parameter. This allows us to extend the density matrix renormalization group and variational matrix product state formalism to quantum field theories and continuum models in 1 spatial dimension. We illustrate our procedure with the Lieb-Liniger model.

We study the escape rate of flux quanta in a long Josephson junction having an asymmetric spatial inhomogeneous critical current density. Such a junction can behave as a ratchet when driven by an ac current in the presence of a magnetic field. This rectification gives rise to a dc voltage $V_{\mathrm{dc}}$ across the junction. The usual approach of particlelike tunneling cannot describe this rectification, and a quantum field theory description is required. We also show that, under specific conditions, the rectification direction, and consequently $V_{\mathrm{dc}}$, can change its sign when varying the temperature $T$ near the crossover temperature $T^{*}$ between the quantum and classical regimes.

Unless protected by the exact integrability, solitons are subject to dissipative forces, originating from a thermally fluctuating background. At low enough temperatures $T$ background fluctuations should be considered as being quantized which enables us to calculate finite lifetime of the solitons $\tau \sim T^{-4}$. We also find that the coherent nature of the quantum fluctuations leads to long-range interactions between the solitons mediated by the superradiation. Our results are of relevance to current experiments with ultracold atoms, while the approach may be extended to solitons in other media.

The Lieb-Robinson bound shows the existence of a maximum speed of signal propagation in discrete quantum mechanical systems with local interactions. This generalizes the concept of relativistic causality beyond field theory, and provides a powerful tool in theoretical condensed matter physics and quantum information science. Here, we extend the scope of this seminal result by considering general Markovian quantum evolution, where we prove that an equivalent bound holds. In addition, we use the generalized bound to demonstrate that correlations in the stationary state of a Markov process decay on a length scale set by the Lieb-Robinson velocity and the system’s relaxation time.

Codeword-stabilized codes are a general class of quantum codes that includes stabilizer codes and many families of nonadditive codes with good parameters. For such a nonadditive code correcting all $t$-qubit errors, we propose an algorithm that employs a single measurement to test all errors located on a given set of $t$ qubits. Compared with exhaustive error screening, this reduces the total number of measurements required for error recovery by a factor of about $3^t$.

We introduce the well-tempered ensemble (WTE) which is the biased ensemble sampled by well-tempered metadynamics when the energy is used as collective variable. WTE can be designed so as to have approximately the same average energy as the canonical ensemble but much larger fluctuations. These two properties lead to an extremely fast exploration of phase space. An even greater efficiency is obtained when WTE is combined with parallel tempering. Unbiased Boltzmann averages are computed on the fly by a recently developed reweighting method [M. Bonomi et al., J. Comput. Chem. 30, 1615 (2009)]. We apply WTE and its parallel tempering variant to the $2d$ Ising model and to a Gō model of HIV protease, demonstrating in these two representative cases that convergence is accelerated by orders of magnitude.

Ising-type non-Abelian anyons are likely to occur in a number of physical systems, including quantum Hall systems, where recent experiments support their existence. In general, non-Abelian anyons may be utilized to provide a topologically error-protected medium for quantum information processing. However, the topologically protected operations that may be obtained by braiding and measuring topological charge of Ising anyons are precisely the Clifford gates, which are not computationally universal. The Clifford gate set can be made universal by supplementing it with single-qubit $\pi /8$-phase gates. We propose a method of implementing arbitrary single-qubit phase gates for Ising anyons by running a current of anyons with interfering paths around computational anyons.

We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as $0.77k_B$ which is about twice as large as the entropy at the Néel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy.

Quantum communication typically involves a linear chain of repeater stations, each capable of reliable local quantum computation and connected to their nearest neighbors by unreliable communication links. The communication rate of existing protocols is low as two-way classical communication is used. By using a surface code across the repeater chain and generating Bell pairs between neighboring stations with probability of heralded success greater than 0.65 and fidelity greater than 0.96, we show that two-way communication can be avoided and quantum information can be sent over arbitrary distances with arbitrarily low error at a rate limited only by the local gate speed. This is achieved by using the unreliable Bell pairs to measure nonlocal stabilizers and feeding heralded failure information into post-transmission error correction. Our scheme also applies when the probability of heralded success is arbitrarily low.