We evaluate the self-diffusion and transport diffusion of interacting particles in a discrete geometry consisting of a linear chain of cavities, with interactions within a cavity described by a free-energy function. Exact analytical expressions are obtained in the absence of correlations, showing that the self-diffusion can exceed the transport diffusion if the free-energy function is concave. The effect of correlations is elucidated by comparison with numerical results. Quantitative agreement is obtained with recent experimental data for diffusion in a nanoporous zeolitic imidazolate framework material, ZIF-8.

We introduce a scheme to perform quantum information processing that is based on a hybrid spin-photon qubit encoding. The proposed qubits consist of spin ensembles coherently coupled to microwave photons in coplanar waveguide resonators. The quantum gates are performed solely by shifting the resonance frequencies of the resonators on a nanosecond time scale. An additional cavity containing a Cooper-pair box is exploited as an auxiliary degree of freedom to implement two-qubit gates. The generality of the scheme allows its potential implementation with a wide class of spin systems.

Entanglement is a resource in quantum information theory when state manipulation is restricted to local operations assisted by classical communication (LOCC). It is therefore of paramount importance to decide which LOCC transformations are possible and, particularly, which states are maximally useful under this restriction. While the bipartite maximally entangled state is well known (it is the only state that cannot be obtained from any other and, at the same time, it can be transformed to any other by LOCC), no such state exists in the multipartite case. In order to cope with this fact, we introduce here the notion of the maximally entangled set (MES) of $n$-partite states. This is the set of states which are maximally useful under LOCC manipulation; i.e., any state outside of this set can be obtained via LOCC from one of the states within the set and no state in the set can be obtained from any other state via LOCC. We determine the MES for states of three and four qubits and provide a simple characterization for them. In both cases, infinitely many states are required. However, while the MES is of measure zero for 3-qubit states, almost all 4-qubit states are in the MES. This is because, in contrast to the 3-qubit case, deterministic LOCC transformations are almost never possible among fully entangled four-partite states. We determine the measure-zero subset of the MES of LOCC convertible states. This is the only relevant class of states for entanglement manipulation.

We investigate numerically the collisions of two distinguishable quantum matter-wave bright solitons in a one-dimensional harmonic trap. We show that such collisions can be used to generate mesoscopic Bell states that can reliably be distinguished from statistical mixtures. Calculation of the relevant $s$-wave scattering lengths predicts that such states could potentially be realized in quantum-degenerate mixtures of ${}^{85}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$. In addition to fully quantum simulations for two distinguishable two-particle solitons, we use a mean-field description supplemented by a stochastic treatment of quantum fluctuations in the soliton’s center of mass: we demonstrate the validity of this approach by comparison to a mathematically rigorous effective potential treatment of the quantum many-particle problem.

Quantum systems in mixed states can be unentangled and yet still nonclassically correlated. These correlations can be quantified by the quantum discord and might provide a resource for quantum information processing tasks. By precisely controlling the interaction of two ionic qubits with their environment, we investigate the capability of noise to generate discord. Firstly, we show that noise acting on only one quantum system can generate discord between two. States generated in this way are restricted in terms of the rank of their correlation matrix. Secondly, we show that classically correlated noise processes are capable of generating a much broader range of discordant states with correlation matrices of any rank. Our results show that noise processes prevalent in many physical systems can automatically generate nonclassical correlations and highlight fundamental differences between discord and entanglement.

We demonstrate precise control of the coupling of each of two trapped ions to the mode of an optical resonator. When both ions are coupled with near-maximum strength, we generate ion-ion entanglement heralded by the detection of two orthogonally polarized cavity photons. The entanglement fidelity with respect to the Bell state ${\Psi }^{+}$ reaches $F\ge (91.9\pm 2.5)\%$. This result represents an important step toward distributed quantum computing with cavities linking remote atom-based registers.

We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Because of the long-range Ising interactions, the various ground state spin configurations are separated by multiple first-order phase transitions, which in our zero temperature system cannot be driven by thermal fluctuations. We instead use a transverse magnetic field as a quantum catalyst to observe the first steps of the complete fractal devil’s staircase, which emerges in the thermodynamic limit and can be mapped to a large number of many-body and energy-optimization problems.

We consider particles moving in rotating saddle-shaped potentials in two dimensions. It is known that such rotating potentials can generate bounded motion for particles with a parabolic dispersion law through the combination of potential, centrifugal, and Coriolis forces in the rotating frame. When applied to massless Dirac particles, for example, electrons in graphene, such a potential is shown to lead to eigenstates that are spatially localized near the center of the saddle at certain energies. Although other states also exist at these energies, they have nonoverlapping support in the oscillator basis, which also tends to give the localized states a substantial lifetime when imperfections are present.

We develop a nonequilibrium model of condensation and lasing of photons in a dye filled microcavity. We examine in detail the nature of the thermalization process induced by absorption and emission of photons by the dye molecules, and investigate when the photons are able to reach a thermal equilibrium Bose-Einstein distribution. At low temperatures, or large cavity losses, the absorption and emission rates are too small to allow the photons to reach thermal equilibrium and the behavior becomes more like that of a conventional laser.

We compute the entanglement entropy of a wide class of models that may be characterized as describing matter coupled to gauge fields. Our principle result is an entanglement sum rule that states that the entropy of the full system is the sum of the entropies of the two components. In the context of the models we consider, this result applies to the full entropy, but more generally it is a statement about the additivity of universal terms in the entropy. Our proof simultaneously extends and simplifies previous arguments, with extensions including new models at zero temperature as well as the ability to treat finite temperature crossovers. We emphasize that while the additivity is an exact statement, each term in the sum may still be difficult to compute. Our results apply to a wide variety of phases including Fermi liquids, spin liquids, and some non-Fermi liquid metals. For example, we prove that our model of an interacting Fermi liquid has exactly the log violation of the area law for entanglement entropy predicted by the Widom formula in agreement with earlier arguments.

Among all entanglement measures negativity arguably is the best known and most popular tool to quantify bipartite quantum correlations. It is easily computed for arbitrary states of a composite system and can therefore be applied to discuss entanglement in an ample variety of situations. However, as opposed to logarithmic negativity, its direct physical meaning has not been pointed out yet. We show that the negativity can be viewed as an estimator of how many degrees of freedom of two subsystems are entangled. As it is possible to give lower bounds for the negativity even in a device-independent setting, it is the appropriate quantity to certify quantumness of both parties in a bipartite system and to determine the minimum number of dimensions that contribute to the quantum correlations.

Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show how to calculate moments of these distributions using $C{P}^{n-1}$ or $R{P}^{n-1}$ and $\mathrm{O}(n)$ $\sigma$ models together with replica techniques. The resulting joint length distribution for macroscopic loops is Poisson-Dirichlet with a parameter $\theta$ fixed by the loop fugacity and by symmetries of the ensemble. We also discuss features of the length distribution for shorter loops, and use numerical simulations to test and illustrate our conclusions.

The infinite-time average of the expectation values of local fields of any interacting quantum theory after a global quench process are key quantities for matching theoretical and experimental results. For quantum integrable field theories, we show that they can be obtained by an ensemble average that employs a particular limit of the form factors of local fields and quantities extracted by the generalized Bethe ansatz.

We compare the ground-state energies of bosons and fermions with the same form of the Hamiltonian. If both are noninteracting, the ground-state energy of bosons is always lower, owing to Bose-Einstein condensation. However, the comparison is nontrivial when bosons do interact. We first prove that, when the hopping is unfrustrated (all the hopping amplitudes are non-negative), hard-core bosons still must have a lower ground-state energy than fermions. If the hopping is frustrated, bosons can have a higher ground-state energy than fermions. We prove rigorously that this inversion indeed occurs in several examples.

We discuss sequential unambiguous state-discrimination measurements performed on the same qubit. Alice prepares a qubit in one of two possible states. The qubit is first sent to Bob, who measures it, and then on to Charlie, who also measures it. The object in both cases is to determine which state Alice sent. In an unambiguous state discrimination measurement, we never make a mistake, i.e., misidentify the state, but the measurement may fail, in which case we gain no information about which state was sent. We find that there is a nonzero probability for both Bob and Charlie to identify the state, and we maximize this probability. The probability that Charlie’s measurement succeeds depends on how much information about the state Alice sent is left in the qubit after Bob’s measurement, and this information can be quantified by the overlap between the two possible states in which Bob’s measurement leaves the qubit. This Letter is a first step toward developing a theory of nondestructive sequential quantum measurements, which could be useful in quantum communication schemes.

The evolution of a system induced by counterdiabatic driving mimics the adiabatic dynamics without the requirement of slow driving. Engineering it involves diagonalizing the instantaneous Hamiltonian of the system and results in the need of auxiliary nonlocal interactions for matter waves. Here, experimentally realizable driving protocols are found for a large class of single-particle, many-body, and nonlinear systems without demanding the spectral properties as an input. The method is applied to the fast decompression of Bose-Einstein condensates in different trapping potentials.

We search for a spin-dependent $P$- and $T$-violating nucleon-nucleon interaction mediated by light pseudoscalar bosons such as axions or axionlike particles. We employ an ultrasensitive low-field magnetometer based on the detection of free precession of colocated ${}^3\mathrm{He}$ and ${}^{129}\mathrm{Xe}$ nuclear spins using SQUIDs as low-noise magnetic flux detectors. The precession frequency shift in the presence of an unpolarized mass was measured to determine the coupling of pseudoscalar particles to the spin of the bound neutron. For boson masses between 2 and $500\mu \mathrm{eV}$ (force ranges between $3\times {10}^{-4}\mathrm{m}$ and ${10}^{-1}\mathrm{m}$) we improved the laboratory upper bounds by up to 4 orders of magnitude.

A numerical method is developed by which the tunnel ionization dynamics of bound systems in laser fields can be isolated from the total wave function, as given by the time-dependent Schrödinger equation. The analysis of the numerical data for a step function field reveals the following definition for the tunnel time. It is the time it takes the ground state to develop the underbarrier wave function components necessary for reaching the static field ionization rate. This definition is generalized to time varying laser fields. The tunnel time is found to scale with the Keldysh tunnel time. Our Letter establishes the physical meaning of the tunnel time, its relation to the Keldysh tunnel time, and suggests how it can be measured.

Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. Though transversal gates alone cannot be computationally universal, they can be combined with specially distilled resource states in order to achieve universality. We show that “triorthogonal” stabilizer codes, introduced for state distillation by Bravyi and Haah [Phys. Rev. A 86, 052329 (2012)], admit transversal implementation of the controlled-controlled-$Z$ gate. We then construct a universal set of fault-tolerant gates without state distillation by using only transversal controlled-controlled-$Z$, transversal Hadamard, and fault-tolerant error correction. We also adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes.

We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit backaction is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a nonclassical weak value and the violation of a Leggett-Garg inequality.