Trapped ions are a versatile platform for the investigation of quantum many-body phenomena, in particular for the study of scenarios where long-range interactions are mediated by phonons. Recent experiments have shown that the trapped ion platform can be augmented by exciting high-lying Rydberg states. This introduces controllable state-dependent interactions that are independent of the phonon structure. However, the many-body physics in this newly accessible regime is largely unexplored. We show that this system grants access to generalized Dicke model physics, where dipolar interactions between ions in Rydberg states drastically alter the collective nonequilibrium behavior. We analyze and classify the emerging dynamical phases and identify a host of nonequilibrium signatures such as multiphase coexistence regions and phonon-lasing regimes. We moreover show how they can be detected and characterized through the fluorescence signal of scattered photons. Our study thus highlights interesting capabilities of trapped Rydberg-ion systems for creating and detecting quantum nonequilibrium phases.

Interatomic Coulombic decay (ICD) is an ultrafast energy transfer process. Via ICD, an excited atom can transfer its excess energy to a neighboring atom which is thus ionized. On the example of the NeHeNe cluster, we recently reported [Phys. Rev. Lett. 119, 083403 (2017)] that the total ICD widths are substantially enhanced in the presence of an ICD inactive atom. The enhancement occurs due to the coupling of the resonance state to intermediate virtual states of the bridge atom—a mechanism named superexchange ICD. In this followup work, we analyze the partial ICD widths in the NeHeNe cluster and show that only some channels are affected by the superexchange ICD process. Furthermore, we consider superexchange ICD in NeHeAr. We show that in this system the enhancement is still present but the energy transfer mediated by the superexchange mechanism is less efficient than in NeHeNe owing to the different ionization potentials of Ar and Ne. The behavior of the computed ICD widths is explained with a simple model based on first-order perturbation theory and a Hartree-Fock-like description of the states.

We unravel the nonequilibrium dynamics of two fermionic impurities immersed in a one-dimensional bosonic gas following an interspecies interaction quench. Monitoring the temporal evolution of the single-particle density of each species we reveal the existence of four distinct dynamical regimes. For weak interspecies repulsions both species either perform a breathing motion or the impurity density splits into two parts which interact and disperse within the bosonic cloud. Turning to strong interactions we observe the formation of dark-bright states within the mean-field approximation. However, the correlated dynamics shows that the fermionic density splits into two repelling density peaks which either travel toward the edges of the bosonic cloud where they equilibrate or they approach an almost steady state propagating robustly within the bosonic gas which forms density dips at the same location. For these strong interspecies interactions an energy transfer process from the impurities to their environment occurs at the many-body level, while a periodic energy exchange from the bright states (impurities) to the bosonic species is identified in the absence of correlations. Finally, inspecting the one-body coherence function for strong interactions enables us to draw conclusions on the spatial localization of the quench-induced fermionic density humps.

We introduce an efficient and numerically stable technique to make use of a BCS trial wave function in the computation of correlation functions of strongly correlated quantum fermion systems. The technique is applicable to any projection approach involving paths of independent-fermion propagators, for example, in mean-field or auxiliary-field quantum Monte Carlo (AFQMC) calculations. Within AFQMC, in the absence of the sign problem, the methodology allows the use of a BCS reference state which can greatly reduce the required imaginary time of projection and improves Monte Carlo sampling efficiency and statistical accuracy for systems where pairing correlations are important. When the sign problem is present, the approach provides a powerful generalization of the constrained-path AFQMC technique which usually uses Slater determinant trial wave functions. As a demonstration of the capability of the methodology, we present benchmark results for the attractive Hubbard model, both spin balanced (no sign problem) and with a finite spin polarization (with sign problem).

Topological phases with a widely tunable number of edge modes have been extensively studied as a typical class of exotic states of matter with potentially important applications. Although several models have been shown to support such phases, they are not easy to realize in solid-state systems due to the complexity of various intervening factors. Inspired by the realization of synthetic spin-orbit coupling in a cold-atom system [Z. Wu et al., Science 354, 83 (2016)], we propose a periodic quenching scheme to realize large-topological-number phases with multiple edge modes in optical lattices. Via introducing the periodic quenching to the Raman lattice, it is found that a large number of edge modes can be induced in a controllable manner from the static topologically trivial system. Our result provides an experimentally accessible method to artificially synthesize and manipulate exotic topological phases with large topological numbers and multiple edge modes.

We investigate the spin-2 chain model corresponding to the small hopping limit of the spin-2 Bose-Hubbard model using density-matrix renormalization-group and time-evolution techniques. We calculate both static correlation functions and the dynamic structure factor. The dynamic structure factor in the dimerized phase differs significantly between parameters near the SU(5)-symmetric point and those deeper in the phase where the dimerization is strong. In the former case, most of the spectral weight is concentrated in a single excitation line, while in the latter case, a broad excitation continuum shows up. For the trimerized phase, we find gapless excitations at momenta $k=\pm 2\pi /3$ in agreement with previous results, although the visibility of these excitations in the dynamic spin response depends strongly on the specific parameters. We also consider parameters for specific atoms which may be relevant for future optical-lattice experiments.

We analyze the optical resonances of a dielectric sphere the surface of which has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and the modified linewidths. Our theory is applicable, for example, to freely levitated liquid drops or solid spheres, which are deformed by thermal surface vibrations, centrifugal forces, or arbitrary surface waves. A dielectric sphere is effectively an open system the description of which requires the introduction of non-Hermitian operators characterized by complex eigenvalues and non-normalizable eigenfunctions. We avoid these difficulties using the Kapur-Peierls formalism, which enables us to extend the popular Rayleigh-Schrödinger perturbation theory to the case of electromagnetic Debye potentials describing the light fields inside and outside the near-spherical dielectric object. We find analytical formulas, valid within certain limits, for the deformation-induced first- and second-order corrections to the central frequency and bandwidth of a resonance. As an application of our method, we compare our results with preexisting ones, finding full agreement.

We address the question of assessing the number of particles sharing genuinely nonlocal correlations in a multipartite system. While the interest in multipartite nonlocality has grown in recent years, its existence in large quantum systems is difficult to confirm experimentally. This is mostly due to the inadequacy of standard multipartite Bell inequalities to many-body systems: Such inequalities usually rely on expectation values involving many parties, usually all, and require individual addressing of each party. In addition, known Bell inequalities for genuine nonlocality are composed of a number of expectation values that scales exponentially with the number of observers, which makes such inequalities impractical from the experimental point of view. In a recent work [Tura et al., Science 344, 1256 (2014)], it was shown that it is possible to detect nonlocality in multipartite systems using Bell inequalities with only two-body correlators. This opened the way for the detection of Bell correlations with trusted collective measurements through Bell correlation witnesses [Schmied et al., Science 352, 441 (2016)]. These witnesses were recently tested experimentally in many-body systems such as Bose-Einstein condensate or thermal ensembles, hence demonstrating the presence of Bell correlations with assumptions on the statistics. Here, we address the problem of detecting nonlocality depth, a notion that quantifies the number of particles sharing nonlocal correlation in a multipartite system. We introduce a general framework allowing us to derive Bell-like inequalities for nonlocality depth from symmetric two-body correlators. We characterize all such Bell-like inequalities for a finite number of parties and we show that they reveal Bell correlation depth $k\le 6$ in arbitrarily large systems. We then show how Bell correlation depth can be estimated using quantities that are within reach in current experiments. On one hand, we use the standard multipartite Bell inequalities such the Mermin and Svetlichny ones to derive Bell correlations witnesses of any depth that involves only two collective measurements, one of which being the parity measurement. On the other hand, we show that our two-body Bell inequalities can be turned into witnesses of depth $k\le 6$ that require measuring total spin components in certain directions. Interestingly, such a witness is violated by existing data from an ensemble of 480 atoms.

Einstein-Podolsky-Rosen (EPR) steering, as one of the most intriguing phenomenon of quantum mechanics, is a useful quantum resource for quantum communication. Understanding the type of EPR steering in a graph state is the basis for application of it in a quantum network. In this paper, we present EPR steering in a Gaussian weighted graph state, including a linear tripartite and a four-mode square weighted graph state. The dependence of EPR steering on weight factor in the weighted graph state is analyzed. Gaussian EPR steering between two modes of a weighted graph state is presented, which does not exist in the Gaussian cluster state (where the weight factor is unit). For the four-mode square Gaussian weighted graph state, EPR steering between one and its two nearest modes is also presented, which is absent in the four-mode square Gaussian cluster state. We also show that Gaussian EPR steering in a weighted graph state is also bounded by the Coffman-Kundu-Wootters monogamy relation. The presented results are useful for exploiting EPR steering in a Gaussian weighted graph state as a valuable resource in multiparty quantum communication tasks.

We show that a shared singlet state (SSS) can supersede a shared reference frame (SRF) in certain quantum communication tasks, i.e., tasks in which two remote players are required to estimate certain parameters of a two-particle state sent to them. This shows that task-specific values of resources may be somewhat different from their common values based on their exchange possibilities.

We use multiple quantum (MQ) nuclear magnetic resonance dynamics of a gas of spin-carrying molecules in nanocavities at high and low temperatures for an investigation of many-particle entanglement. A distribution of MQ NMR intensities is obtained at high and low temperatures in a system of 201 spins $\frac{1}{2}$. The second moment of the distribution, which provides a lower bound on the quantum Fisher information, sheds light on the many-particle entanglement in the system. The dependence of the many-particle entanglement on the temperature is investigated. Almost all spins are entangled at low temperatures.

Analytic higher-order momentum correlation functions associated with the time-of-flight spectroscopy of three ultracold fermionic atoms singly confined in a linear three-well optical trap are presented, corresponding to the $W$- and Greenberger-Horne-Zeilinger–type states that belong to characteristic classes of tripartite entanglement and represent the strong-interaction regime captured by a three-site Heisenberg Hamiltonian. The methodology introduced here contrasts with and goes beyond that based on the standard Wick factorization scheme; it enables determination of both third-order and second-order spin resolved and spin unresolved momentum correlations, aiming at matter-wave interference investigations with trapped massive particles in analogy with, and having the potential for expanding the scope of, recent three-photon quantum-optics interferometry.

We study systematically the quantum corrections to a weakly interacting Bose-Einstein condensate with spin-orbit coupling. We show that quantum fluctuations, enhanced by the spin-orbit coupling, modify quantitatively the mean-field properties such as the superfluid density, spin polarizability, and sound velocity. We find that the phase boundary between the plane wave and zero momentum phases is shifted to a smaller transverse field. We also calculate the Beliaev and Landau damping rates and find that the Landau process dominates the quasiparticle decay even at low temperature.

We study the bound states in the continuum for a system of $n$ two-level quantum emitters, coupled with a one-dimensional photon field, when a single excitation is shared among the different components of the system. The emitters are equally spaced at fixed positions. We first consider the approximation of distant emitters and exhibit degenerate eigenspaces of bound states corresponding to resonant discrete values of the energy. We then consider the full form of the eigenvalue equation, in which the effects of the finite spacing and the field dispersion relation become relevant, yielding significant nonperturbative effects that can lift some degeneracies. We explicitly solve the cases $n=3$ and $n=4$ emitters.

Periodically driven parametric oscillators offer a convenient way to simulate classical Ising spins. When many parametric oscillators are coupled dissipatively, they can be analogous to networks of Ising spins, forming an effective coherent Ising machine (CIM) that efficiently solves computationally hard optimization problems. In the companion paper, we studied experimentally the minimal realization of a CIM, i.e. two coupled parametric oscillators [L. Bello, M. Calvanese Strinati, E. G. Dalla Torre, and A. Pe'er, Phys. Rev. Lett. 123, 083901 (2019)]. We found that the presence of an energy-conserving coupling between the oscillators can dramatically change the dynamics, leading to everlasting beats which transcend the Ising description. Here, we analyze this effect theoretically by solving numerically and, when possible, analytically the equations of motion of two parametric oscillators. Our main tools include (i) a Floquet analysis of the linear equations, (ii) a multiscale analysis based on a separation of timescales between the parametric oscillations and the beats, and (iii) the numerical identification of limit cycles and attractors. Using these tools, we fully determine the phase boundaries and critical exponents of the model, as a function of the intensity and the phase of the coupling and of the pump. Our study highlights the universal character of the phase diagram and its independence on the specific type of nonlinearity present in the system. Furthermore, we identify phases of the model with more than two attractors, possibly describing a larger spin algebra.

A three-level atom in $\mathrm{\Lambda }$ configuration is reduced to an effective two-level system, under appropriate conditions, and its $\mathcal{PT}$ symmetric properties are investigated. This effective qubit system, when subjected to a beam-splitter type of interaction, provides the scope of directly (indirectly) probing the nonclassical properties of the output (input) state. Here, we study nonclassical properties of the output state by using some well-known measures of nonclassical correlations like the measurement-induced disturbance, concurrence, and negativity. The nonclassical features are found to enhance in the $\mathcal{PT}$ symmetric (PTS) phase compared to the $\mathcal{PT}$ symmetry broken (PTB) phase. Further, the output ports of the beam splitter are subjected to different quantum noise channels, both non-Markovian, e.g., random telegraph noise as well as Markovian, e.g., phase damping and amplitude damping noise. The application of noise channels is found to decrease the degree of nonclassicality, though continuing to exhibit distinct behavior in PTS and PTB phases, with the dominant behavior appearing in the former case. Further, the results are compared with the case when dynamics is governed by a Hermitian Hamiltonian. This allows one to demarcate the contributions to nonclassicality from different types of dynamics.

Grover's algorithm is one of the most famous algorithms which explicitly demonstrates how the quantum nature can be utilized to accelerate the searching process. In this work, Grover's quantum search problem is mapped to a time-optimal control problem. Resorting to Pontryagin's minimum principle, we find that the time-optimal solution has the bang-singular-bang structure. This structure can be derived naturally, without integrating the differential equations, using the geometric control technique where Hamiltonians in Schrödinger's equation are represented as vector fields. In view of optimal control, Grover's algorithm uses the bang-bang protocol to approximate the optimal protocol with a minimized number of bang-to-bang switchings to reduce the query complexity. Our work provides a concrete example of how Pontryagin's minimum principle is connected to quantum computation, and offers insight into how a quantum algorithm can be designed.

We show that deep neural networks can be integrated into, or fully replace, the Kohn-Sham density functional theory (DFT) scheme for multielectron systems in simple harmonic oscillator and random external potentials with no feature engineering. We first show that self-consistent charge densities calculated with different exchange-correlation functionals can be used as input to an extensive deep neural network to make predictions for correlation, exchange, external, kinetic, and total energies simultaneously. Additionally, we show that one can make all of the same predictions with the external potential rather than the self-consistent charge density, which allows one to circumvent the Kohn-Sham DFT scheme altogether. We then show that a self-consistent charge density found from a nonlocal exchange-correlation functional can be used to make energy predictions for a semilocal exchange-correlation functional. Lastly, we use a deep convolutional inverse graphics network to predict the charge density given an external potential for different exchange-correlation functionals and assess the viability of the predicted charge densities. This work shows that extensive deep neural networks are generalizable and transferable given the variability of the potentials (maximum total energy range $\approx 100$ Ha) because they require no feature engineering and because they can scale to an arbitrary system size with an $O\left(N\right)$ computational cost.

We developed single-shot shaped pulses for ultrahigh (UH)-fidelity population transfer on a three-level quantum system in $\mathrm{\Lambda }$ configuration. To ensure high fidelity, we use the Lewis-Riesenfeld (L-R) method to derive a family of solutions leading to an exact transfer, where the solutions follow a single dynamical mode of the L-R invariant. Among this family, we identify a tracking solution with a single parameter to control simultaneously the fidelity of the transfer, the population of the excited state, and robustness. We define a measure of the robustness of an UH-fidelity transfer as the minimum percentile deviation on the pulse areas at which the infidelity rises above ${10}^{-4}$. The robustness of our shaped pulses is found to be superior to that of Gaussian and adiabatically optimized pulses for moderate pulse areas.

We describe a method to dispersively detect all three vector components of an external magnetic field using alkali-metal atoms based on the Voigt effect. Our method relies on measuring the linear birefringence of the radio-frequency dressed atomic medium via polarization homodyning. This gives rise to modulated polarization signals at the first and second harmonic of the dressing frequency. The vector components of the external magnetic field are mapped onto the quadratures of these harmonics. We find that our scheme can be utilized in both cold and hot atomic gases to detect such external fields in shielded and unshielded environments. In the shielded hot vapor case we achieve field sensitivities in the $\mathrm{pT}/\sqrt{\mathrm{Hz}}$ range for all three vector components, using pump-probe cycles with 125-Hz repetition rate, and limited by the short coherence time of the cell. Finally, our scheme has a simple single axis beam geometry, making it advantageous for miniature magnetic-field sensors.