We test ideas put forward, e.g., by Żukowski et al. [M. Żukowski et al., Phys. Rev. A 95, 042113 (2017)], which suggest that using rates in quantum optics can lead to better indicators of nonclassicality for states of quantum optical fields with undefined photon numbers. By rate we mean the ratio of registered photons in a given detector to the total number of detected photons in all detectors in a run of the experiment. For the Hong-Ou-Mandel effect for parametric down-conversion fields, we show that by using two detector correlation functions, which are defined in terms of averages of products of measured rates, rather than usual intensities, one can observe nonclassical visibilities beyond $1/2$ for significantly higher pump rates. At such rates we already have the partially stimulated emission, which leads to significant amplitudes for multiple pairs production, still the approach allows us to clearly see the nonclassical dip. We consider both the perfect and imperfect detection efficiency.

We propose a framework for the systematic and quantitative generalization of Bell's theorem using causal networks. We first consider the multiobjective optimization problem of matching observed data while minimizing the causal effect of nonlocal variables and prove an inequality for the optimal region that both strengthens and generalizes Bell's theorem. To solve the optimization problem (rather than simply bound it), we develop a genetic algorithm treating as individuals causal networks. By applying our algorithm to a photonic Bell experiment, we demonstrate the trade-off between the quantitative relaxation of one or more local causality assumptions and the ability of data to match quantum correlations.

We study the relation between quantum fluctuations and the significant enhancement of the performance of quantum annealing in a mean-field Hamiltonian. First-order quantum phase transitions were shown to be reduced to second order by antiferromagnetic transverse interactions in a mean-field-type many-body-interacting Ising spin system in a transverse field, which means an exponential speedup of quantum annealing by adiabatic quantum computation. We investigate if and how quantum effects manifest themselves around these first- and second-order phase transitions to understand if the antiferromagnetic transverse interactions appended to the conventional transverse-field Ising model induce notable quantum effects. By measuring the proximity of the semiclassical spin-coherent state to the true ground state as well as the magnitude of the concurrence representing entanglement, we conclude that significant quantum fluctuations exist around second-order transitions, whereas quantum effects are much less prominent at first-order transitions. Although the location of the transition point can be predicted by the classical picture, system properties near the transition need quantum-mechanical descriptions for a second-order transition but not necessarily for first order. It is also found that quantum fluctuations are large within the ferromagnetic phase after a second-order transition from the paramagnetic phase. These results suggest that the antiferromagnetic transverse interactions induce marked quantum effects, and this fact would be related to closely to the significant enhancement of the performance of quantum annealing.

We examine the moment-reconstruction performance of both the homodyne and heterodyne (double-homodyne) measurement schemes for arbitrary quantum states and introduce moment estimators that optimize the respective schemes for any given data. In the large-data limit, these estimators are as efficient as the maximum-likelihood estimators. We then illustrate the superiority of the heterodyne measurement for the reconstruction of the first and second moments by analyzing Gaussian states and many other significant nonclassical states. Finally, we present an extension of our theories to two-mode sources, which can be straightforwardly generalized to all other multimode sources.

Strong-field quantum-state control is investigated, taking advantage of the full—amplitude and phase—characterization of the interaction between matter and intense ultrashort pulses via transient-absorption spectroscopy. As an example, we apply the method to a nondegenerate $V$-type three-level system modeling atomic Rb, and use a sequence of intense delayed pulses, whose parameters are tailored to steer the system into a desired quantum state. We show how to experimentally enable this optimization by retrieving all quantum features of the light-matter interaction from observable spectra. This provides a full characterization of the action of strong fields on the atomic system, including the dependence upon possibly unknown pulse properties and atomic structures. Precision and robustness of the scheme are tested, in the presence of surrounding atomic levels influencing the system's dynamics.

Most previous studies of high-order-harmonic generation have focused on the regime beyond the ionization threshold; the dynamical origin of below- and near-threshold harmonics, particularly for the molecular systems, is less understood and largely unexplored. Here, we report a self-interaction free time-dependent density-functional-theory study along with an extended semiclassical study for the nonperturbative probing of the dynamical origin of below- and near-threshold harmonic generation of the ${\mathrm{H}}_2$ molecule in an intense near-infrared laser field. Our approach allows an accurate study of the electron trajectories as a function of energy, time, and position for below-, near-, and above-threshold harmonics for electrons departing initially from each of the individual hydrogen cores of the ${\mathrm{H}}_2$ molecule. We discover that short trajectories are multiphoton dominated and can have multiple returns for below-threshold harmonics, and excited-state resonances can have significant effects on the generation of neighboring below-threshold harmonics. Furthermore, we find that the electron dynamics for below-threshold long, short, and resonant trajectories differ greatly depending upon which hydrogen core (left or right) the electron was released from initially. An intuitive and appealing picture of near- and below-threshold harmonic generation discovered in our study can give guidance to future experiments in this forefront area of ultrafast atomic, molecular, and optical physics.

We discuss the emergence of $p$-wave superfluidity of identical atomic fermions in a two-dimensional optical lattice. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices the scattering amplitude is strongly reduced compared to free space due to a small overlap of wave functions of fermions sitting in the neighboring lattice sites, which suppresses the $p$-wave superfluidity. However, for moderate lattice depths the enhancement of the density of states can compensate the decrease of the scattering amplitude. Moreover, the lattice setup significantly reduces inelastic collisional losses, which allows one to get closer to a $p$-wave Feshbach resonance. This opens possibilities to obtain the topological $p_x+i{p}_y$ superfluid phase, especially in the recently proposed subwavelength lattices. We demonstrate this for the two-dimensional version of the Kronig-Penney model allowing a transparent physical analysis.

We consider a system with spin-orbit coupling and derive equations of motion which include the effects of Berry curvatures. We apply these equations to investigate the dynamics of particles with equal Rashba-Dresselhaus spin-orbit coupling in one dimension. In our derivation, the adiabatic transformation is performed first and leads to quantum Heisenberg equations of motion for momentum and position operators. These equations explicitly contain position-space, momentum-space, and phase-space Berry curvature terms. Subsequently, we perform the semiclassical approximation and obtain the semiclassical equations of motion. Taking the low-Berry-curvature limit results in equations that can be directly compared to previous results for the motion of wave packets. Finally, we show that in the semiclassical regime, the effective mass of the equal Rashba-Dresselhaus spin-orbit-coupled system can be viewed as a direct effect of the phase-space Berry curvature.

A microscopic configuration-interaction (CI) methodology is introduced to enable bottom-up Schrödinger-equation emulation of unconventional superconductivity in ultracold optical traps. We illustrate the method by exploring the properties of ${}^6\mathrm{Li}$ atoms in a single square plaquette in the hole-pairing regime and by analyzing the entanglement (symmetry preserving) and disentanglement physics (via symmetry breaking, associated with the separation of charge and spin density waves) of two coupled plaquettes in the same regime. The single-occupancy resonating valence bond states contribute only partially to the exact many-body solutions and the CI results map onto a Hubbard Hamiltonian, but not onto the double-occupancy-excluding $t-J$ one. For the double-plaquette case, effects brought about by breaking the symmetry between two weakly interacting plaquettes, either by distorting or by tilting and detuning one of the plaquettes with respect to the other, as well as spectral changes caused by increased coupling between the two plaquettes, are explored.

We analyze numerically the formation and the subsequent dynamics of two-dimensional matter wave dark solitons in a Thomas-Fermi rubidium condensate using various techniques. An initially imprinted sharp phase gradient leads to the dynamical formation of a stationary soliton as well as very shallow gray solitons, whereas a smooth gradient only creates gray solitons. The depth and hence, the velocity of the soliton is provided by the spatial width of the phase gradient, and it also strongly influences the snake-instability dynamics of the two-dimensional solitons. The vortex dipoles stemming from the unstable soliton exhibit rich dynamics. Notably, the annihilation of a vortex dipole via a transient dark lump or a vortexonium state, the exchange of vortices between either a pair of vortex dipoles or a vortex dipole and a single vortex, and so on. For sufficiently large width of the initial phase gradient, the solitons may decay directly into vortexoniums instead of vortex pairs, and also the decay rate is augmented. Later, we discuss alternative techniques to generate dark solitons, which involve a Gaussian potential barrier and time-dependent interactions, both linear and periodic. The properties of the solitons can be controlled by tuning the amplitude or the width of the potential barrier. In the linear case, the number of solitons and their depths are determined by the quench time of the interactions. For the periodic modulation, a transient soliton lattice emerges with its periodicity depending on the modulation frequency, through a wave number selection governed by the local Bogoliubov spectrum. Interestingly, for sufficiently low barrier potential, both Faraday pattern and soliton lattice coexist. The snake instability dynamics of the soliton lattice is characteristically modified if the Faraday pattern is present.

We propose that a tunable generalized three-dimensional Hofstadter Hamiltonian can be realized by engineering the Raman-assisted hopping of ultracold atoms in a cubic optical lattice. The Hamiltonian describes a periodic lattice system under artificial magnetic fluxes in three dimensions. For certain hopping configurations, the bulk bands can have Weyl points and nodal loops, respectively, allowing the study of both the two nodal semimetal states within this system. Furthermore, we illustrate that with proper rational fluxes and hopping parameters, the system can exhibit the three-dimensional quantum Hall effect when the Fermi level lies in the band gaps, which is topologically characterized by one or two nonzero Chern numbers. Our proposed optical-lattice system provides a promising platform for exploring various exotic topological phases in three dimensions.

We describe the coupling of moving atoms to a one-dimensional photonic waveguide in the regime where the atomic velocities are comparable to the effective speed of light. Such conditions could be achieved, for example, in photonic crystals or coupled resonator arrays, where the maximal photonic group velocity is significantly reduced compared to free space. In this case, the interplay between a velocity-induced directionality and the emergence of new divergencies in the photonic density of states gives rise to a range of novel phenomena and nonperturbative effects in the emission of photons and the resulting photon-mediated interactions between moving atoms. We show that apart from potential implementations with optical waveguides, Rydberg atoms flying above a coupled array of superconducting microwave resonators provide a versatile platform for exploring this new regime of atom-light interactions under experimentally accessible conditions.

We present a theoretical study of the resonance fluorescence of a four-level double-$\mathsf{V}$-type quantum emitter near a plasmonic nanostructure. The quantum system interacts with two orthogonal circularly polarized laser fields with the same frequency and intensity, but with different phases. For the plasmonic nanostructure we consider a two-dimensional array of metal-coated dielectric nanospheres. We show that the presence of the plasmonic nanostructure leads to strong modification of both the resonance fluorescence spectrum and the transition from antibunching to bunching for the fluorescent photons. In addition, we show that both the resonance fluorescence spectrum and the second-order correlation function are strongly phase-dependent so that the relative phase of laser fields can be used for the efficient control of the resonance fluorescence characteristics. The results are explained by using a dressed-state picture.

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold Rydberg gases, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, nonequilibrium setting of cavity QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability, a foundational and patently nonequilibrium model of cavity QED, the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by making new connections between traditional techniques from many-body physics (functional integrals) and quantum optics (the system-size expansion). To lowest order in a controlled expansion—organized around the experimentally relevant limit of weak interactions—the full quantum dynamics reduces to nonequilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, revealing that canonical behavior associated with the Ising model manifests readily in simple experimental observables.

We show that the coherent forward scattering (CFS) interference peak amplitude sharply jumps from zero to a finite value upon crossing a metal-insulator transition. Extensive numerical simulations reveal that the CFS peak contrast obeys the one-parameter scaling hypothesis and gives access to the critical exponents of the transition. We also discover that the critical CFS peak directly controls the spectral compressibility at the transition where eigenfunctions are multifractal, and we demonstrate the universality of this property with respect to various types of disorder.

Local realism in recent experiments is excluded on condition of freedom or randomness of choice combined with no signaling between observers by implementations of simple quantum models. Both no signaling and the underlying quantum model can be directly checked by analysis of experimental data. For particular tests performed on the data, it is shown that two of these experiments give the probability of the data under no-signaling (or choice independence in one of them) hypothesis at the level of 5%, accounting for the look-elsewhere effect, moderately suggesting that no signaling is violated with 95% confidence. On the other hand, the data from the two other experiments violate the assumption of the simple quantum model. Further experiments are necessary to clarify these issues and freedom and randomness of choice.

The security analysis of quantum key distribution is difficult to perform when there is efficiency mismatch between various threshold detectors involved in an experimental setup. Even the verification that the device actually performs in the quantum domain, referred to as the task of entanglement verification, is hard to perform. In this article we provide such an entanglement-verification method for characterized detection-efficiency mismatch. Our method does not rely on a cutoff of photon numbers in the optical signal. It can be applied independently of the degrees of freedom involved, thus covering, for example, efficiency mismatch in polarization and time-bin modes, but also in spatial modes. The evaluation of typical experimental scenarios suggests that an increase of detection-efficiency mismatch will drive the performance of a given setup out of the quantum domain.

Bound secret information is classical information that contains secrecy but from which secrecy cannot be extracted. The existence of bound secrecy has been conjectured but is currently unproven, and in this work we provide analytical and numerical evidence for its existence. Specifically, we consider two-way postprocessing protocols in prepare-and-measure quantum key distribution based on the well-known six-state signal states. In terms of the quantum bit-error rate $Q$ of the classical data, such protocols currently exist for $Q<\frac{5-\sqrt{5}}{10}\approx 27.6\%$. On the other hand, for $Q\ge \frac{1}{3}$ no such protocol can exist as the observed data are compatible with an intercept-resend attack. This leaves the interesting question of whether successful protocols exist in the interval $\frac{5-\sqrt{5}}{10}\le Q<\frac{1}{3}$. Previous work has shown that a necessary condition for the existence of two-way postprocessing protocols for distilling secret keys is breaking the symmetric extendability of the underlying quantum state shared by Alice and Bob. Using this result, it has been proven that symmetric extendability can be broken up to the $27.6\%$ lower bound using the advantage distillation protocol. In this work, we first show that to break symmetric extendability it is sufficient to consider a generalized form of advantage distillation consisting of one round of postselection by Bob on a block of his data. We then provide evidence that such generalized protocols cannot break symmetric extendability beyond $27.6\%$. We thus have evidence to believe that $27.6\%$ is an upper bound on two-way postprocessing and that the interval $\frac{5-\sqrt{5}}{10}\le Q<\frac{1}{3}$ is a domain of bound secrecy.