We investigate the dimension of the phase-space attractor of a quantum chaotic many-body ratchet in the mean-field limit. Specifically, we explore a driven Bose-Einstein condensate in three distinct dynamical regimes—Rabi oscillations, chaos, and self-trapping regimes—and for each of them we calculate the correlation dimension. For the ground state of the ratchet formed by a system of field-free noninteracting particles, we find four distinct pockets of chaotic dynamics throughout these regimes. We show that a measurement of local density in each of the dynamical regimes has an attractor characterized by a higher fractal dimension, $D_R=2.59\pm 0.01$, $D_C=3.93\pm 0.04$, and $D_S=3.05\pm 0.05$, compared to the global measure of current, $D_R=2.07\pm 0.02$, $D_C=2.96\pm 0.05$, and $D_S=2.30\pm 0.02$. The deviation between local and global measurements of the attractor's dimension corresponds to an increase towards higher condensate depletion, which remains constant for long time scales in both Rabi and chaotic regimes. The depletion is found to scale polynomially with particle number $N$, namely, as $N^{\beta }$ with ${\beta }_R=0.51\pm 0.004$ and ${\beta }_C=0.18\pm 0.004$ for the two regimes. Thus, we find a strong deviation from the mean-field results, especially in the chaotic regime of the quantum ratchet. The ratchet also reveals quantum revivals in the Rabi and self-trapping regimes but not in the chaotic regime, with revival times scaling linearly in particle number for Rabi dynamics. Based on the obtained results, we outline pathways for the identification and characterization of emergent phenomena in driven many-body systems. This includes the identification of many-body localization from the many-body measures of the system, the influence of entanglement on the rate of the convergence to the mean-field limit, and the establishment of a polynomial scaling of the Ehrenfest time at which the mean-field description fails to describe the dynamics of the system.

Labouvie et al. [Phys. Rev. Lett. 116, 235302 (2016)] have described an experiment with a weakly interacting Bose-Einstein condensate trapped in a one-dimensional optical lattice with localized loss created by a focused electron beam. We show that by setting suitable initial currents between neighboring sites, it is possible to create $\mathcal{PT}$-symmetric quasistationary and $\mathcal{PT}$-symmetry-broken decaying states in an embedded two-mode subsystem. This subsystem exhibits gain provided by the coupling to the reservoir sites and localized loss due to the electron beam and shows the same dynamics as a non-Hermitian two-mode system with symmetric real and antisymmetric imaginary time-independent potentials, except for a proportionality factor in the chemical potential. We also show that there are three other equivalent scenarios and that the presence of a localized loss term significantly reduces the size of the condensate required for the realization.

Coupled $XY$ model systems consisting of three-dimensional (3D) systems with disordered interlayer physics are of significant theoretical interest. We realize a set of coupled quasi-2D layers of ${}^{87}\mathrm{Rb}$ in the presence of disordered interlayer coupling. This is achieved with our high bandwidth arbitrary optical lattice to obviate restrictions on the dimensionality of disorder with speckle-generated optical fields. We identify phase crossover regions compatible with the existence of a pair of intermediate Griffiths phases between a thermal state and the emergence of bulk 3D superfluidity.

The absence of a characteristic momentum scale in the pseudopotential description of atomic interactions in ultracold (two-component Fermi) gases is known to lead to divergences in perturbation theory. Here we show that they also plague the calculation of the dynamics of the total energy following a quantum quench. A procedure to remove the divergences is devised, which provides finite answers for the time evolution of the total energy after a quench in which the interaction strength is ramped up according to an arbitrary protocol. An important result of this analysis is the time evolution of the asymptotic tail of the momentum distribution (related to Tan's contact) to leading order in the scattering length. Explicit expressions for the dynamics of the total energy and the contact for a linear interaction ramp are obtained, as a function of the interaction ramp time in the crossover from the sudden quench to the adiabatic limit. In the sudden quench limit, the contact, following a rapid oscillation, reaches a stationary value which is different from the equilibrium one. In the adiabatic limit, the contact grows quadratically in time and later saturates to the equilibrium value for the final value of the scattering length.

We show that the realization of synthetic magnetic fields via light-matter coupling in the $\mathrm{\Lambda }$ scheme implements a natural geometrical construction of magnetic fields, namely, as the pullback of the area element of the sphere to Euclidean space via certain maps. For suitable maps, this construction generates linked and knotted magnetic fields, and the synthetic realization amounts to the identification of the map with the ratio of two Rabi frequencies which represent the coupling of the internal energy levels of an ultracold atom. We consider examples of maps which can be physically realized in terms of Rabi frequencies and which lead to linked and knotted synthetic magnetic fields acting on the neutral atomic gas. We also show that the ground state of the Bose-Einstein condensate may inherit the topological properties of the synthetic gauge field, with linked and knotted vortex lines appearing in some cases.

We describe vacuum fluctuations and photon-field correlations in interacting quantum mechanical light-matter systems by generalizing the application of mixed quantum classical dynamics techniques. We employ the multitrajectory implementation of Ehrenfest mean-field theory, traditionally developed for electron-nuclear problems, to simulate the spontaneous emission of radiation in a model quantum electrodynamical cavity-bound atomic system. We investigate the performance of this approach in capturing the dynamics of spontaneous emission from the perspective of both the atomic system and the cavity photon field through a detailed comparison with exact benchmark quantum mechanical observables and correlation functions. By properly accounting for the quantum statistics of the vacuum field, while using mixed quantum classical (mean-field) trajectories to describe the evolution, we identify a surprisingly accurate and promising route towards describing quantum effects in realistic correlated light-matter systems.

We experimentally demonstrate the emergence of an azimuthally polarized vectorial vortex beam with a phase singularity upon Brewster reflection of focused circularly polarized light from a dielectric substrate. The effect originates from the polarizing properties of the Fresnel reflection coefficients described in Brewster's law. An astonishing consequence of this effect is that the reflected field's Cartesian components acquire local phase singularities at Brewster's angle. Our observations are crucial for polarization microscopy and open avenues for the generation of exotic states of light based on spin-to-orbit coupling, without the need for sophisticated optical elements.

The analysis of single-mode photon fluctuations and their counting statistics at the superradiant phase transition is presented. The study concerns the equilibrium Dicke model in a regime where the Rabi frequency, related to a coupling of the photon mode with a finite-number qubit environment, plays the role of the transition's control parameter. We use the effective Matsubara action formalism based on the representation of Pauli operators as bilinear forms with complex and Majorana fermions. Then, we address fluctuations of superradiant order parameter and quasiparticles. The average photon number, the fluctuational Ginzburg-Levanyuk region of the phase transition, and Fano factor are evaluated. We determine the cumulant-generating function which describes a full counting statistics of equilibrium photon number. Exact numerical simulation of the superradiant transition demonstrates quantitative agreement with analytical calculations.

Recently, based on some quantum states which are locally irreducible in all bipartitions, strong quantum nonlocality has been presented by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)]. However, the remaining questions are whether a set of quantum states can reveal strong quantum nonlocality when these states are locally irreducible in all tripartitions or more multipartitions and how to construct strong nonlocality of orthogonal product states in more than tripartite quantum systems. Here we present a general definition of strong quantum nonlocality based on the local irreducibility. Then, using a $3\otimes 3\otimes 3$ quantum system as an example, we show three sets of locally indistinguishable orthogonal product states to explain the general definition of strong quantum nonlocality. Furthermore, in $3\otimes 3\otimes 3\otimes 3$, we construct a set of strong nonlocality of orthogonal product states; these states do not form a complete basis. Our results demonstrate the phenomenon of strong nonlocality without entanglement for the multipartite quantum systems.

The ability of an eavesdropper (Eve) to perform an intercept-resend attack on a free-space quantum-key-distribution (QKD) receiver by precisely controlling the incidence angle of an attack laser has been previously demonstrated. However, such an attack could be ineffective in the presence of atmospheric turbulence due to beam wander and spatial mode aberrations induced by the air's varying index of refraction. We experimentally investigate the impact turbulence has on Eve's attack on a free-space polarization-encoding QKD receiver by emulating atmospheric turbulence with a spatial light modulator. Our results identify how well Eve would need to compensate for turbulence to perform a successful attack by either reducing her distance to the receiver or using beam wavefront correction via adaptive optics. Furthermore, we use an entanglement-breaking scheme to find a theoretical limit on the turbulence strength that hinders Eve's attack.

Quantum key distribution (QKD) offers a secret way to share keys between legitimate users which is guaranteed by the law of quantum mechanics. Most recently, the limitation of transmission distance without quantum repeaters was broken through by twin-field QKD [M. Lucamarini et al., Nature (London) 557, 400 (2018)]. Based on its main idea, sending or not-sending (SNS) QKD protocol was proposed [X. B. Wang et al. Phys. Rev. A 98, 062323 (2018)], which filled the remaining security loopholes and can tolerate large misalignment errors. In this paper, we give a more general model for SNS QKD, where two legitimate users, Alice and Bob, can possess asymmetric quantum channels. By applying the method present in the paper, the legitimate users can achieve dramatically increased key generation rates and transmission distances compared with compensating the channel asymmetry and utilizing the original symmetric protocol. Therefore, our present paper represents a further step along the progress of practical QKD.

We report a measurement of the valence orbital momentum profiles of tetrabromomethane (${\mathrm{CBr}}_4$) using symmetric noncoplanar $(e,2e)$ experiments at the impact energies of about 600 and 1200 eV. The experimental momentum profiles for the individual orbitals $5t_1, 13t_2, 5e, 12t_2$, and $9a_1$ and the branching ratio of $5t_1$ to $13t_2$ and $5e$ to $13t_2$ are obtained and compared with two kinds of calculations under the plane-wave impulse approximation. One is theoretical momentum profiles that have been calculated at the equilibrium geometry, the other is those that involve vibrational effects using a thermal sampling molecular dynamics method. The calculations considering molecular vibrations are in better agreement with experiment than the equilibrium geometry calculations, indicating the important role of nuclear motions on the valence orbital electronic structures of ${\mathrm{CBr}}_4$. The distorted-wave effects are observed in the experimental momentum profiles of $5t_1, 5e$, and $12t_2$ which display dynamic dependencies on the impact energies. A multicenter interference or bond oscillation effect has been observed from the momentum profile ratios of $5t_1$ to $13t_2$ and $5e$ to $13t_2$ which has direct information about the bond length of a molecule.

An important physical process unique to neutral-ion systems is the charge-transfer reaction. Here, we present measurements of and models for charge-transfer processes between cotrapped ultracold Ca atoms and Yb ions under well-controlled conditions. The theoretical analysis suggests the existence of three reaction mechanisms when lasers from a magneto-optical trap and an additional catalyst laser are present. We show that the near-degeneracy of the excited $\mathrm{Ca}\left({}^{1}P_1\right)+{\mathrm{Yb}}^{+}\left({}^{2}S\right)$ and ${\mathrm{Ca}}^{+}\left({}^{2}S\right)+\mathrm{Yb}\left({}^{3}D_2\right)$ asymptotic limits leads to large charge-transfer rate coefficients that can be controlled by changing the frequency of the catalyst laser and the ion temperature. Our model agrees with experimental rate-coefficient measurements between 50 mK and 1 K, with and without the catalyst laser, using just a single free parameter.

The Stark problem in quantum-confined geometries is challenging in high fields. In particular, the localization of electrons near sample boundaries is hard to accurately capture in perturbation methods. We analyze the problem for spherical quantum dots using a combination of numerical diagonalization and analytical perturbation approaches. Closed-form expressions for polarizabilities and hyperpolarizabilities of arbitrary states are obtained. In addition, a hypergeometric resummation ansatz replicating the correct high-field behavior is constructed. We find that a simple resummation approach is superior to even 14th-order perturbation series.

The dynamical properties of a one-dimensional system of two and three bosons escaping from an open potential well are studied in terms of the momentum distributions of particles. In the case of a two-boson system, it is shown that the single- and two-particle momentum distributions undergo a specific transition as the interaction strength is tuned through the point where tunneling switches from the pair tunneling to the sequential one. Characteristic features in the momentum spectra can be used to quantitatively determine the participation of specific decay processes. A corresponding analysis is also performed for the three-boson system, showing a scheme for generalizations to higher particle numbers. For completeness, the time-dependent Tan contact of the system is also examined and its dynamics is found to undergo a similar transition. The results provide insight into the dynamics of decaying few-body systems and offer potential interest for experimental research.

A uniform or periodic dielectric slab can serve as an optical waveguide for which guided modes are important, and it can also be used as a diffraction structure for which resonant modes with complex frequencies are relevant. Guided modes are normally studied below the lightline where they exist continuously and emerge from points on the lightline, but isolated guided modes may exist above the lightline and they are the so-called bound states in the continuum. Resonant modes are usually studied above the lightline (defined using the real part of the complex frequency), but they are not connected to the guided modes on the lightline. In this work, through analytic and numerical calculations for uniform and periodic slabs, we establish an indirect link between the resonant and guided modes. It is shown that as the (Bloch) wave number is increased, a resonant mode continues its existence below the lightline, until it reaches its end at an exceptional point (EP) where a pair of improper modes emerge, and one branch of improper modes eventually approaches the lightline at the starting point of a guided mode. Leaky modes with a real frequency and a complex (Bloch) wave number (propagation constant) are also related to the improper modes. They emerge at EPs in eigenvalue formulations where the frequency is regarded as a parameter. Our study is based on a non-Hermitian eigenvalue formulation that includes resonant, improper, and leaky modes, and provides a complete picture for different kinds of eigenmodes on uniform and periodic slabs.

High-order harmonic generation (HHG) in imperfect crystals, where the disorder is modeled by random shifts of the ionic positions, is studied using time-dependent density-functional theory. When irradiated by midinfrared laser pulses, the disorder-free system produces HHG spectra with two plateaus. Compared with the disorder-free system, disordered systems are found to emit suppressed harmonics in the first plateau region and enhanced harmonics in the second plateau region. The suppression of harmonics in the first plateau becomes less pronounced when decreasing the displacement of the nuclei, while the enhancement in the second plateau region is insensitive to the range of the ionic displacement. We have confirmed these findings for many different disordered sample systems and for different laser field strengths. The increase of the HHG signals in the second plateau region is proposed to stem from a change of the dynamics in the system, evidenced by the transition matrix elements between the field-free Kohn-Sham orbitals. In addition, a time-frequency profile of HHG spectra shows that the emission of harmonics is less regular in the time domain for a disordered system than for the disorder-free system.

Electron-ion coincidence experimental data obtained following argon $1s$ photoionization are reported. Slow photoelectrons were measured in coincidence with ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}^{2+}$ ions, and the $\beta$ angular distribution parameter was obtained. The measured beta parameter for the ${\mathrm{Ar}}^{2+}$-photoelectron coincidence measurements shows a significant deviation from the $\beta =2$ expected value. With the support of a quantum mechanical theory of post-collision interaction (PCI) which goes beyond the standard model, we attribute this deviation to angular-momentum exchange due to the interaction of the photoelectron with the Auger electron, while the role of the residual ion is negligible. The main mechanism of angular-momentum transfer and its effect on the asymmetry parameter $\beta$ near the photoionization threshold are considered.

Recently, two independent experiments reported the observation of long-lived polarons in a Bose-Einstein condensate, providing an excellent setting to study the generic scenario of a mobile impurity interacting with a quantum reservoir. Here we expand the experimental analysis by disentangling the effects of trap inhomogeneities and the many-body continuum in one of these experiments. This makes it possible to extract the energy of the polaron at a well-defined density as a function of the interaction strength. Comparisons with quantum Monte Carlo as well as diagrammatic calculations show good agreement, and provide a more detailed picture of the polaron properties at stronger interactions than previously possible. Moreover, we develop a semiclassical theory for the motional dynamics and three-body loss of the polarons, which partly explains a previously unresolved discrepancy between theory and experimental observations for repulsive interactions. Finally, we utilize quantum Monte Carlo calculations to demonstrate that the findings reported in the two experiments are consistent with each other.

Indirect spin-spin interactions between nuclei bound in a molecule are well known in nuclear magnetic resonance, but such interactions between unbound atoms are less well studied and are often assumed to be zero. We present a precision calculation of this interaction between ${}^{129}\mathrm{Xe}$ and ${}^3\mathrm{He}$ nuclei in a gas. Relativistic, state-of-the-art electronic structure theory is used to compute the scalar coupling constant $J\left(R\right)$ and the interatomic potential energy function $V\left(R\right)$ as functions of the Xe-He internuclear distance $R$. Using virial expansion we find the nuclear spin enhancement factor $\kappa =-0.0105\pm 0.0015$, in excellent agreement with recent experiments. This interaction is particularly important for precision measurements using nuclear spin comagnetometers.