We develop a general approach for calculating the characteristic function of the work distribution of quantum many-body systems in a time-varying potential, whose many-body wave function can be cast in the Slater determinant form. Our results are applicable to a wide range of systems including an ideal gas of spinless fermions in one dimension, the Tonks-Girardeau (TG) gas of hard-core bosons, as well as a one-dimensional gas of hard-core anyons. In order to illustrate the utility of our approach, we focus on the TG gas confined to an arbitrary time-dependent trapping potential. In particular, we use the determinant representation of the many-body wave function to characterized the nonequilibrium thermodynamics of the TG gas and obtain exact and computationally tractable expressions— in terms of Fredholm determinants—for the mean work, the work probability distribution function, the nonadiabaticity parameter, and the Loschmidt amplitude. When applied to a harmonically trapped TG gas, our results for the mean work and the nonadiabaticity parameter reduce to those derived previously using an alternative approach. We next propose to use periodic modulation of the trap frequency in order to drive the system to highly non-equilibrium states by taking advantage of the phenomenon of parametric resonance. Under such driving protocol, the nonadiabaticity parameter may reach large values, which indicates a large amount of irreversible work being done on the system as compared to sudden quench protocols considered previously. This scenario is realizable in ultracold atom experiments, aiding fundamental understanding of all thermodynamic properties of the system.

The collective response of an atomic ensemble is shaped by its macroscopic environment. We demonstrate this effect in the near-resonant transmission of light through a thermal rubidium vapor confined in a planar nanocavity. Our model reveals density-dependent line shifts and broadenings beyond continuous electrodynamics models that oscillate with cavity width and have been observed in recent experiments. We predict that the amplitudes of these oscillations can be controlled by coatings that modify the cavity's finesse.

Multiphoton quantum interference is the underlying principle for optical quantum information processing protocols. Indistinguishability is the key to quantum interference. Therefore, the success of many protocols in optical quantum information processing relies on the availability of photon states with a well-defined spatial and temporal mode. Photons in single spatial mode can be obtained from nonlinear processes in single-mode waveguides. For the temporal mode, the common approach is to engineer the nonlinear processes so as to achieve the required spectral properties for the generated photons. But, this approach is complicated because the spectral properties and the nonlinear interaction are often intertwined through phase-matching condition. In this paper, we study a different approach that separates the spectral control from nonlinear interaction, leading to versatile and precise engineering of the spectral properties of nonlinear parametric processes. The approach is based on an SU(1,1) nonlinear interferometer with a pulsed pump and a controllable linear spectral phase shift for precise engineering. We systematically analyze the important figures of merit such as modal purity and heralding efficiency in characterizing a photon state and use this analysis to investigate the feasibility of this interferometric approach. Specifically, we analyze in detail the requirement on the spectral phase engineering to optimize the figures of merit and apply numerical simulations to the nonlinear four-wave mixing process in dispersion-shifted fibers with a standard single-mode fiber as the phase control medium. Both modal purity and efficiency are improved simultaneously with this technique. Furthermore, a multistage nonlinear interferometer is proposed and shown to achieve more precise state engineering for near-ideal single-mode operation and near-unity efficiency. We also extend the study to the case of high pump power when the high gain is achieved in the four-wave mixing process for the spectral engineering of quantum entanglement in continuous variables. Our investigation provides an approach for precisely tailoring the spectral property of quantum light sources, especially, photon pairs can be engineered to simultaneously possess the features of high purity, high collection efficiency, high brightness, and high flexibility in wavelength and bandwidth selection.

Based on a Heisenberg equation of motion description of the feedback dynamics in quantum optics, we discuss the impact of phase noise on the excitation dynamics and provide examples in which noise itself is not detrimental but supports and enhances typical features of quantum feedback such as self-stabilization of the electronic population. We furthermore establish a connection between coherent quantum feedback and an Ornstein-Uhlenbeck-type process in quantum optics in the presence of phase noise. The interfering and time-shifted amplitudes introduce a finite memory kernel which, convoluted with a white noise process, results in a resonance fluorescence dynamics of a damped random walk.

We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincaré disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to experimentally resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.

We report on the attainment of a degenerate Fermi gas of ${}^6\mathrm{Li}$ in contact with a Bose-Einstein condensate (BEC) of ${}^{84}\mathrm{Sr}$. A degeneracy of $T/T_F=0.33\left(3\right)$ is observed with $1.6\times {10}^5{}^6\mathrm{Li}$ atoms in the two lowest-energy hyperfine states together with an almost pure BEC of $3.1\times {10}^5{}^{84}\mathrm{Sr}$ atoms. The elastic $s$-wave scattering length between ${}^6\mathrm{Li}$ and ${}^{84}\mathrm{Sr}$ is estimated to be $|a_{{}^6\mathrm{Li}{-}^{84}\mathrm{Sr}}|=(7.1_{-1.7}^{+2.6})a_0$ ($a_0$ is the Bohr radius) from measured interspecies thermalization rates in an optical dipole trap.

In classical scattering theory, the term “glory scattering” implies the divergence of the classical differential cross section that occurs as soon as the deflection function goes through zero for a nonzero value of the impact parameter. This critical effect also occurs in slow photoelectron imaging where near-threshold atomic photoionization is performed in the presence of an external static electric field. In this case, glory scattering manifests itself by the appearance of an intense peak at the center of the photoelectron momentum distribution. In the present work we examine the magnitude variation of this central peak as a function of electron energy. We experimentally study near-threshold two-photon ionization of ground state magnesium atoms, below as well as above the field-free ionization limit. It is found that, apart from its behavior of classical origin, the glory signal additionally exhibits strong oscillations and beating effects over the full spectral range of the recordings. Of particular interest are its oscillations above the zero-field limit, many aspects of which are expected to be independent of the atomic target. Our results are analyzed with the help of classical, semiclassical, and quantum mechanical calculations devoted to the hydrogenic Stark effect. It is theoretically found that these continuum glory oscillations are related to the resonantlike Stark structures appearing under certain conditions in the total photoionization cross section and implying energy quantization in the continuum. The striking outcome of the present study, however, is that both theory and experiment clearly support the connection between the energy- and static field-dependent periodicity of glory oscillations with the classical dynamics of electron motion. In particular, it is shown that the Fourier transform of the glory signal provides information on the differences between the origin-to-detector times of flight corresponding to specific pairs of classical electron trajectories.

In the framework of nonlinear spin optics, we investigate self-confined light beams in reorientational nematic liquid crystals. Using modulation theory and numerical experiments, we analyze spatial solitary waves supported by the geometric phase arising in a uniaxial when subject to a nonlinear modulation of its optic axis distribution. Spin evolution and optical reorientation in an index-homogeneous medium give rise to a longitudinally periodic, transversely inhomogeneous potential able to counteract the diffraction of a polarized bell-shaped beam, generating a spin-optical solitary wave. Spin-optical solitary waves evolve in polarization and have an oscillatory character in amplitude, size, and ellipticity.

Single- and double-electron capture processes in ${\mathrm{N}}^{5+}+{\mathrm{H}}_2$ collisions are investigated in a broad energy domain ranging from 0.25 to 150 keV/$u$. Total and partial cross sections are calculated using a three-center, two-active-electron, semiclassical nonperturbative approach. For single-electron capture cross sections the present results show an excellent agreement below 10 keV/$u$ where theoretical and experimental data are available and discriminate between them when disagreement exists. Furthermore, it is shown that the cross sections for double-electron capture into autoionizing states are particularly significant and thus contribute substantially to the total single-electron capture cross sections through postcollisional autoionization. The cross sections for double-electron capture processes into bound states of ${\mathrm{N}}^{3+}$ are also reported and show severe discrepancies with the rare available data.

We propose a state-sensitive scheme to optically detect a single molecule without a closed transition, through strong coupling to a high-$Q$ whispering-gallery-mode resonator. A background-free signal can be obtained by detecting a molecule-induced transparency in a photon bus waveguide that is critically coupled to the resonator, with a suppressed depumping rate to other molecular states by the cooperativity parameter $C$. We numerically calculate the dynamics of the molecule-resonator coupled system using Lindblad master equations, and develop analytical solutions through the evolution of quasisteady states in the weak-driving regime. Using ${\mathrm{Rb}}_2$ triplet ground-state molecules as an example, we show that high-fidelity state readout can be achieved using realistic resonator parameters. We further discuss the case of multiple molecules collectively coupled to a resonator, demonstrating near-unity detection fidelity and negligible population loss.

Based on numerically optimized real-device gates and parameters we study the performance of the phase-flip (repetition) code on a linear array of gallium arsenide (GaAs) quantum dots hosting singlet-triplet qubits. We first examine the expected performance of the code using simple error models of circuit-level and phenomenological noise, reporting, for example, a circuit-level depolarizing noise threshold of approximately $3\%$. We then perform density-matrix simulations using a maximum-likelihood and minimum-weight matching decoder to study the effect of real-device dephasing, readout error, and quasistatic as well as fast gate noise. Considering the tradeoff between qubit readout error and dephasing time ($T_2$) over measurement time, we identify a subthreshold region for the phase-flip code which lies within experimental reach.

We discuss quantum state tomography via a stepwise reconstruction of the eigenstates of the mixed states produced in experiments. Our method is tailored to the experimentally relevant class of nearly pure states, or simple mixed states, which exhibit dominant eigenstates and thus lend themselves to low-rank approximations. The developed scheme is applicable to any pure-state tomography method, promoting it to mixed-state tomography. Here, we demonstrate it with machine learning-inspired pure-state tomography based on neural-network representations of quantum states. The latter have been shown to efficiently approximate generic classes of complex (pure) states of large quantum systems. We test our method by applying it to experimental data from trapped ion experiments with four to eight qubits.

In recent experiments with ultracold atoms, both two-dimensional (2D) Chern insulators and one-dimensional topological charge pumps have been realized. Without interactions, both systems can be described by the same Hamiltonian, when some variables are being reinterpreted. In this paper, we study the relation of both models when Hubbard interactions are added, using the density-matrix renormalization-group algorithm. To this end, we express the fermionic Hofstadter model in a hybrid-space representation, and define a family of interactions, which connects 1D Hubbard charge pumps to 2D Hubbard Chern insulators. We study a three-band model at particle density $\rho =2/3$, where the topological quantization of the 1D charge pump changes from Chern number $C=2$ to $C=-1$ as the interaction strength increases. We find that the $C=-1$ phase is robust when varying the interaction terms on narrow-width cylinders. However, this phase does not extend to the limit of the 2D Hofstadter-Hubbard model, which remains in the $C=2$ phase. We discuss the existence of both topological phases for the largest cylinder circumferences that we can access numerically. We note the appearance of a ferromagnetic ground state between the strongly interacting 1D and 2D models. For this ferromagnetic state, one can understand the $C=-1$ phase from a band structure argument. Our method for measuring the Hall conductivity could similarly be realized in experiments: We compute the current response to a weak, linear potential, which is applied adiabatically. The Hall conductivity converges to integer-quantized values for large system sizes, corresponding to the system's Chern number.

We describe, realize, and experimentally investigate a method to perform physical rotations of ion chains, trapped in a segmented surface Paul trap, as a building block for large-scale quantum computational sequences. Control of trapping potentials is achieved by parametrizing electrode voltages in terms of spherical harmonic potentials. Voltage sequences that enable crystal rotations are numerically obtained by optimizing time-dependent ion positions and motional frequencies, taking into account the effect of electrical filters in our setup. We minimize rotation-induced heating by expanding the sequences into Fourier components, and optimizing the resulting parameters with a machine-learning approach. Optimized sequences rotate ${}^{40}\mathrm{Ca}^{+}$–${}^{40}\mathrm{Ca}^{+}$ crystals with axial heating rates of $\mathrm{\Delta }{\overline{n}}_{\text{com}}=0.6_{(-2)}^{(+3)}$ and $\mathrm{\Delta }{\overline{n}}_{\text{str}}=3.9\left(5\right)$ phonons per rotation for the common and stretch modes, at mode frequencies of 1.24 and 2.15 MHz. Qubit coherence loss is $0.2\left(2\right)\%$ per rotation. We also investigate rotations of mixed species crystals (${}^{40}\mathrm{Ca}^{+}$–${}^{88}\mathrm{Sr}^{+}$) and achieve unity success rate.

Braiding defects in topological stabilizer codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We prove that a universal gate set for quantum computing cannot be realized by supplementing locality-preserving logical operators with defect braiding, even in more than two dimensions. However, notwithstanding this no-go theorem, we demonstrate that higher-dimensional defect-braiding schemes have the potential to play an important role in realizing fault-tolerant quantum computing. Specifically, we present an approach to implement the full Clifford group via braiding in any code possessing twist defects on which a fermion can condense. We explore three such examples in higher-dimensional codes, specifically, in self-dual surface codes; the three-dimensional Levin-Wen fermion mode; and the checkerboard model. Finally, we show how our no-go theorems can be circumvented to provide a universal scheme in three-dimensional surface codes without magic-state distillation. Specifically, our scheme employs adaptive implementation of logical operators conditional on logical measurement outcomes to lift a combination of locality-preserving and braiding logical operators to universality.

The behavior of an electron spin interacting with a linearly polarized laser field is analyzed. In contrast to previous considerations of the problem, the initial state of the electron represents a localized wave packet, and a spatial envelope is introduced for the laser pulse along its propagation direction, which allows one to take into account the finite size of both objects. Special attention is paid to ultrashort pulses possessing a high degree of unipolarity. Within a classical treatment (both nonrelativistic and relativistic), proportionality between the change of the electron-spin projections and the electric-field area of the pulse is clearly demonstrated. We also perform calculations of the electron-spin dynamics according to the Dirac equation. Evolving the electron wave function in time, we compute the mean values of the spin operator in various forms. It is shown that the classical relativistic predictions are accurately reproduced when using the Foldy-Wouthuysen operator. The same results are obtained when using the Lorentz transformation and the nonrelativistic (Pauli) spin operator in the particle's rest frame.

We study the dynamical generation and storage of spin-squeezed states, as well as more entangled states up to macroscopic superpositions, in a system composed by a few ultracold atoms trapped in a one-dimensional optical lattice. The system, initially in the superfluid phase with each atom in a superposition of two internal states, is first dynamically entangled by atom-atom interactions and then adiabatically brought to the Mott-insulator phase with one atom per site where the quantum correlations are stored. Exact numerical diagonalization allows us to explore the structure of the stored states by looking at various correlation functions, on-site and between different sites, both at zero temperature and at finite temperature, as it could be done in an experiment with a quantum gas microscope.

Ensembles of alkali-metal or noble-gas atoms at room temperature and above are widely applied in quantum optics and metrology owing to their long-lived spins. Their collective spin states maintain nonclassical nonlocal correlations, despite the atomic thermal motion in the bulk and at the boundaries. Here we present a stochastic, fully quantum description of the effect of atomic diffusion in these systems. We employ the Bloch-Heisenberg-Langevin formalism to account for the quantum noise originating from diffusion and from various boundary conditions corresponding to typical wall coatings, thus modeling the dynamics of nonclassical spin states with spatial interatomic correlations. As examples, we apply the model to calculate spin noise spectroscopy, temporal relaxation of squeezed spin states, and the coherent coupling between two spin species in a hybrid system.

Point-source atom interferometry is a promising approach for implementing robust, high-sensitivity, rotation sensors using cold atoms. However, its scale factor, i.e., the ratio between the interferometer signal and the actual rotation rate, depends on the initial conditions of the atomic cloud, which may drift in time and result in bias instability, particularly in compact devices with short interrogation times. We present two methods to stabilize the scale factor. One relies on a model-based correction which exploits correlations between multiple features of the interferometer output and works on a single-shot basis. The other is a self-calibrating method where a known bias rotation is applied to every other measurement, requiring no prior knowledge of the underlying model but reducing the sensor bandwidth by a factor of two. We demonstrate both schemes experimentally with complete suppression of scale-factor drifts, maintaining the original rotation sensitivity and allowing for bias-free operation over several hours.

We theoretically study a system composed of a waveguide and a quantum emitter moving in a one-dimensional potential along the waveguide axis. We focus on the single-excitation subspace and treat the emitter motional degrees of freedom fully quantum mechanically. We first characterize single-photon scattering off a single moving quantum emitter, showing both direction-dependent transmission and recoil-induced reduction of the quantum emitter motional energy. We then characterize the bound states within the band gap, which display a motion-induced asymmetric phase in real space. We also demonstrate how these bound states form a continuous band with exotic dispersion relations. Finally, we study the spontaneous emission of an initially excited quantum emitter with various initial momentum distributions, finding strong deviations with respect to the static emitter counterpart both in the occupation dynamics and in the spatial distribution of the emitted photons. Our work extends the waveguide-QED toolbox by including the quantum motional degrees of freedom of emitters, whose impact on the few-photon dynamics could be harnessed for quantum technologies.