We study collective modes and superfluidity of spin-1 bosons with antiferromagnetic interactions in an optical lattice based on the time-dependent Ginzburg-Landau (TDGL) equation derived from the spin-1 Bose-Hubbard model. Specifically, we examine the stability of supercurrents in the polar phase in the vicinity of the Mott insulating phase with even filling factors. Solving the linearized TDGL equation, we obtain gapless spin-nematic modes and gapful spin-wave modes in the polar phase that arise due to the breaking of $S^2$ symmetry in spin space. Supercurrents exhibit dynamical instabilities induced by growing collective modes. In contrast to the second-order phase transition, the critical momentum for mass currents is finite at the phase boundary of the first-order superfluid-Mott insulator (SF-MI) phase transition. Furthermore, the critical momentum remains finite throughout the metastable SF phase and approaches zero towards the phase boundary, at which the metastable SF state disappears. We also study the stability of spin currents motivated by recent experiments for spinor gases. The critical momentum for spin currents is found to be zero, where a spin-nematic mode causes the dynamical instability. We investigate the origin of the zero critical momentum for spin currents and find it attributed to the fact that the polar state becomes energetically unstable even in the presence of an infinitesimal spin current. We discuss implications of the zero critical momentum for spin currents for the stability of the polar state.

We analyze the transfer function of a three-dimensional atomic Bragg beamsplitter formed by two counterpropagating pulsed Laguerre-Gaussian laser beams. Even for ultracold atomic ensembles, the transfer efficiency depends significantly on the residual velocity of the particles as well as on losses into higher diffraction orders. Additional aberrations are caused by the spatial intensity variation and wavefront curvature of the Laguerre-Gaussian laser beam envelope, studied with (3+1)-dimensional numerical simulations. The temporal pulse shape also affects the transfer efficiency significantly. Thus, we consider the practically important rectangular, Gaussian, Blackman, and hyperbolic secant pulses. For the last, we can describe the time-dependent response analytically with the Demkov-Kunike method. The experimentally observed stretching of the $\pi$-pulse time is explained from a renormalization of the simple Pendellösung frequency. Finally, we compare the analytical predictions for the velocity-dependent transfer function with effective (1+1)-dimensional numerical simulations for pulsed Laguerre-Gaussian laser beams, as well as experimental data, and find very good agreement considering a mixture of Bose-Einstein condensate and thermal cloud.

Tailoring wavelength correlations in fiber-optical sources through nonlinear phenomena could drive many quantum optics applications. However, to date, such correlations have not been explored within fiber-optical parametric oscillators (FOPO), which are now widespread wavelength-agile sources. We experimentally investigate the real-time dynamics of a synchronously pumped picosecond FOPO with a combination of statistical tools using time-stretch spectroscopy. The study of wavelength correlations allows us to unveil particular spectrotemporal dynamics and correlation patterns. Specifically, we demonstrate that combining mutual information (MI) analysis and least-squares regression with large ensembles of shot-to-shot spectra allows to efficiently track energy transfers from pump to parametric waves. In addition, we show that tuning the FOPO parameters enables the shaping of spectral correlations to a certain extent.

In this work, we develop a physically transparent Coulomb-interaction model from simplification of a general many-body theory and apply this model to study interacting electron dynamics for transient occupation and quantum coherence in both single and double quantum dots under laser irradiation. Our theory considers self-consistently the Coulomb-renormalized Rabi coupling to light by using an induced optical-depolarization field, corresponding to dynamical exchange interaction between two electrons within the same quantum dot. Meanwhile, we employ evanescent-field coupling for dynamical Coulomb interaction between two electrons in different quantum dots based on a surface-plasmon model. In particular, we explore the quantum interference between a pair of laser-induced quantum coherence in three-level quantum-dot systems, which gives rise to indirect transition of electrons for sum- and difference-frequency transient optical responses. By varying laser frequency detuning, the control of laser-dressed electronic states becomes possible and can be utilized for switching among off-state, partial, and complete on-states. This study will be useful for controlling the phase entanglement of two laser-dressed states of quantum dots, as well as for enhancing the electro-optical performance through sum- and difference-frequency transitions in many optoelectronic devices.

We study the radiation of a circular dipole nearby a subwavelength spherical particle. The circular dipole spins in a plane containing a great circle of the spherical particle (meridional plane). We derive general conditions for which radiation vanishes in any direction lying in the meridional plane, yielding directional radiation whose angular orientation can be changed by switching the handedness of the circular dipole. The radiative response (far field) of this dipole-scatterer system can be synthesized as arising from an effective electric dipole in the meridional plane and an effective magnetic dipole perpendicular to the meridional plane; both dipoles are located at the center of the sphere. We consider a nonabsorbing sphere and explore the radiative characteristics (radiation pattern, directivity, radiated power, and spin angular momentum) in which radiation is nullified along two particular axes lying in the meridional plane; particular geometrical configurations and dielectromagnetic properties of the dipole-scatterer system are given. The directional radiation and spin angular momentum patterns can be rotated $\pi \mathrm{rad}$ around the axis joining the dipole position and the center of the spherical scatterer by changing the handedness of the circular dipole, excepting for the cases of null radiation in the forward and backward directions. Our work might have implications for transferring quantum spin states to electromagnetic modes, controlling of radiation by emitters, routing of light in networks, manipulating of light propagation with metasurfaces, and sensing and locating molecules.

Laguerre-Gaussian optical sum-sideband generation via orbital angular momentum exchange has been studied analytically beyond the linearized approach. We obtain the analytical expression for the amplitudes of these signals within the semiclassical approximation. The pump power dependence of Laguerre-Gaussian sum-sideband generation is discussed, and we find that Laguerre-Gaussian sum-sideband generation can be remarkable even at low power through the satisfaction of matching conditions. The matching conditions for Laguerre-Gaussian sum-sideband generation in an optorotational system are discussed and summarized in detail, and the physical interpretation of matching conditions is discussed. The role of the topological charge value $l$ on the sum-sideband generation is studied, which exhibits a saturation effect for the peak value of the normalized amplitude and consequently limits further improvement of the Laguerre-Gaussian sum-sideband generation. Our results may find applications in Laguerre-Gaussian optical frequency comb and communications and provide a potential method for the determination of the orbital angular momentum of light fields with high topological charges.

Inside a closed many-body system undergoing the unitary evolution, a small partition of the whole system exhibits a local relaxation. If the total degrees of freedom of the whole system is a large but finite number, such a local relaxation would come across a recurrence after a certain time, namely, the dynamics of the local system suddenly appears random after a well-ordered oscillatory decay process. It is found in this paper, among a collection of N two-level systems (TLSs), the local relaxation of one TLS inside has a hierarchy structure hiding in the randomness after such a recurrence: similar recurrences appear in a periodical way, and the later recurrence brings in stronger randomness than the previous one. Both analytical and numerical results that we obtained well explains such hierarchy recurrences: the population of the local TLS (as an open system) diffuses out and regathers back periodically due to the finite-size effect of the bath [the remaining $(\mathrm{N}-1)$ TLSs]. We also find that the total correlation entropy, which sums up the entropy of all the n TLSs, approximately exhibit a monotonic increase; in contrast, the entropy of each single TLS increases and decreases from time to time, and the entropy of the whole n-body system keeps constant during the unitary evolution.

We present a state estimation scheme for spins using a modified setup of the Stern-Gerlach experiment in which a beam of neutral spin-1/2 point particles interacts with a quadrupolar magnetic field. The proposed estimation procedures, based either on a quadrant or a continuous intensity distribution detection, require a suitable initial spatial state of the beam. The statistical characterization of the estimators of the initial spin state allows us not only to associate an error to the estimated parameters, but also to define a measure for comparing estimation procedures corresponding to different Stern-Gerlach setups.

Due to the limitations of present-day quantum hardware, it is especially critical to design algorithms that make the best possible use of available resources. When simulating quantum many-body systems on a quantum computer, straightforward encodings that transform many-body Hamiltonians into qubit Hamiltonians use $N$ of the available basis states of an $N$-qubit system, whereas $2^N$ are in theory available. We explore an efficient encoding that uses the entire set of basis states, where terms in the Hamiltonian are mapped to qubit operators with a Hamiltonian that acts on the basis states in Gray code order. This encoding is applied to the commonly studied problem of finding the ground-state energy of a deuteron with a simulated variational quantum eigensolver (VQE). It is compared to a standard “one-hot” encoding, and various trade-offs that arise are analyzed. The energy distribution of VQE solutions has smaller variance than the one obtained by the one-hot encoding even in the presence of simulated hardware noise, despite an increase in the number of measurements. The reduced number of qubits and a shorter-depth variational Ansatz enables the encoding of larger problems on current-generation machines. This encoding also demonstrates improvements for simulating time evolution of the same system, producing circuits for the evolution operators with reduced depth and roughly half the number of gates compared to a one-hot encoding.

Characterizing and analyzing a system often requires learning an unknown function, such as the response of a system or the profile of a field. The standard approach is to opportunely sample the function at fiducial points and then interpolate. When the quantity of interest is embodied in physical objects accessible with quantum-enhanced measurements, it becomes relevant to investigate how to transfer this advantage from the individual sampled points to the estimation of the whole function. In this article we report the experimental quantum-enhanced function estimation of the optical response of a liquid crystal. Our results illustrate that optimizing the employment of the resources is not as straightforward as it may appear at a first glance: Quantum advantage becomes substantial only past a sampling density that depends on the interpolation method, and on the function at hand. Our results show how quantum resources should successfully be employed to access the rich information contained in continuous signals.

Noisy intermediate-scale quantum (NISQ) devices offer unique platforms to test and evaluate the behavior of quantum computing. However, validating circuits on NISQ devices is difficult due to fluctuations in the underlying noise sources and other nonreproducible behaviors that generate computational errors. Here we present a test-driven approach that decomposes a noisy, application-specific circuit into a series of bootstrapped experiments on a NISQ device. By characterizing individual subcircuits, we generate a composite noise model for the original quantum circuit. We demonstrate this approach to model applications of Greenberger-Horne-Zeilinger(GHZ)-state preparation and the Bernstein-Vazirani algorithm on a family of superconducting transmon devices. We measure the model accuracy using the total variation distance between predicted and experimental results, and we demonstrate that the composite model works well across multiple circuit instances. Our approach is shown to be computationally efficient and offers a trade-off in model complexity that can be tailored to the desired predictive accuracy.

We study, in the presence of an external electrostatic field, the interatomic interaction between two ground-state atoms coupled with vacuum electromagnetic fluctuations within the dipole coupling approximation based on the perturbation theory. We show that, up to the fourth order, the electrostatic-field-induced interatomic interaction is just the classical dipole-dipole interaction, which disagrees with the recent result from Fiscelli et al. [G. Fiscelli et al., Phys. Rev. Lett. 124, 013604 (2020)]. However, to higher orders, there exist external-field-related quantum corrections to the induced classical electrostatic dipole-dipole interaction. In the sixth order, the external field effectively modifies the atomic polarizability to give rise to a two-photon-exchange quantum correction, while in the eighth order, the external field enables an additional process of three-photon exchange which is not allowed in the absence of the external field, and this process generates an $r^{-11}$ term in the interaction potential in the far regime, where $r$ is the interatomic separation. Numerical estimations show that these external-field-related quantum corrections are much smaller than the two-photon-exchange Casimir-Polder interaction.

The Coulomb explosion of an atomic gas steered by laser-controlled time-dependent charging can be modeled by a macroscopic system of identical charges whose number is not conserved. We show that such a system can evolve in the spatially homogeneous and isotropic fashion that mimics accelerating cosmic expansions. Specifically, for a constant rate of charge production, the resulting Friedmann-Coulomb equations have a stable fixed point corresponding to an analog of de Sitter space.

We study the stability and the attractor dynamics of an elongated Bose-Einstein condensate (BEC) with dark or gray kink solitons in the presence of localized dissipation. To this end, the three-dimensional Gross–Pitaevskii equation with an additional imaginary potential is solved numerically. We analyze the suppression of the snaking instability in dependence of the dissipation strength and extract the threshold value for the stabilization of the dark soliton for experimentally realistic parameters. Below the threshold value, we observe the decay into a solitonic vortex. Above the stabilization threshold, we observe the attractor dynamics towards the dark soliton when initially starting from a gray soliton. We find that for all initial conditions the dark soliton is the unique steady-state of the system—even when starting from the BEC ground state.

Propagation of a light beam through a collisional and inhomogeneous beam of neutral particles is investigated. The light beam can be manipulated through the refractive index that is affected by the gaseous medium. Simultaneously, neutral particles experience optical dipole force and scattering force due to atomic polarizability, leading to particle trapping. The simulation results of fully coupled light-particle propagation show agreement with experimental data from the literature. The effects of particle density, detuning frequency with respect to the resonance frequency, and light intensity on the mutual guiding of light and particle beams is studied for particle beam densities below the critical density that results in single-mode operation of optical waveguides.

We propose and analyze a setup to tailor the wave functions of quantum states. Our setup is based on the quantum teleportation circuit, but instead of the usual two-mode squeezed state, a two-mode non-Gaussian entangled state is used. Using this setup, we can generate various classes of quantum states such as Schrödinger cat states, four-component cat states, superpositions of Fock states, and cubic phase states. These results demonstrate the versatility of our system as a state generator and suggest that conditioning using homodyne measurements is an important tool in the generation of the non-Gaussian states complementarily to photon number detection.

Finding the optimal estimator capable of saturating the Cramér-Rao bound is important for quantum parameter estimation. The maximum likelihood estimator (MLE) is well known to be asymptotically optimal, but it is usually nonanalytic and hence requires extensive numerical computation. On the other hand, the inversion estimator is widely used in experiments due to its simplicity, but it is usually suboptimal. Here we derive an estimator based on the linear combination of multiple inversion estimators associated with the occurrence probability of different measurement outcomes. This linear combination estimator shares the asymptotic optimality of the MLE and the simplicity of the inversion estimator and is applicable to general multi-outcome measurements, irrespective of the specific system and the noise in the system. We demonstrate this estimator for the intensity-difference measurement to a six-photon twin-Fock input state.

We analyze whether circuit QED Hamiltonians are stoquastic, focusing on systems of coupled flux qubits. We show that scalable sign-problem-free path integral Monte Carlo simulations can typically be performed for such systems. Despite this, we corroborate the recent finding [I. Ozfidan et al., Phys. Rev. Appl. 13, 034037 (2020)] that an effective, nonstoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits. We find that if the capacitive coupling is sufficiently small, this nonstoquasticity of the effective qubit Hamiltonian can be avoided if we perform a canonical transformation prior to projecting onto an effective qubit Hamiltonian. Our results shed light on the power of circuit QED Hamiltonians for the use of quantum adiabatic computation and the subtlety of finding a representation which cures the sign problem in these systems.

We present a comprehensive framework for quantum state tomography of time-bin qudits sent through a fiber. Starting from basic assumptions, we define a positive-operator valued measure which is then applied to the quantum state reconstruction problem. A realistic scenario is considered where the time uncertainty of the detector is treated as a source of experimental noise. The performance of the quantum tomography framework is examined through a series of numerical simulations conducted for different parameters describing the apparatus. The quality of state recovery, quantified by the notion of minimum fidelity, is depicted on graphs for a range of fiber lengths. Special attention is paid to relative phase reconstruction for qubits and qutrits. The results present relevant interdependence between the fiber length and the detector jitter.

Gradient-based algorithms provide the fundamental tools for the optimizations and are the essential components of many modern technologies. Theoretically, the extreme points of a cost function can be found by iterative descent(ascent) of the variable along the direction of the gradient. However, the time complexity to calculate a gradient is at a level of $O(poly\left(d\right))$ for the $d$-dimension problems. For processing the high-dimension case, especially modern machine-learning engineering with the number of optimized parameters being in billions, quantum techniques are introduced. Via the dressed amplitude encoding and nonunitary module, a gradient-based quantum optimization algorithm for general polynomials is proposed, aiming at solving the fast-convergence problems with both time and memory complexity in $O(poly(logd))$. Furthermore, numerical simulations are carried out to inspect the performance of the newly born protocol by considering the noises or perturbations during the initialization, operations, and truncations. For the potential values in high-dimension optimizations, this gradient-based quantum optimization algorithm is supposed to facilitate the polynomial optimizations, being a subroutine for future practical quantum computers.