The strong-field approximation (SFA) is a widely used theoretical framework that describes the process of high-order harmonic generation of atoms and molecules. Here, we propose a generalization of the dipole SFA towards weakly relativistic contributions to the laser-electron interaction. These weakly relativistic contributions are closely related to the spatial structure of the light field and imply a correction of the relativistic order $1/c$. Within this generalized nondipole SFA (GN-SFA), we demonstrate how to obtain explicit results and discuss their physical aspects. This approach enables one to investigate the nondipole effects of linear polarized plane waves as well as the influence of structured light fields, such as twisted light, that have not yet been captured by the currently available models. In order to utilize our generalized nondipole SFA, we consider a linearly polarized plane wave and demonstrate the decrease of the harmonic yield that is directly related to the nondipole effects of the laser field. Furthermore, we discuss the GN-SFA with regard to other nondipole SFA approaches by determining their physical and mathematical context. Finally, the GN-SFA is a powerful theoretical framework that extends the nonrelativistic SFA rigorously to the weakly relativistic regime and therefore will be a useful model for further theoretical investigations.

Efficient measures to determine the similarity of quantum states, such as the fidelity metric, have been widely studied. In this paper, we address the problem of defining a similarity measure for quantum operations that can be efficiently estimated. Given two quantum operations, $U_1$ and $U_2$, represented in their circuit forms, we first develop a quantum sampling circuit to estimate the normalized Schatten 2-norm of their difference ($\parallel U_1-U_2{\parallel }_{S_2}$) with precision $\epsilon$, using only one clean qubit and one classical random variable. We prove a $\text{Poly}\left(\frac{1}{\epsilon }\right)$ upper bound on the sample complexity, which is independent of the size of the quantum system. We then show that such a similarity metric is directly related to a functional definition of similarity of unitary operations using the conventional fidelity metric of quantum states ($\mathcal{F}$): If $\parallel U_1-U_2{\parallel }_{S_2}$ is sufficiently small (e.g., $\le \frac{\epsilon }{1+\sqrt{2(1/\delta -1)}}$) then the fidelity of states obtained by processing the same randomly and uniformly picked pure state $|\psi \rangle$ is as high as needed $[\mathcal{F}(U_1|\psi \rangle ,U_2|\psi \rangle )\ge 1-\epsilon ]$ with probability exceeding $1-\delta$. We provide example applications of this efficient similarity metric estimation framework to quantum circuit learning tasks, such as finding the square root of a given unitary operation.

We present a hydrodynamic model of ultracold, but not yet quantum condensed, dipolar bosonic gases. Such systems present both $s$-wave and dipolar scattering, the latter of which results in anisotropic transport tensors of thermal conductivity and viscosity. This paper presents an analytic derivation of the viscosity tensor coefficients, utilizing the methods established by Wang and Bohn [R. R. W. Wang and J. L. Bohn, Phys. Rev. A 106, 023319 (2022)], where the thermal conductivities were derived. Taken together, these transport tensors then permit a comprehensive description of hydrodynamics that is now embellished with dipolar anisotropy. An analysis of attenuation in linear waves illustrates the effect of this anisotropy in dipolar fluids, where we find a clear dependence on the dipole orientation relative to the direction of wave propagation.

Quantum simulation of the $XXZ$ model with a two-component Bose- or Fermi-Hubbard model based on a Mott insulator background has been widely used in the investigations of quantum magnetism with ultracold neutral atoms. In most cases, the diagonal spin-spin interaction is always accompanied by a large spin-exchange interaction which hinders the formation of long-range magnetic order at low temperature. Here, we show that the spin-exchange interaction can be strongly reduced in a Mott insulator of paired atoms, while the diagonal spin-spin interaction remains unaffected. Thus, the effective magnetic models become the exact quantum Ising models in a one-dimensional (1D) or two-dimensional (2D) lattice. Meanwhile, we analyzed an experimentally achievable three-component Fermi-Hubbard model of ${}^6\mathrm{Li}$ with two hyperfine levels of atoms paired in the lattice. We find the long-range antiferromagnetism of such a three-component Fermi-Hubbard model can be much stronger than that of a typical two-component Fermi-Hubbard model at low temperature. Our results may be useful for experimental investigations of the quantum phase transition and quantum criticality of the 1D and 2D quantum Ising models with ultracold neutral atoms.

The formation and stability of dissipative solitons in the vector Lugiato-Lefever model are considered for the case when only one of the field components (polarization) is excited by the external coherent pump. It is shown that linearly polarized solitons can be destabilized because of the growth of the excitations belonging to the orthogonal polarization. Vector (elliptically polarized) solitons bifurcating from linearly polarized ones are found, and the stability and dynamics of the vector solitons are studied.

We analyze the reaction of a massless ($1+1$)-dimensional spinor field to the harmonic motion of one cavity wall. In our model, the oscillation amplitude of the harmonic oscillator is promoted to a quantum operator, providing the system with an additional quantum degree of freedom having bosonic nature. After obtaining the interaction Hamiltonian, we estimate the correction to both the ground state and its energy. We demonstrate that the system is able to convert bosons into fermion pairs at the lowest perturbative order. Extension of our model to multiple bags is contemplated.

We investigate the steady-state nonconservative open-system dynamics of an atom in a generic complex structured electromagnetic environment at finite temperature $T$. In such systems, when the atom moves along a translation-invariant axis of the environment, a frictional force acts on the particle. The effective viscosity due to friction results from the nonequilibrium interaction with the fluctuating (quantum) electromagnetic field, which effectively sets a privileged reference frame. We study the impact of both quantum and thermal fluctuations on the interaction, highlighting how they induce qualitatively different types of viscosity. To this end, we develop a self-consistent non-Markovian description that contains quantum and blackbody friction as special cases. In particular, we show how the interplay between the nonequilibrium dynamics, the quantum and the thermal properties of the radiation, as well as the confinement of light at the vacuum-material interface is responsible for several intriguing features. Our analysis is relevant for an experimental test of noncontact friction and the resulting electromagnetic viscosity.

We devise a quantum-circuit algorithm to solve the ground state and ground energy of artificial graphene. The algorithm implements a Trotterized adiabatic evolution from a purely tight-binding Hamiltonian to one including kinetic, spin-orbit, and Coulomb terms. The initial state is obtained efficiently using Gaussian-state preparation, while the readout of the ground energy is organized into seventeen sets of measurements, irrespective of the size of the problem. The total depth of the corresponding quantum circuit scales polynomially with the size of the system. A full simulation of the algorithm is performed and ground energies are obtained for lattices with up to four hexagons. Our results are benchmarked with exact diagonalization for systems with one and two hexagons. For larger systems we use the exact state vector and approximate matrix product state simulation techniques. The latter allows us to systematically trade off precision with memory and therefore to tackle larger systems. We analyze adiabatic and Trotterization errors, providing estimates for optimal periods and time discretizations given a finite accuracy. In the case of large systems we also study approximation errors.

The charging of a quantum battery by a four-stroke quantum machine that works either as an engine or a refrigerator is investigated. The presented analysis provides the energetic behavior of the combined system in terms of the heat- and workflows of the machine, the average, the variance of the battery's energy, as well as the coherent and incoherent parts of its ergotropy. To monitor the battery state, its energy is measured either after the completion of any cycle or after a prescribed number of cycles is carried out. The resulting battery performances greatly differ for those two cases. During the first charging epoch with an engine, the regular measurements speed up the charging, whereas the gain of ergotropy is more pronounced in the absence of measurements. In a later stage, the engine fails to work as such, while it still continues charging the battery that eventually reaches the maximally charged state in the absence of intermediate measurements and a suboptimally charged state for a periodically measured battery. For a refrigerator, the charging of the measured battery also proceeds faster during the first epoch. Only during the second stage, when the machine fails to extract heat from the cold bath, the influence of the measurements becomes less pronounced, leading to rather similar asymptotic states for the two measurement scenarios.

In this paper, we study the efficiency of charging a quantum battery through optical pumping. The battery consists of a qutrit and is connected to a natural thermal reservoir and an external coherent drive in the limit where its upper energy level can be adiabatically eliminated from the dynamics. In this scenario, the drive plus spontaneous emission optically pumps the intermediate energy level of the qutrit, and the battery can be understood as being charged by an effective higher temperature reservoir that takes it out of equilibrium with the natural reservoir and stores useful energy in it. We also analyze the efficiency of using this battery and charging scheme as the work fluid of a two-stroke thermal machine. The thermal machine includes a fourth level through which work is extracted from the battery via a unitary transformation, therefore setting the limit of maximum efficiency of the machine.

We demonstrate continuous real-time Bayesian estimations of magnetic-field fluctuations by monitoring single-photon emissions from a diamond nitrogen vacancy center under the setting of coherent population trapping, for which the time sequence of the single-photon emissions is correlated with the underlying magnetic-field fluctuations. The Bayesian estimations are combined with a feedback loop and are followed by a separate verification and optimization process, which uses the spin-dephasing rate in the presence of the feedback as a cost function. The dephasing rate is measured with Ramsey interferometry and is minimized by systematically varying the statistical parameters used in the estimations. The Bayesian estimations aided by the feedback and verification enable continuous real-time sensing at the single-photon level regardless of the prior availability of the statistical parameters of the underlying dynamics.

Quantum repeaters are used to overcome the exponential photon loss scaling that quantum states acquire as they are transmitted over long distances. While repeaters for discrete-variable encodings of quantum information have existed for some time, approaches for continuous-variable encoding quantum repeaters have only recently been proposed. In this work, we present a method of using a discrete-variable repeater protocol to distribute continuous-variable states and utilize it to compare the rates of continuous-variable entanglement distribution between first-generation continuous- and discrete-variable quantum repeaters. Such a comparison allows us to begin to benchmark the two quite different approaches.

We use the difference between theory and experiment for energy intervals in simple atomic systems (hydrogen, muonium, positronium, and deuteron) to find limits on the size of extra space dimensions in the Arkani-Hamed–Dimopoulos–Dvali model for gravitational potential on short distances. As an additional experimental fact we use the absence of the small size gravitational bound states of elementary particles. We demonstrate that the perturbation theory approach does not work and more reliable results are obtained by solving the Dirac equations for an electron in Coulomb and gravitational fields. These results probe smaller distances than the distance between nuclei in molecules and the limits are significantly stronger than the limits on the size of extra dimensions obtained using the spectra of hydrogen molecules.

We characterize the low-lying excitations of a quantum vortex in a quasi-two-dimensional Bose-Einstein condensate (BEC) using the standard definition of the density of states (DOS) and a modified version that is sensitive to complementary aspects of the excitation's spectrum. The latter proves to be particularly relevant to studying the polaronic state realized when an impurity is embedded in a quantum vortex. We establish that the impurity becomes sensitive to the transversal fluctuations of the vortex, via its remnant kelvon mode, and to the phase fluctuations of the BEC Nambu-Goldstone mode. The presence of the vortex yields an anomalous excitation spectrum with a finite energy gap and nonlinear DOS at low energies. We find that the high sensitivity of the kelvon mode to external potentials provides a quantum-level control channel over impurities trapped in a vortex. This extra control channel may be of practical use for the proposal of using vortex-trapped impurities as qubit units for quantum information processing.

We report on the derivation of determinant representations for the Green's functions and spectral function of the trapped Tonks-Girardeau gas on the lattice and in the continuum. Our results are valid for any type of statistics of the constituent particles, at zero and finite temperature and arbitrary confining potentials, including nonequilibrium scenarios induced by sudden changes of the external potential. In addition, they are also extremely efficient and easy to implement numerically with the main computational effort being represented by the calculation of partial overlaps of the dynamically evolved single-particle wave functions. In the lattice case we show that the spectral function of a system with a strong harmonic potential presents only two singular lines compared with three singular lines in the case of a homogeneous system.

Formation of a peculiar lasing pattern leading to a ${\mathrm{TEM}}_{00}$-like mode accompanied by a nonzero bright outer-ring emission (namely, a modified ${\mathrm{TEM}}_{00}$ mode) was observed in a 300-$\mu \mathrm{m}$-thick ${\mathrm{LiNdP}}_4{\mathrm{O}}_{12}$ laser with reflective flat end mirrors that was pumped with a laser diode whose focused spot size was larger than the lasing-beam spot size determined by the thermal lens effect. The photon lifetimes of the laser oscillations were found to be greatly shortened to ${\tau }_{\mathrm{p}}=6.74\mathrm{ps}$ as compared with those in pure ${\mathrm{TEM}}_{00}$ mode operation, while the fluorescence lifetime was $\tau =130\mu \mathrm{s}$. The formation of the peculiar transverse mode was theoretically treated in terms of the pump-intensity-dependent thermal lens effect, which yields the lasing-beam spot sizes in the resultant optical cavity. In addition, transverse spatial hole burning of population inversions due to the preceding transverse eigenmode intensity and the associated antiguidance of the pure ${\mathrm{TEM}}_{00}$ field leading to formation of the ${\mathrm{TEM}}_{00}$ with an emergent outer-ring emission was shown to appear with increasing pump power through the electric lens (i.e., population lens) effect, in which almost all of the population inversion contributes to lasing with a pronounced effective modal gain. Self-mixing laser Doppler velocimetry (LDV) experiments and numerical simulations revealed that spontaneous emission factors in the peculiar mode oscillations were greatly decreased in comparison with those in pure ${\mathrm{TEM}}_{00}$ mode operation. The present thin-slice solid-state laser possessing a large fluorescence-to-photon lifetime and decreased spontaneous emission factor enabled us to detect LDV signals in the regime of a few feedback photons per observation period.

This paper describes optical propagation beyond the paraxial limit in rotational symmetric short Fabry-Pérot cavities and long fibers with parabolic-index profiles. Frequency shifts due to paraxial and nonparaxial effects, the so-called spectral fine structure and vector corrections, are calculated with perturbation theory and expressed in a single dimensionless expansion parameter. The results obtained for short cavities and fibers have similar functional forms but are surprisingly different. These similarities and differences are pointed out and discussed, including their consequences for mode multiplexing in fibers.

We theoretically demonstrate the possibility to produce unipolar pulses of varying temporal profile in an extended layer of a resonant medium with the nonlinear coupling to the driving electric field. The proposed approach relies on the coherent control of the low-frequency medium oscillations by a sequence of ultrashort excitation pulses as well as the collective emission of multiple resonant centers along an optically thick medium layer. In particular, we show that creating an inhomogeneous spatial profile of the density of resonant centers allows obtaining unipolar pulses of adjustable waveform, such as rectangular or triangular ones. Such optical response could be realized in Raman-active media, e.g., in molecular crystals with well-resolved vibrational terahertz resonances.