Spectral function is a key tool for understanding the behavior of Bose-Einstein condensates of cold atoms in random potentials generated by a laser speckle. In this paper we introduce a method for computing the spectral functions in disordered potentials. Using a combination of the Wigner-Weyl approach with the localization-landscape theory, we build an approximation for the Wigner distributions of the eigenstates in the phase space and show its accuracy in all regimes, from the deep quantum regime to the intermediate and semiclassical. Based on this approximation, we devise a method to compute the spectral functions using only the landscape-based effective potential. The paper demonstrates the efficiency of the proposed approach for disordered potentials with various statistical properties without requiring any adjustable parameters.

We develop a model of a binary fermionic mixture, consisting of a large number of atoms, applicable at nonzero temperatures, in the normal phase. We use this approach to study the dynamics of degenerate Fermi systems under various perturbations. For example, we analyze the spin-dipole oscillations of a two-component fermionic mixture, demonstrating that the ferromagnetic phase shows up at a stronger repulsion between components while the temperature rises. We study as well the radial oscillations of weakly interacting repulsive Fermi gases. We obtain a good agreement with experimental data when available. Otherwise, we compare our results with the outcome of the Hartree-Fock orbital calculations done for a system with a small number of fermions.

Lorentz reciprocity, energy conservation, and time-reversal symmetry are three important global constraints of Maxwell's equations. Unlike time-reversal symmetry, Lorentz reciprocity and energy conservation usually are not considered as symmetries, i.e., they are not associated with operators. In this paper, we provide a unified treatment of these three global constraints from a perspective of internal symmetry. We define operators of transformations associated with each of these constraints, referred to as internal transformations. When Maxwell's equations are written as a linear system of equations, these internal transformations correspond to the operations of transpose, conjugate transpose, and conjugate of the system matrix, respectively. We show the three global constraints naturally follow from three fundamental identities of linear systems under the three matrix operations. We discuss the properties of electromagnetic fields and scattering matrices associated with these internal transformations. These internal transformations form the Klein four-group $V_4={\mathbb{Z}}_2\times {\mathbb{Z}}_2$, and the internal symmetry group of any photonic structure corresponds to one of the five subgroups of $V_4$. Our paper provides a theoretical foundation for further exploration of symmetries in photonic systems.

We study the scattering property of a normally incident plane wave scattered by random media whose second-order potential correlation function has parity-time $\left(\mathcal{PT}\right)$ or classical symmetry. Based on the weak-potential-scattering theory, we show analytically that when the random media have classical symmetry, the far-zone spectral density is centrosymmetric. However, the spectral density becomes asymmetric for the $\mathcal{PT}$ random scatterer. The reason is the odd-symmetric distribution of the phase in the potential correlation function of the $\mathcal{PT}$ random media. We demonstrate numerically the asymmetric far-zone spectral density with two types of potential correlations, i.e., Schell-model-correlated and nonuniform-correlated correlations.

We propose a scheme to achieve the nonreciprocal amplification in a hybrid cavity magnonics system. Because of the destructive interference between different paths and the introduction of the pumping of the magnon, the nonreciprocal amplification can be observed. Owing to the gain and dissipation, with the varying of parameters, the eigenvalues of the effective Hamiltonian exhibit exceptional points (EPs). We investigate the relation between EPs and the nonreciprocal amplification transmission and find that EPs divide the parameters in different regions at which the behavior of amplification transmission is different; thus the EPs can help us understand the amplification transmission as well as find the optimized parameters.

Representing signals with sparse vectors has a wide spectrum of applications that ranges from image and video coding to shape representation and health monitoring. In many applications with real-time requirements or that deal with high-dimensional signals, the computational complexity of the encoder that finds the sparse representation plays an important role. Quantum computing has recently shown promising speedups in many representation learning tasks. In this work, we propose a quantum version of the well-known matching-pursuit algorithm. Assuming the availability of a fault-tolerant quantum random access memory, our quantum matching pursuit lowers the complexity of its classical counterpart by a polynomial factor, at the cost of some error in the computation of the inner products, enabling the computation of sparse representations of high-dimensional signals. Besides proving the computational complexity of our algorithm, we provide numerical experiments that show that its error is negligible in practice. This work opens the path to further research on quantum algorithms for finding sparse representations, showing suitable quantum computing applications in signal processing.

The resonator-induced phase gate is a two-qubit operation in which driving a bus resonator induces a state-dependent phase shift on the qubits equivalent to an effective $ZZ$ interaction. In principle, the dispersive nature of the gate offers flexibility for qubit parameters. However, the drive can cause resonator and qubit leakage, the physics of which cannot be fully captured using either the existing Jaynes-Cummings or Kerr models. In this paper, we adopt an ab initio model based on Josephson nonlinearity for transmon qubits. The ab initio analysis agrees well with the Kerr model in terms of capturing the effective $ZZ$ interaction in the weak-drive dispersive regime. In addition, however, it reveals numerous leakage transitions involving high-excitation qubit states. We analyze the physics behind such novel leakage channels, demonstrate the connection with specific qubit-resonator frequency collisions, and lay out a plan toward device parameter optimization. We show that this type of leakage can be substantially suppressed using very weakly anharmonic transmons. In particular, weaker qubit anharmonicity mitigates both collision density and leakage amplitude, while larger qubit frequency moves the collisions to occur only at large anharmonicity not relevant to experiment. Our work is broadly applicable to the physics of weakly anharmonic transmon qubits coupled to linear resonators. In particular, our analysis confirms and generalizes the measurement-induced state transitions noted in Sank et al. [Phys. Rev. Lett. 117, 190503 (2016)] and lays the groundwork for both strong-drive resonator-induced phase gate implementation and strong-drive dispersive qubit measurement.

State preparation via postselected weak measurements in a three-wave mixing process is studied. We assume the signal input mode is prepared in a vacuum state, coherent state, or squeezed vacuum state, while the idler input is prepared in a weak coherent state and passes the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of the idler beam's path, the signal output channel is prepared in a single-photon Fock state, single-photon-added coherent state, or single-photon-added squeezed vacuum state with very high fidelity, depending upon the input signal states and related controllable parameters. The properties of squeezing, signal amplification, second-order correlation, and the Wigner functions of the weak-measurement-based output states are also investigated. Our scheme promises to provide an alternate effective method for producing useful nonclassical states in quantum information processing.

The time-dependent kinetics of formation and evolution of nanosize atomic clusters is investigated and illustrated with the nucleation dynamics of ion-seed ${\mathrm{Ar}}_n{\mathrm{H}}^{+}$ particles. The rates of growth and degradation of Ar-atomic shells around the seed ion are inferred from molecular dynamics (MD) simulations. Simulations of cluster formation have been performed with accurate quantum-mechanical binary interaction potentials. Both the nonequilibrium and equilibrium growth of ${\mathrm{Ar}}_n{\mathrm{H}}^{+}$ are investigated at different temperature and densities of the atomic gas and seed ions. Formation of ${\mathrm{Ar}}_{n\le 40}$ shells is the main mechanism which regulates the kinetics of nanocluster growth and the diffusive fluctuations of the cluster size distribution. The time evolution of the cluster intrinsic energy and cluster size distributions are analyzed at the nonthermal, quasiequilibrium, and thermal equilibrium stages of ${\mathrm{Ar}}_n{\mathrm{H}}^{+}$ formation. We have determined the self-consistent model parameters for the temporal fluctuations of the cluster size and found coefficients of the diffusive growth mechanism describing the equilibrium distribution of nanoclusters. Nucleation of haze and nanodust particles in astrophysical and atmospheric ionized gases is discussed.

We investigated helium-mediated translational and rotational thermalization of the aluminum monofluoride (AlF) molecule at cryogenic temperatures via an ab initio potential energy surface (PES) and quantum multichannel scattering theory. Our examination of the elastic and rotationally inelastic channels revealed that helium is an efficient quencher of AlF at temperatures relevant to buffer gas cooling experiments ($\sim 1$ mK to 10 K). We also showed that this conclusion is robust against possible inaccuracies of the PES.

The static electric-dipole polarizability $\alpha$ of the neon atom was determined with a relative uncertainty of only about 0.003% using state-of-the-art ab initio approaches. The new value, $\alpha =2.661067\left(77\right)\mathrm{a}.\mathrm{u}.$, is almost five times more accurate than the previous ab initio estimate, $\alpha =2.66080\left(36\right)\mathrm{a}.\mathrm{u}.$, by Lesiuk et al. [Phys. Rev. A 102, 052816 (2020)]. Similar to their work, we calculated $\alpha$ using ab initio methods up to full configuration interaction and added corrections for finite nuclear mass and size, relativistic, and quantum electrodynamics (QED) effects. The uncertainty reduction of this work was achieved in particular by employing extremely large basis sets, including newly developed ones of 11Z, 12Z, and 13Z quality. Moreover, the finite nuclear mass effects and most of the relativistic contributions were calculated at much higher levels of theory than in the work of Lesiuk et al. However, we adopted their values for the orbit-orbit part of the relativistic correction and for the Bethe logarithm needed to compute the QED correction. The uncertainty of our final value is still an order of magnitude larger than that of the experimental value recently measured by Gaiser and Fellmuth [Phys. Rev. Lett. 120, 123203 (2018)] with an uncertainty of only a few parts per million using dielectric-constant gas thermometry. Yet, our ab initio value agrees with their value, ${\alpha }_{\exp }=2.661057\left(7\right)\mathrm{a}.\mathrm{u}.$, almost within the experimental uncertainty. This could indicate that the higher-order relativistic corrections and QED contributions, which dominate our uncertainty budget, are more accurate than expected considering the uncontrolled approximations involved in their calculation.

We present an experimental and theoretical study of symmetric ${\text{Xe}}^{54+}+\text{Xe}$ collisions at 50, 30, and 15 MeV/u, corresponding to strong perturbations with $v_K/v_{\text{p}}=1.20$, 1.55, and 2.20, respectively ($v_K$ is the classical $K$-shell orbital velocity and $v_{\text{p}}$ is the projectile velocity), as well as ${\text{Xe}}^{53+}+\text{Xe}$ collisions at 15 MeV/u. For each of these systems, x-ray spectra are measured under a forward angle of ${35}^{\circ }$ with respect to the projectile beam. Target satellite and hypersatellite radiation $K{\alpha }_{2,1}^{\mathrm{s}}$ and $K{\alpha }_{2,1}^{\mathrm{hs}}$, respectively, are analyzed and used to derive cross-section ratios for double-to-single target $K$-shell vacancy production. We compare our experimental results to relativistic time-dependent two-center calculations.

Dynamic core-electron polarization (DCeP) is a correction to the single-active electron (SAE) approximation by considering a response of the core electrons to the time-dependent laser field. Despite being initially construed as a perturbative correction, in some cases especially atoms and molecules with large polarizabilities, DCeP can qualitatively alter predictions produced by the bare SAE theory. In this study, we unambiguously demonstrate the nonperturbative role of DCeP in the resolved odd-even high-order harmonic generation (HHG) of the CO molecule. In particular, we find that the even-to-odd ratio, i.e., the ratio between the harmonic intensities of even order and average of the two adjacent odd orders, changes by as much as one order of magnitude when DCeP is included, making the theoretically predicted values remarkably consistent with the experimental ones. This strong manifestation allows us to verify the DCeP role in HHG by experimental data. Furthermore, our analysis of the harmonic time profile shows that this agreement is not an artifact of the numerical method but reflects relevant physics, establishing that DCeP must be incorporated into the standard framework for strong-field physics.

The ultracold mixture of ${}^{23}\mathrm{Na}$ and ${}^{87}\mathrm{Rb}$ atoms has become an important system for investigating physics in Bose-Bose atomic mixtures and for forming ultracold ground-state polar molecules. In this work, we provide an improved characterization of the most commonly used Feshbach resonance near 347.64 G between ${}^{23}\mathrm{Na}$ and ${}^{87}\mathrm{Rb}$ in their absolute ground states. We form Feshbach molecules using this resonance and measure their binding energies by dissociating them via magnetic-field modulation. We use the binding energies to refine the singlet and triplet potential-energy curves, using coupled-channel bound-state calculations. We then use coupled-channel scattering calculations on the resulting potentials to produce a high-precision mapping between magnetic field and scattering length. We also observe ten additional $s$-wave Feshbach resonances for ${}^{23}\mathrm{Na}$ and ${}^{87}\mathrm{Rb}$ in different combinations of Zeeman sublevels of the $F=1$ hyperfine states. Some of the resonances show two-body inelastic decay due to spin exchange. We compare the resonance properties with coupled-channel scattering calculations that full take account of inelastic properties.

The Imbert-Fedorov (IF) shift at the optical interface of Weyl semimetal (WSM) is extremely significant to recognize the optical characteristics of WSM. In this paper, we have studied the spatial IF shift on the surface of a bulk WSM by theoretically deriving a 4 × 4 magneto-optic matrix. It is found that the phenomenon of spatial IF shift changing from positive to negative occurs at an incident angle near the Brewster angle. Remarkably, this special phenomenon can be regulated by changing the frequency of incident light, tilt degree, and Weyl node separation. Specially, for a fixed Weyl node separation, the phenomena of spatial IF shift changing from positive to negative can be realized at different tilt degrees by simply changing the frequency, and there exists one-to-one correspondence between the tilt degree and frequency at these situations. Similarly, for a fixed tilt degree, these phenomena can be achieved at different Weyl node separations by changing the frequency, and there also exists one-to-one correspondence between the Weyl node separation and frequency. Therefore, these tunable phenomena of spatial IF shift changing from positive to negative enable the feasibility of accurate determination of tilt degree and Weyl node separation. Our study can also provide a reference for the research of IF shift in such similar structures.

Quantum annealing in the transverse-field Ising model (TFIM) with open-system dynamics is known to use thermally assisted tunneling to drive computation. However, it is still subject to debate whether quantum systems in the presence of decoherence are more useful than those using classical dynamics to drive computation. We contribute to this debate by introducing the perturbed ferromagnetic chain (PFC), a chain of frustrated subsystems where the degree of frustration scales inversely with the perturbation introduced by a tunable parameter. This gives us an easily embeddable gadget whereby problem hardness can be tuned for systems of constant size. We outline the properties of the PFC and compare classical spin-vector Monte Carlo (SVMC) variants with the adiabatic quantum master equation. We demonstrate that SVMC methods get trapped in the exponentially large first-excited-state manifold when solving this frustrated problem, whereas evolution using quantum dynamics remains in the lowest energy eigenstates. This results in significant differences in ground-state probability when using either classical or quantum annealing dynamics in the TFIM.

There is currently much interest in the recycling of entangled systems, for use in quantum information protocols by sequential observers. In this work, we study the sequential generation of Bell nonlocality via recycling one or both components of two-qubit states. We first give a description of two-valued qubit measurements in terms of measurement bias, strength, and reversibility, and derive useful tradeoff relations between them. Then, we derive one-sided monogamy relations for unbiased observables that strengthen the recent conjecture by Cheng et al. [Phys. Rev. A 104, L060201 (2021)] that if the first pair of observers violate Bell nonlocality then a subsequent independent pair cannot, and give semianalytic results for the best possible monogamy relation. We also extend the construction by Brown and Colbeck [Phys. Rev. Lett. 125, 090401 (2020)] to obtain (i) a broader class of two-qubit states that allow the recycling of one qubit by a given number of observers on one side and (ii) a scheme for generating Bell nonlocality between arbitrarily many independent observers on each side, via the two-sided recycling of multiqubit states. Our results are based on a formalism that is applicable to more general problems in recycling entanglement and hence is expected to aid progress in this field.

The coherence resource theory needs to study the operational value and efficiency which can be broadly formulated as the question: when can one coherent state be converted into another under incoherent operations? We answer this question completely for one-mode continuous-variable systems by characterizing conversion of coherent Gaussian states under incoherent Gaussian operations in terms of their first and second moments. The no-go theorem of purification of coherent Gaussian states is also built. The structure of incoherent Gaussian operations of two-mode continuous-variable systems is discussed further and is applied to coherent conversion for pure Gaussian states with standard second moments. The standard second moments are images of all second moments under local linear unitary Bogoliubov operations. As concrete applications, we obtain some peculiarities of a Gaussian system: (1) there does not exist a maximally coherent Gaussian state which can generate all coherent Gaussian states; (2) the conversion between pure Gaussian states is reversible; (3) the coherence of input pure state and the coherence of output pure state are equal.

We consider probe-based quantum thermometry and show that machine classification can provide model-independent estimation with quantifiable error assessment. Our approach is based on the $k$-nearest-neighbor algorithm. The machine is trained using data from either computer simulations or a calibration experiment. This yields a predictor which can be used to estimate the temperature from new observations. The algorithm is highly flexible and works with any kind of probe observable. It also allows one to incorporate experimental errors, as well as uncertainties about experimental parameters. We illustrate our method with an impurity thermometer in a Bose gas, as well as in the estimation of the thermal phonon number in the Rabi model.