The maximum-entropy principle (max-ent) is a valuable and extensively used tool in statistical mechanics and quantum information theory. It provides a method for inferring the state of a system by utilizing a reduced set of parameters associated with measurable quantities. However, the computational cost of employing max-ent projections in simulations of quantum many-body systems is a significant drawback, primarily due to the computational cost of evaluating these projections. In this work, a different approach for estimating max-ent projections is proposed. The approach involves replacing the expensive max-ent induced local geometry, represented by the Kubo-Mori-Bogoliubov scalar product, with a less computationally demanding geometry. Specifically, a new local geometry is defined in terms of the quantum analog of the covariance scalar product for classical random variables. Relations between induced distances and projections for both products are explored. Connections with standard variational and dynamical mean-field approaches are discussed. The effectiveness of the approach is calibrated and illustrated by its application to the dynamic of excitations in a $XX$ Heisenberg spin-$\frac{1}{2}$ chain model.

The numerical approach to calculating the $S$-matrix poles associated with virtual states in electron-molecule collisions is proposed within the modified effective-range theory frame. The $S$-matrix continuation into the complex momentum plane is possible thanks to the analytical properties of modified Mathieu functions, that is, the exact solutions of the Schrödinger equation with the long-range polarization potential ($\sim r^{-4}$). The short-range electron-molecule interaction is included in the introduced numerical approach by model comparison with experimental integral, differential, and momentum-transfer elastic cross sections. The influence of the polarization potential on the virtual-state pole positions is analyzed for nonpolar targets such as ${\mathrm{N}}_2, {\mathrm{CH}}_4, {\mathrm{CO}}_2$, and ${\mathrm{SF}}_6$. The relation between the $S$-matrix pole position and the $s$-wave scattering length is discussed.

The impulsive limit (the “sudden approximation”) has been widely employed to describe the interaction between molecules and short, far-off-resonant laser pulses. This approximation assumes that the timescale of the laser-molecule interaction is significantly shorter than the internal rotational period of the molecule, resulting in the rotational motion being instantaneously “frozen” during the interaction. This simplified description of the laser-molecule interaction is incorporated in various theoretical models predicting rotational dynamics of molecules driven by short laser pulses. In this theoretical work, we develop an effective theory for ultrashort laser pulses by examining the full time-evolution operator and solving the time-dependent Schrödinger equation at the operator level. Our findings reveal a critical angular momentum, $l_{\mathrm{crit}}$, at which the impulsive limit breaks down. In other words, the validity of the sudden approximation depends not only on the pulse duration but also on its intensity, since the latter determines how many angular momentum states are populated. We explore both ultrashort multicycle (Gaussian) pulses and the somewhat less studied half-cycle pulses, which produce distinct effective potentials. We discuss the limitations of the impulsive limit and propose a method that rescales the effective matrix elements, enabling an improved and more accurate description of laser-molecule interactions.

We calculate the superfluid fraction of an interacting Fermi gas, in the presence of a one-dimensional periodic potential of strength $V_0$ and wave vector $q$. Special focus is given to the unitary Fermi gas, characterized by the divergent behavior of the $s$-wave scattering length. Comparison with the Leggett's upper bound ${(\langle n_{1D}\rangle <1/n_{1D}>)}^{-1}$, with $n_{1D}$ the one-dimensional column density, explicitly shows that differently from the case of a dilute interacting Bose gas, the bound significantly overestimates the value of the superfluid fraction, except in the phonon regime of small $q$. Sum rule arguments show that the combined knowledge of the Leggett bound and of the actual value of the superfluid fraction allows for the determination of curvature effects, providing the deviation of the dispersion of the Anderson-Bogoliubov mode from the linear phonon dependence. The comparison with the predictions of the weakly interacting BCS Fermi gas points out the crucial role of two-body interactions. The implications of our predictions on the anisotropic behavior of the sound velocity are also discussed.

We investigate the behavior of a mobile spin-1/2 impurity atom immersed in a Fermi gas, where the interacting spin-$\uparrow$ and noninteracting spin-$\downarrow$ states of the impurity are Rabi coupled via an external field. This scenario resembles the classic problem of a two-state system interacting with a dissipative environment, but with an added dimension provided by the impurity momentum degree of freedom. In this case, the impurity can become “dressed” by excitations of the Fermi sea to form a Fermi polaron quasiparticle. For the steady-state system, where the impurity has thermalized with the medium, we derive exact thermodynamic relations that connect the impurity magnetization with quasiparticle properties such as the number of fermions in the dressing cloud. We show how the thermodynamic properties evolve with increasing Rabi coupling and we present exact analytical results in the limits of weak and strong Rabi coupling. For the dynamics of the Rabi-driven Fermi polaron, we formulate a theoretical approach based on correlation functions that respects conservation laws and allows the efficient calculation of Rabi oscillations for a range of timescales and impurity momenta beyond what has been achieved previously. Our results are in good agreement with recent experiments on the Rabi oscillations of the attractive polaron, and they reveal how the Rabi oscillations are influenced by the interplay between the polaron and its dressing cloud.

We investigate the dynamical characterization theory for periodically driven systems in which Floquet topology can be fully detected by emergent topological patterns of quench dynamics in momentum subspaces called band-inversion surfaces. We improve the results of a recent work [Zhang et al., Phys. Rev. Lett. 125, 183001 (2020)] and propose a more flexible scheme to characterize a generic class of $d$-dimensional Floquet topological phases classified by $\mathbb{Z}$-valued invariants by applying a quench along an arbitrary spin-polarization axis. Our basic idea is that by disassembling the Floquet system into multiple static subsystems that are periodic in quasienergy, a full characterization of Floquet topological phases reduces to identifying a series of bulk topological invariants for time-independent Hamiltonians, which greatly enhances the convenience and flexibility of the measurement. We illustrate the scheme by numerically analyzing two experimentally realizable models in two and three dimensions, respectively, and adopting two different but equivalent viewpoints to examine the dynamical characterization. Finally, considering the imperfection of experiment, we demonstrate that the present scheme can also be applied to a general situation where the initial state is not completely polarized. This study provides an immediately implementable approach for dynamically classifying Floquet topological phases in ultracold atoms or other quantum simulators.

Ghost imaging enables two-dimensional reconstruction of an object even though particles transmitted or emitted by the object of interest are detected with a single pixel detector without spatial resolution. This is possible because for the particular implementation of ghost imaging presented here, the incident beam is spatially modulated with a nonconfigurable attenuating mask whose orientation is varied (e.g. via transverse displacement or rotation) in the course of the ghost imaging experiment. Each orientation yields a distinct spatial pattern in the attenuated beam. In many cases ghost imaging reconstructions can be dramatically improved by factoring the measurement matrix which consists of measured attenuated incident radiation for each of many orientations of the mask at each pixel to be reconstructed as the product of an orthonormal matrix $Q$ and an upper triangular matrix $R$, provided that the number of orientations of the mask ($N$) is greater than or equal to the number of pixels ($P$) reconstructed. For the $N<P$ case, we present a data augmentation method that enables $QR$ factorization of the measurement matrix. To suppress noise in the reconstruction, we determine the Moore-Penrose pseudoinverse of the measurement matrix with a truncated singular value decomposition approach. Since the resulting reconstruction is still noisy, we denoise it with the adaptive weights smoothing method. In simulation experiments our method outperforms a modification of an existing alternative orthogonalization method where rows of the measurement matrix are orthogonalized by the Gram-Schmidt method. We apply our ghost imaging methods to experimental x-ray fluorescence data acquired at Brookhaven National Laboratory.

In this work, we study the quantum synchronization and quantum $\varphi$ synchronization of two mechanical oscillators in a coupled optomechanical system. The oscillators are coupled to an optical cavity filled with a Kerr nonlinear medium and subjected to periodic modulation of the cavity detunings and driving amplitudes by a common driving field. Our results show that the quantum synchronization and quantum $\varphi$ synchronization in nonlinear systems exhibit more favorable behaviors than in linear systems. In addition, we have investigated the performances of two synchronization measurements to various parameters by analyzing the sensitivity of $\varphi$. Accordingly, perfect synchronization can be achieved under specific parameters by periodically modulating the cavity and driving field. Our findings could offer insights into other quantum effects and pave the way for studying quantum correlations.

Utilizing realistic simulations of high-order harmonic generation (HHG) in several materials, we study how different regions of the Brillouin zone contribute to the nonlinear response. It is often assumed that the electronic trajectories that start in the vicinity of the $\mathrm{\Gamma }$ point are predominantly responsible for the HHG spectrum, but it is shown here that such an approximation is generally inaccurate. While examples can be identified where merely 0.4% of the Brillouin zone produces semiquantitatively accurate HHG spectra, in most situations one must include at least 30%–50% of the Brillouin-zone volume to obtain accurate above-the-gap harmonics. For the harmonic peaks below the band-gap energy, the current-density responses from the entire Brillouin zone must always be integrated. We also identify the minimal set of electronic bands necessary for the construction of reduced but still realistic HHG models. The results should be useful for a number of HHG applications, including all-optical reconstructions of the band structure and light-matter couplings or considerations involving semiclassical approaches to solid-state high-order harmonic radiation.

We propose a technique for optimizing parameterized circuits in variational quantum algorithms based on the probabilistic tensor sampling optimization. This method allows one to relax random initialization issues or heuristics for generating initial guess of variational parameters, and can be used to avoid local minima. We illustrate our approach on the example of the quantum approximate optimization algorithm (QAOA) applied to the $\text{max}\text{−}k\text{−}\text{cut}$ problem based on the binary encoding efficient in the number of qubits. We discuss the advantages of our technique for searching optimal variational parameters of QAOA circuits in comparison to classical optimization methods.

The wave function is the cornerstone of quantum theory, and various techniques have been proposed for its direct measurement. The reconstruction of the wave function can be achieved by utilizing the real and imaginary components of momentum weak value, which correspond to amplitude and phase differentiation, respectively. However, these methods are limited in their applicability to wave functions with large phase gradients due to the weak coupling condition, which is a fundamental constraint. In this paper, we propose a method for reconstructing wave functions with large phase gradients based on optical differentiation through weak measurement. We have developed a more generalized theory of phase differentiation and implemented a common optical path and fast measurement for wave functions with large phase gradients. The experimental detection of wave functions with varying phase gradients has validated the reliability of our method. This work expands the range of applications for weak measurement while retaining its high resolution and sensitivity advantages, particularly in the field of wavefront sensing.

Multidimensional beamsplitters play crucial roles in the development of multidimensional atom interferometers and have the potential for applications in quantum information in higher dimensions. We present different configurations of multidimensional beamsplitters using both conventional two-photon Raman transitions and recently discovered four-photon Raman transitions. The differences between these configurations arise from the selection of external magnetic fields to serve as quantization axes. We explored and estimated statistical and systematic errors that may occur when multiple Raman transitions are used to construct multidimensional atom interferometers with deviated quantization axes. Our results demonstrated a tradeoff between the simplicity of axis alignment relative to the beams and the required optical power. These considerations are pertinent to the future design and optimization of multidimensional atom interferometry systems.

We study the all-to-all Ising model in the presence of dissipation and periodic external field. The corresponding Lindblad equation has a time-periodic Liouvillian. The dynamics of magnetizations is explored by using both the mean-field theory and numerical simulation at a finite number of spins. The mean-field result exhibits a transition from the periodic response at small field amplitude to the chaotic dynamics at large amplitude. The Lyapunov exponents are calculated, which supports the existence of a classical chaotic phase. However, in the numerical simulation at a finite number of spins, the response is periodic at both small and large amplitudes. The scaling analysis of the Floquet Liouvillian spectrum suggests that the periodic response persists even in the thermodynamic limit. Further analysis shows that, in the classical chaotic regime, the density-matrix elements have a wide dispersion, instead of being localized. Such a delocalization of wave packets explains the failure of mean-field approximation.

We report calculations of the high-order harmonic spectra of few-atomic clusters of two noble gases, helium and krypton, subjected to laser pulses of intensities above ${10}^{13}$ W/${\mathrm{cm}}^2$. We employ a fully ab intio framework, namely, the real-time time-dependent configuration interaction singles coupled to a discrete Gaussian basis set. Our model reproduces the observed higher-than-quadratic dependence between the high-order harmonic yield and the number of atoms, and the obtained value of the enhancement rate is in quantitative agreement with experimental results. We suggest a mechanism responsible for the high-order harmonic enhancement, according to which, after the tunneling ionization, the residual ion polarizes the electron densities of surrounding atoms in the cluster, which leads to increased electron-electron repulsion during the recollision. The proposed mechanism is not only fully consistent with both our calculations and the experimental data, but can also explain the limitations of previous theoretical studies on high-order harmonic generation in clusters.

The transverse field structure and diffraction loss of the resonant modes of Fabry-Pérot optical cavities are acutely sensitive to the alignment and shape of the mirror substrates. We develop extensions to the mode-mixing method applicable to arbitrary mirror shapes, which both facilitate fast calculation of the modes of cavities with transversely misaligned mirrors and enable the determination and transformation of the geometric properties of these modes. We show how these methods extend previous capabilities by including the practically motivated case of transverse mirror misalignment, presenting the ability to study the rich and complex structure of the resonant modes.

The concept of block coherence encompasses the case where experimental capabilities are not so delicate to perform arbitrary refined measurements on individual atoms. We develop a framework which facilitates further investigation of this resource theory in several respects. Using this framework, we investigate the problem of state conversion by incoherent operations and show that a majorization condition is the necessary and sufficient condition for state transformation by block-incoherent operations. We also determine the form of the maximally coherent state from which all other states and all unitary gates can be constructed by incoherent operations. Thereafter, we define the concept of block-cohering and block-decohering powers of quantum channels and determine these powers for several types of channels. Finally, we explore the relation between block coherence and a previous extension of coherence, known as $k$ coherence.

We study nonlinear Landau-Zener-Stückelberg-Majorana (LZSM) tunneling with a $\mathcal{PT}$-symmetric potential, which can be converted to a non-Hermitian nonlinear two-level model by a two-mode approximation. Then, we construct an equivalent Hermitian model through a transformation, verify that the tunneling probabilities obtained by the two models are consistent, and comprehensively analyze the effect of the gain-dissipation term on tunneling. In addition, due to the gain-dissipation properties, the total population density of the non-Hermitian model is no longer a conserved quantity, which will increase or decay to a fixed value as the model evolves. Finally, we prove that the spatial inversion symmetry breaking of the Hamiltonian leads to nonreciprocal tunneling, and the numerical simulation results confirm our analysis. These studies provide alternative ideas to study the nonlinear dynamics of non-Hermitian systems in the future.

Recently, the polarization measurement of $L$-shell radiative recombination $\left(L\text{−}\mathrm{RR}\right)$ x rays was performed on the Tokyo-EBIT [N. Numadate et al., Phys. Rev. A 105, 023109 (2022)], and the reported theoretical result performed by the flexible atomic code (FAC) was higher than the experimental value. We present joint theoretical investigations on the linear polarization of x rays emitted from the RR into Kr, Xe, Bi, and U ions by two distinct theoretical approaches, i.e., the present relativistic calculations and the revised FAC using the density matrix formalism, in which the relativistic and multipole effects are fully considered. In addition, the energy and atomic number $Z$ dependences of $L$-RR x-ray polarization are further investigated. Our results are in good agreement with experimental values for $K$ shells and are closer to those for $L$ shells than previous calculations. However, deviations still exist between the theoretical calculations and experimental results for $L$ shells. It is found that the effect of the configuration interaction and the finite nuclear size on the polarization of $L$-RR x rays is not substantial. More theories and experiments are required to explain these deviations.

An impurity particle interacting with a Bose-Einstein condensate (BEC) leads to the formation of a quasiparticle known as the Bose polaron. We investigate the properties of the two-dimensional Bose polaron, applying a variational ansatz that contains up to three Bogoliubov excitations of the BEC. Similar to its three-dimensional counterpart, we observe the existence of two quasiparticle branches, namely, the attractive and the repulsive polarons, at different coupling strengths. We find that their energies agree well with recent quantum Monte Carlo calculations. In particular, we observe that the inclusion of three excitations is crucial to capture the attractive polaron energy towards the regime of strong attraction, where the quasiparticle properties are dominated by few-body correlations. We also calculate the attractive polaron effective mass and residue, where we find significant differences between considering a weakly interacting Bose medium and taking the noninteracting limit, signaling enhanced impurity dressing by excitations in the latter case. By contrast, the spectral weight of the metastable repulsive polaron is largely insensitive to the interactions in the BEC and the number of Bogoliubov excitations. Our model may be experimentally realized in dilute atomic vapors and atomically thin semiconductors.