Thermalization of a system when interacting with a thermal bath is an interesting problem. If a system eventually reaches a thermal state in the long time limit, it's expected that its density matrix would resemble the mean-force Gibbs state. Moreover, the correlation function must satisfy the Kubo-Martin-Schwinger (KMS) condition, or equivalently, the fluctuation-dissipation relation (FDR). In this paper, we derive a formal expression for the non-Markovian two-point function within the context of the weak coupling limit. Using this expression, we explicitly compute the two-point function for specific models, demonstrating their adherence to the KMS. In addition, we formulate a nonperturbative approach in the form of a self-consistent approximation that includes a partial resummation of perturbation theory. This approach can capture strong coupling phenomena while still relying on simple equations. Notably, we verify that the two-point function obtained through this method also satisfies the KMS condition.

The transfer matrix of scattering theory in one dimension can be expressed in terms of the time-evolution operator of an effective nonunitary quantum system. In particular, it admits a Dyson series expansion which turns out to facilitate the construction of the low-frequency series expansion of the scattering data. In two and three dimensions, there is a similar formulation of stationary scattering in which the scattering properties of the scatterer are extracted from the evolution operator for a corresponding effective quantum system. We explore the utility of this approach to scattering theory in the study of the scattering of low-frequency time-harmonic scalar waves $e^{-i\omega t}\psi \left(\mathbf{r}\right)$, with $\psi \left(\mathbf{r}\right)$ satisfying the Helmholtz equation, $[{\nabla }^2+k^2\widehat{\varepsilon }(\mathbf{r};k)]\psi \left(\mathbf{r}\right)=0$; $\omega$ and $k$ being, respectively, the angular frequency and wave number of the incident wave; and $\widehat{\varepsilon }(\mathbf{r};k)$ denoting the relative permittivity of the carrier medium, which, in general, takes complex values. We obtain explicit formulas for low-frequency scattering amplitude, examine their effectiveness in the study of a class of exactly solvable scattering problems, and outline their application in devising a low-frequency cloaking scheme.

As is well known, within the single-excitation subspace, the Su-Schrieffer-Heeger (SSH) model exhibits a remarkable ability to transfer an excitation from one end of the lattice to the other. In this work, by relaxing the restriction of the single excitation, we find that a topological channel formed by the topological edge modes of the SSH model can also realize the transfer of arbitrary Gaussian states. Specifically, we investigate the state transfer process within a one-dimensional (1D) optomechanical lattice, which can be mapped to the SSH model with tunable coupling strength. By initially preparing the first optical mode in a squeezed vacuum state and adiabatically varying the system parameters over a full cycle, the squeezed vacuum state can be transferred to the $N\mathrm{th}$ mechanical mode. Furthermore, we extend our investigation to the transfer of arbitrary Gaussian states. Since Gaussian states can be described by the covariance matrix of the system, we reformulate the evolution equation of the covariance matrix in a Schrödinger-type equation. This reformulation provides us with an intuitive way to show how an arbitrary Gaussian state is transferred. Our work broadens the application of topological systems for quantum state transfer, demonstrating that not only single-excitation states but also arbitrary Gaussian states, which include multiple excitations and quantum coherence, can be efficiently transferred, with potential implications for quantum information processing.

The entropic uncertainty principle imposes a limit on how precisely two incompatible observables can be measured, which can be reduced when quantum memory is involved. We theoretically investigate the dynamics of the quantum-memory-assisted entropic uncertainty relation when either quantum memory alone or both the measured particle and the quantum memory interact with a squeezed-vacuum bath through energy-preserving interactions. We show that in both scenarios, the squeezing phase of the reservoir decreases the entropic uncertainty (EU), whereas the squeezing strength increases the EU. In addition, we find that EU can be significantly reduced when both the measured particle and quantum memory are subjected to a common squeezed-vacuum bath. Furthermore, we explore the key factors controlling the behavior of EU by exploring the competition between quantum discord and minimal missing information. Moreover, we examine the tightness of the entropic uncertainty bound (EUB) in both system-environment setups and observe that the EUB is less tight when both the measured particle and quantum memory are coupled to a common squeezed-vacuum bath.

In this work we perform a comprehensive study of the machine learning (ML) methods for the purpose of characterizing the quantum set of correlations. As our main focus is on assessing the usefulness and effectiveness of the ML approach, we focus exclusively on the Clauser-Horne-Shimony-Holt scenario, both the four-dimensional variant, for which an analytical solution is known, and the eight-dimensional variant, for which no analytical solution is known but numerical approaches are relatively well understood. We consider a wide selection of approaches, ranging from simple data science models to dense neural networks. The two classes of models that perform well are support vector machines and dense neural networks, and they are the main focus of this work. We conclude that while it is relatively easy to achieve good performance on average, it is hard to train a model that performs well on the hard cases, i.e., points in the vicinity of the boundary of the quantum set, which are precisely the cases that are interesting from the academic point of view. In order to improve performance on hard cases we must, especially for the eight-dimensional problem, resort to a tailored choice of training data, which means that we are implicitly feeding our intuition and biases into the model. We feel that this is an important and often overlooked aspect of applying ML models to academic problems, where data generation or data selection is performed according to some implicit subjective criteria. In this way, it is possible to unconsciously steer our model so that it exhibits features that we are interested in seeing. Hence, special care must be taken while determining whether ML methods can be considered objective and unbiased in the context of academic problems.

Long-range Rydberg molecules are typically bound in wells formed in their oscillatory potential energy curves. In alkaline Rydberg molecules, bound vibrational states exist even when these potential wells are disrupted by level repulsion from the steep butterfly potential energy curve induced by a scattering shape resonance. The binding in this case is attributed to quantum reflection. However, the rapidly varying regions of the potential energy landscape where quantum reflection occurs often coincide with regions where nonadiabatic coupling becomes significant. By comparing the molecular states calculated within the Born-Oppenheimer approximation, where quantum reflection is the only binding mechanism, with those obtained from the full set of coupled channel equations, we assess the effects of nonadiabatic coupling on vibrational energies and lifetimes. Our findings show that these couplings can stabilize the molecule by providing an additional barrier which protects the vibrational states from predissociation and nonradiative transitions. There can also be extreme cases where nonadiabatic coupling completely dominates the binding and the molecular lifetimes saturate at the atomic Rydberg lifetime.

It is important to evaluate the total spin angular momentum of alkali-metal atoms if the atoms serve as a reservoir of angular momenta. We use an absorption-monitoring technique to measure $\langle F_z\rangle$, i.e., the expectation values of the quantization ($z$) axis components of the total angular momentum of Cs atoms in the electronic ground state in both uncoated and antirelaxation-coated vacuum cells at room temperature. Cs atoms are polarized via optical pumping and probed using their $D_2$ transitions. The probe laser frequency is varied across the Doppler-broadened $D_2$ transition; the $\langle F_z\rangle$ values are derived using the integrated absorption coefficients. The largest $\langle F_z\rangle$ is 2.5 for the coated cell. We then use a simple model of spin flow through vapor cells to estimate the atomic spin relaxation probabilities after a single surface collision.

We demonstrate coherent Doppler-free three-photon excitation of the ${}^{1}S_0\leftrightarrow {}^{3}P_0$ optical clock transition and the ${}^{1}S_0\leftrightarrow {}^{3}P_1$ intercombination transition in free-space thermal clouds of ${}^{88}\mathrm{Sr}$ atoms. By appropriate orientation of the wave vectors of three lasers incident on the atoms, the first-order Doppler shift can be eliminated for all velocity classes. Three-photon excitation of the ${}^{1}S_0\leftrightarrow {}^{3}P_1$ transition enables high-contrast Ramsey spectroscopy with interrogation times comparable to the $21\mu \mathrm{s}$ natural lifetime using a single near-resonant laser source. Three-photon spectroscopy on the ${}^{1}S_0\leftrightarrow {}^{3}P_0$ clock transition, using only laser frequencies nearly resonant with the ${}^{1}S_0\leftrightarrow {}^{3}P_0$ and ${}^{1}S_0\leftrightarrow {}^{3}P_1$ transitions, enables a reduction in Doppler broadening by two orders of magnitude and a corresponding $\sim 470\mathrm{Hz}$ linewidth without a confining potential.

We study the relaxation of a highly collisional, ultracold but nondegenerate gas of polar molecules. Confined within a harmonic trap, the gas is subject to fluid-gaseous coupled dynamics that lead to a breakdown of first-order hydrodynamics. An attempt to treat these higher-order hydrodynamic effects was previously made with a Gaussian ansatz and coarse-graining model parameter [R. R. W. Wang and J. L. Bohn, Phys. Rev. A 108, 013322 (2023)], leading to an approximate set of equations for a few collective observables accessible to experiments. Here we present substantially improved reduced-order models for these same observables, admissible beyond previous parameter regimes, discovered directly from particle simulations using the WSINDy algorithm (Weak-form Sparse Identification of Nonlinear Dynamics). The interpretable nature of the learning algorithm enables estimation of previously unknown physical quantities and discovery of model terms with candidate physical mechanisms, revealing new physics in mixed collisional regimes. Our approach constitutes a general framework for data-driven model identification leveraging known physics.

We study magnon-driven spin and heat transport in a magnetic linear junction (MLJ) formed by two ferromagnets in optical lattices linked via linearly aligned bonds. Using the Schwinger-Keldysh formalism, we uncover that under weak effective Zeeman fields, where Bose-Einstein statistics of magnons dominate, magnonic criticality dramatically enhances spin and thermal conductances. These singular transport properties depend on the junction geometry, and the transport properties qualitatively differ between the linear junction in this paper and the point contact in our previous work. The quantum-enhanced conductances result in the breakdown of the magnonic Wiedemann-Franz (WF) law. In the classical regime at temperatures much lower than magnon energy gaps, we find that a magnonic Lorenz number becomes independent of temperature yet dependent on junction geometry, sharply contrasting with the universal WF law for Fermi liquids. We also find that the interface geometry of the MLJ decouples spin and heat relaxations between ferromagnets with decay times insensitive to temperature and effective Zeeman fields. These dynamics reveal junction-geometry-sensitive magnon transport distinct from Fermi liquids, paving the way for new avenues in thermomagnetic research leveraging the tunability of cold atomic systems.

We numerically discover an alternative type of super-regular breather (SRB) that exhibits an asymmetric geometric stair structure in its spatiotemporal amplitude distribution. This kind of geometric-stair-shaped SRB is induced by the $\mathcal{PT}$-symmetric nonlocal nonlinearity and is effectively excited by localized periodic perturbations on a plane wave. By adjusting the amplitude and phase differences of the initial perturbations, we can control the direction and rate of its ascent or descent. Interestingly, due to the presence of $\mathcal{PT}$-symmetric nonlinearity, applying a spatial offset to the initial wave can excite an SRB with a significantly larger peak value, which can reach over 100 times the amplitude of the plane wave. Our results provide a method for exciting SRBs with spatial asymmetry and can offer different insights for the experimental observation of extremely asymmetric modulation instability phenomena.

Dipole-induced transparency (DIT) is one of the most well-known transparency effects in quantum optics and has wide applications in scalable quantum information processing and quantum computation. However, most of the existing literatures only focuses on the DIT effect with coherent dipole-cavity coupling, thus its universality in other types of coupling is still to be clarified. Here, we propose a feasible scheme to realize dissipative dipole-cavity coupling with the assistance of a highly dissipative microcavity, and explicitly exhibit cavity-mode attraction. We then investigate the DIT effect in a cavity-waveguide system with attractive cavity modes and find that it can still be achievable even though the probe light is resonant with two attractive cavity modes. Furthermore, we reveal its underlying transparency mechanism with eigenfrequencies and the effective susceptibility of the dipole-cavity system, and show that its transparency lies in the destructive interference of two attractive cavity modes with splitting damping rates instead of splitting resonance frequencies in coherent coupling. Moreover, we find that the attractive and repulsive phenomena of the effective susceptibility, which also plays an important role in the DIT effect, exist in the dipole-cavity system. Our findings may not only be of importance for gaining a more comprehensive understanding on the DIT effect, but also have potential applications in quantum networks.

Quantum realism, as introduced by Bilobran and Angelo [Europhys. Lett. 112, 40005 (2015)], states that projective measurements in quantum systems establish the reality of physical properties, even in the absence of a revealed outcome. This framework provides a nuanced perspective on the distinction between classical and quantum notions of realism, emphasizing the contextuality and complementarity inherent in quantum systems. While prior works quantified violations of quantum realism (VQRs) using measures based on entropic distances, here we extend the theoretical framework to geometric distances. Building on an informational approach, we derive geometric monotones of VQRs using trace distance, Hilbert-Schmidt distance, Schatten $p$ distances, and Bures and Hellinger distances. We identify Bures and Hellinger distances as uniquely satisfying all minimal criteria for a bona fide VQR monotone. Remarkably, these distances can be expressed in terms of symmetric Rényi and sandwiched Rényi divergences, aligning geometric and entropic approaches. Our findings suggest that the realism-information relation implies a deep connection between geometric and entropic frameworks, with only those geometric distances expressible as entropic quantities qualifying as valid monotones of VQRs. This work highlights the theoretical and practical advantages of geometric distances, particularly in contexts where computational simplicity or symmetry is important.

In this work, we introduce and characterize a broad class of quantum operations with a unique fixed point, termed quantum ergodic channels. We derive Lindblad-type master equations for these channels in arbitrary finite dimensions and analyze their non-Markovian dynamics using established measures. When the fixed point is a passive state, the channels exhibit ergotropy dynamics with notable thermodynamic implications. Specifically, under Markovian processes, ergotropy (a measure of the extractable work from a system under unitary evolution) monotonically decreases. However, in non-Markovian dynamics, ergotropy fluctuates, leading to a backflow effect that highlights memory-induced resource recovery. Our findings suggest that this ergotropy backflow could serve as an operationally meaningful indicator of non-Markovianity, offering new perspectives on the interplay between memory effects and thermodynamic behavior in open quantum systems. This study enhances the theoretical framework for understanding energy dynamics under ergodic channels and highlights new avenues for exploring the implications of memory effects in quantum batteries.

Generative quantum machine learning has gained significant attention for its ability to produce quantum states with desired distributions. Among various quantum generative models, quantum denoising diffusion probabilistic models (QuDDPMs) [Zhang et al., Phys. Rev. Lett. 132, 100602 (2024)] provide a promising approach with stepwise learning that resolves the training issues. However, the requirement of high-fidelity scrambling unitaries in QuDDPMs poses a challenge to near-term implementation. We propose a mixed-state quantum denoising diffusion probabilistic model (MSQuDDPM) to eliminate the need for scrambling unitaries. Our approach focuses on adapting the quantum noise channels to the model architecture, which integrates depolarizing noise channels in the forward diffusion process and parameterized quantum circuits with projective measurements in the backward denoising steps. We also introduce several techniques to improve MSQuDDPM, including a cosine-exponent schedule of noise interpolation, the use of a single-qubit random ancilla, and superfidelity-based cost functions to enhance the convergence. We evaluate MSQuDDPM on quantum ensemble generation tasks, demonstrating its successful performance.

Exceptional points (EPs) in propagation states induce intriguing properties as the group velocities. However, superluminal propagation near EPs is challenging due to the smoothing caused by symmetry breaking. In this study, we propose a photonic crystal waveguide design with glide and time-reversal symmetry and derive an effective Hamiltonian to realize fast-light edge states. We adopt a systematic method to generate EPs in edge states by introducing non-Hermitian perturbations to Dirac points guaranteed by glide symmetry, which ensures that EP modes are free from out-of-plane radiation losses. We identify the conditions for exact EP restoration and provide an analytical solution to offset the EP smoothing due to symmetry breaking, which significantly reduces the group velocity contrast. A glide symmetry of the photonic crystal waveguide allows us to derive the effective Hamiltonian in a simple form, and the EPs can be restored by adjusting the real part of the permittivity. Furthermore, we design a feasible photonic crystal slab waveguide incorporating graphene as the absorbing material, and numerically demonstrate a group velocity reaching $v_g=3.3c$ near the EP, which is up to 25 times that of the original structure. The proposed setup based on non-Hermitian photonics paves the way for the realization of superluminal devices in nanophotonics. In addition, the method for restoring EPs also addresses challenges in the phenomena arising from non-Hermitian properties.

Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, parity-time ($\mathcal{PT}$) symmetry, and resonances. However, the quantum simulation of these models has been limited by the extensive resources necessary in iterative methods with exponentially small postselection success probability. Here we employ a fixed-depth variational circuit to circumvent these limitations, enabling simulation deep into the $\mathcal{PT}$-broken regime surrounding an exceptional point. Quantum simulations are carried out using IBM superconducting qubits. The results underscore the potential for variational quantum circuits and machine learning to push the boundaries of quantum simulation, offering new methods for exploring quantum phenomena with near-term intermediate-scale quantum technology.

The path-integral approach to topological quantum error correction provides a unified way to construct and analyze fault-tolerant circuits in spacetime. In this work, we demonstrate its utility and versatility at hand of a simple example: We construct a fault-tolerant circuit for the toric-code phase by traversing its path integral on a $(x,y,z)$ cubic lattice in the $x+y$ direction. The circuit acts on qubits on a square lattice, and alternates between horizontal nearest-neighbor $CX$ gates and vertical nearest-neighbor $ZZ$ and $XX$ measurements. We show how to incorporate boundaries and corners into the fault-tolerant circuit and how to perform topologically protected logic gates. As a specific example, we consider performing a fault-tolerant logical $ZZ$ measurement via lattice surgery of two spatial rectangular blocks of our fault-tolerant circuit.

Using linearly polarized two-color femtosecond laser fields and coincidence measurements, we experimentally study the three-body fragmentation of the argon trimer following double ionization, resulting in two ionic fragments, $\mathrm{A}{\mathrm{r}}^{+}$, and one neutral fragment, Ar. This three-body channel is distinguished from the raw data by analyzing the correlation between the sum momentum vectors of the two ionic fragments $\mathrm{A}{\mathrm{r}}^{+}$ versus their total kinetic energy releases. Two distinct fragmentation pathways, concerted and sequential, are confirmed by a detailed examination of the kinetic energy releases’ correlation spectra, Newton diagrams, and Dalitz plots of the fragments. The emission directions of the neutral fragments from the sequential pathway are manipulated by adjusting the relative phase of the two-color laser fields. The observed relative phase-dependent asymmetry patterns are attributed to the enhanced ionization induced asymmetric emission of residual $\mathrm{A}{{\mathrm{r}}_2}^{+}$ in the first dissociation step. Our findings offer valuable insights into the dissociative ionization of argon trimers and are expected to stimulate further research into the ultrafast dynamics of clusters in femtosecond laser fields.