Cavity optomechanical systems are a paradigmatic setting for the conversion of electromagnetic energy into mechanical work. Experiments with atoms coupled to cavity modes are realized in nonequilibrium conditions, described by phenomenological models encoding nonthermal dissipative dynamics and falling outside the framework of weak system-bath couplings. This fact makes their interpretation as quantum engines, e.g., the derivation of a well-defined efficiency, quite challenging. Here, we present a consistent thermodynamic description of open quantum cavity-atom systems. Our approach takes advantage of their nonequilibrium nature and arrives at an energetic balance which is fully interpretable in terms of persistent dissipated heat currents. The interaction between atoms and cavity modes can further give rise to nonequilibrium phase transitions and emergent behavior and allows us to assess the impact of collective many-body phenomena on the engine operation. To enable this, we define two thermodynamic limits, one related to a weak optomechanical coupling and one related to a strong optomechanical coupling. We illustrate our ideas by focusing on a time-crystal engine and discuss power generation, energy-conversion efficiency, and the emergence of metastable behavior in these limits.

The interaction between light and mechanical vibrations in a cavity is often exploited to produce higher-order sidebands (HOSs) or combs, which are used in optical communication networks and spectroscopy, among other things. Although an extensive study of optomechanically induced HOSs has been done, their proper control and manipulation using only continuous-wave (cw) laser drive are still to be explored. Here, we employ a mechanical parity-time-($\mathcal{PT}$) symmetric structure with optically induced gain and loss. It allows us to manipulate the flow of mechanical energies between the cavities, which has consequences on the optical response of the cavities. Based on our numerical investigations, we find that the higher-order optical sidebands start to emerge if $\mathcal{PT}$ symmetry is broken. We precisely control the number of higher-order sideband lines by adjusting the coupling rate between the cavities with fixed drive power. In addition, we observe that the exceptional point (EP) induces the formation of two synchronized higher-order optical-sideband spectra, which opens a promising EP-based platform for the realization of optical readout of various mechanical synchronization phenomena, copies of the optomechanical frequency comb, sensing, and synchronization of remote clock time, among other things.

The Aharonov-Bohm (AB) cage enables localized confinement with nondiffractive propagation for arbitrary excitation. In this study, we introduce an anti-parity-time (anti-$\mathcal{PT}$) symmetric imaginary coupling in a generalized Creutz ladder to construct a non-Hermitian AB cage with tunable flat-band energy. We investigate compact localized states and complete localization dynamics, and show that non-Hermiticity affects the localization probability distributions and increases the oscillation period of the AB cage dynamics. Non-Hermitian engineering of the decoupled core of the AB cage is the essential point in our proposal. Our approach is widely applicable to a more general situation and can facilitate the manipulation of localization in physics.

We systematically investigate the spatial-temporal patterns of rogue waves in $N$-component coupled defocusing nonlinear Schrödinger equations where $N\ge 2$. The fundamental rogue-wave solutions are given in a unified form for both focusing and defocusing cases. We establish the quantitative correspondence between modulation instability and rogue-wave patterns, which develops the previously reported inequality relation into an equation correspondence. As an example, we demonstrate phase diagrams for rogue-wave patterns in a two-component coupled system, based on the complete classification of their spatial-temporal structures. The phase diagrams enable us to predict various rogue-wave patterns, such as the ones with a four-petaled structure in both components. These results are meaningful for controlling the rogue-wave excitations in two orthogonal polarization optical fibers.

In this work we employ a unitary transformation with a suitable parameter to convert the quantum Rabi-Stark model into a Jaynes-Cummings-like model. Subsequently we derive the analytical energy spectra in the ultrastrong coupling regime. The energy spectra exhibit a phenomenon known as spectral collapse, indicating the instability of the model due to the unboundedness of its energy from below at higher coupling parameters. To stabilize the Rabi-Stark model, we introduce a nonlinear photon-photon interaction term. We then compare the modified model with the original model in the classical oscillator limit. Interestingly, we observe a regular “staircase” pattern in the mean photon number of the ground state. This pattern exhibits a fixed slope and equal step width, which we determine analytically. Moreover, we analytically determine the phase boundary, which slightly differs from that in the original Rabi-Stark model. These findings offer insights into the investigation of those superradiant phase transitions that are unbounded from below due to the phenomenon of spectral collapse.

Quantum correlations that violate the Bell inequality cannot be explained by any local-hidden-variable theory that is measurement independent. However, this violation merely signifies the incompatibility of the underlying assumptions of reality, locality, and measurement independence, without providing a quantitative measure of the extent to which each assumption is violated. In contrast, Hall introduced a measure for each of the following assumptions: indeterminism, signaling, and measurement dependence, and Hall also generalized the Bell-Clauser-Horne-Shimony-Holt inequality, which provides a quantitative trade-off relationship between these assumptions. In this paper, we consider the introduction of hidden variables to be an essential assumption of Bell's theorem and introduce a quantification of hidden variables, which we term “hiddenness.” We derive a trade-off relation between hiddenness and measurement dependence that applies to any local-hidden-variable theory.

Quantum parameter estimation with Hermitian systems has been applied in various fields, but there are relatively few results concerning non-Hermitian systems. Here, we study the quantum parameter estimation for general non-Hermitian Hamiltonians and derive an intuitive expression of quantum Fisher information (QFI) for pure states. Furthermore, we propose the condition for optimal measurements, which is applicable to both Hermitian and non-Hermitian Hamiltonians. To illustrate these results, we calculate and study the QFI of a specific parity-time $\left(\mathcal{PT}\right)$ -symmetric non-Hermitian Hamiltonian and give the optimal measurement. Surprisingly, we find some interesting properties of this $\mathcal{PT}$-symmetric Hamiltonian QFI, such as the mutations in QFI at exceptional point. Moreover, we also compare the variance of estimation generated by the optimal measurement with the theoretical precision bound to verify the condition for optimal measurements we proposed.

Synchronization blockade refers to an interferometric cancellation of quantum synchronization. In this paper, we show how the choice of synchronization measure and Hamiltonian symmetries affect the discussion of synchronization blockade. Using counting principles, we prove a general theorem that synchronization blockade cannot be observed in an $N$-level system when the coherent state used to define the diagonal limit-cycle state is in the full $\text{SU}\left(N\right)$ group. We present several illustrative examples of synchronization blockade in multilevel systems and prove that information-theoretic measures of synchronization can also observe synchronization-blockade-like behavior by an appropriate choice of the set of limit-cycle states.

Fermionic Ansatz state preparation is a critical subroutine in many quantum algorithms such as the variational quantum eigensolver for quantum chemistry and condensed-matter applications. The shallowest circuit depth needed to prepare Slater determinants and correlated states to date scales at least linearly with respect to the system size $N$. Inspired by data-loading circuits developed for quantum machine learning, we propose an alternate paradigm that provides shallower, yet scalable, $O\left(d{log}_2^{2}N\right)$ two-qubit gate-depth circuits to prepare such states with $d$ fermions, offering a subexponential reduction in $N$ over existing approaches in second quantization, enabling high-accuracy studies of $d\ll O(N/{log}_2^{2}N)$ fermionic systems with larger basis sets on near-term quantum devices.

A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum algorithm that proves the superiority of quantum computing over classical computing. It has a quadratic reduction in the query complexity of a database search and is known to be optimal when no a priori information about the elements of the database is provided. In this work we consider a probabilistic Grover search algorithm allowing nonzero probability of failure for a database with a general a priori probability distribution of the elements and minimize the number of oracle calls by optimizing the initial state of the quantum system and the reflection axis of the diffusion operator. The initial state and the reflection axis are allowed to not coincide and thus the quantum search algorithm rotates the quantum system in a three-dimensional subspace spanned by the initial state, the reflection axis, and the search target state in general. The number of oracle calls is minimized by a variational method, and formal results are obtained with the assumption of low failure probability. The results show that for a nonuniform a priori distribution of the database elements, the number of oracle calls can be significantly reduced given a small decrease in the success probability of the quantum search algorithm, leading to a lower average query complexity to find the solution of the search problem. The results are applied to a simple but nontrivial database model with two-value a priori probabilities to show the power of the optimized quantum search algorithm. The paper concludes with a discussion about the generalization to higher-order results that allows for a larger failure probability for the quantum search algorithm.

We consider the problem of devising suitable quantum error correction (QEC) procedures for a generic quantum noise acting on a quantum circuit. In general, there is no analytic universal procedure to obtain the encoding and correction unitary gates, and the problem is even harder if the noise is unknown and has to be reconstructed. The existing procedures rely on variational quantum algorithms (VQAs) and are very difficult to train since the size of the gradient of the cost function decays exponentially with the number of qubits. We address this problem using a cost function based on the quantum Wasserstein distance of order 1 ($Q{W}_1$). At variance with other quantum distances typically adopted in quantum information processing, $Q{W}_1$ lacks the unitary invariance property which makes it a suitable tool to avoid getting trapped in local minima. Focusing on a simple noise model for which an exact QEC solution is known and can be used as a theoretical benchmark, we run a series of numerical tests that show how, guiding the VQA search through the $Q{W}_1$, can indeed significantly increase both the probability of a successful training and the fidelity of the recovered state, with respect to the results one obtains when using conventional approaches.

Extracting electroweak observables from experiments on atomic parity violation (APV) using the Stark interference technique requires accurate knowledge of transition polarizabilities. In cesium, the focus of our paper, the $6S_{1/2}\to 7S_{1/2}$ APV amplitude is deduced from the measured ratio of the APV amplitude to the vector transition polarizability $\beta$. This ratio was measured with a $0.35\%$ uncertainty by the Boulder group [Science 275, 1759 (1997)]. Currently, there is a sizable discrepancy in different determinations of $\beta$ critically limiting the interpretation of the APV measurement. The most recent value [Phys. Rev. Lett. 123, 073002 (2019)] of $\beta =27.139\left(42\right)\mathrm{a}.\mathrm{u}.$ was deduced from a semi-empirical sum-over-states determination of the scalar transition polarizability $\alpha$ and the measured $\alpha /\beta$ ratio [Phys. Rev. A 55, 1007 (1997)]. This value of $\beta$, however, differs by $\approx 0.7\%$ or $2.8\sigma$ from the previous determination of $\beta =26.957\left(51\right)$ by [Phys. Rev. A 62, 052101 (2000)] based on the measured ratio $M1/\beta$ of the magnetic-dipole $6S_{1/2}\to 7S_{1/2}$ matrix element to $\beta$. Here, we revise the determination of $\beta$ by [Phys. Rev. Lett. 123, 073002 (2019)], using a more consistent and more theoretically complete treatment of contributions from the excited intermediate states in the sum-over-states $\alpha /\beta$ method. Our result of $\beta =26.887\left(38\right)\mathrm{a}.\mathrm{u}.$ resolves the tension between the $\alpha /\beta$ and $M1/\beta$ approaches. We recommend the value of $\beta =26.912\left(30\right)$ obtained by averaging our result and that of [Phys. Rev. A 62, 052101 (2000)].

From the generalized fluctuation-dissipation theorem, it is known that a body at rest made of nonreciprocal material may experience a torque, even in vacuum, if it is not in thermal equilibrium with its environment. However, it does not experience self-propulsion in such circumstances, except in higher order. Nevertheless, such a body may experience both a normal torque and a lateral force when adjacent to an ordinary surface with transverse translational symmetry. We explore how these phenomena arise, discuss what terminal velocities might be achieved, and point out some of the limitations of applying our results to observations, including the Lorenz-Lorentz correction and the cooling due to radiation. In spite of these limitations, the effects discussed would seem to be observable.

We developed a theoretical method to study the high-order harmonic generation (HHG) from a gas target in an intense laser pulse. We obtain the microscopic HHG by solving the time-dependent Schrödinger equation with a single-active-electron approximation and the macroscopic HHG by summing over all the microscopic HHG with phase matching and self-absorption in two scales. One is in the laser wavelength scale, within which the laser peak intensity does not change while the propagation phase changes. Another is in the laser beam waist scale, within which the laser intensity and Gouy phase shift change. Taking the Ar atom as an example, we calculate the macroscopic HHG energy distribution and divergence. We also discuss the dependency of the macroscopic HHG on the gas pressure and gas jet position.

A pair of vortices, one of the multiple vortices, exhibits more adjustable parameters and attractive characteristics compared with a single vortex. By introducing a vortex pair on the Gaussian beam, we not only realize both longitudinal and transverse asymmetrical spin splittings, but also achieve the symmetrical ones via the purely optical strategy. Namely, the symmetries of the spin splittings can be controlled flexibly by the tunable vortices, offering another degree of freedom for the photonic spin Hall effect. Based on the geometric phase theory, physical insights into the symmetry-controllable spin Hall shifts involving the initial phase from the incident vortex beam are provided. These findings reveal the influence of vortices on the symmetry of the photonic spin Hall effect and provide further potential methods for developing spin-based nanophotonic applications.

Spontaneous parametric down-conversion (SPDC) has shown great promise in the generation of pure and indistinguishable single photons. Photon pairs produced in bulk crystals are highly correlated in terms of transverse space and frequency. These correlations limit the indistinguishability of photons and result in inefficient photon sources. Domain-engineered crystals with a Gaussian nonlinear response have been explored to minimize spectral correlations. Here we study the impact of such domain engineering on spatial correlations of generated photons. We show that crystals with a Gaussian nonlinear response reduce the spatial correlations between photons. However, the Gaussian nonlinear response is not sufficient to fully eliminate the spatial correlations. Therefore, the development of a comprehensive method to minimize these correlations remains an open challenge. Our solution to this problem involves simultaneous engineering of the pump beam and crystal. We achieve purity of single-photon state up to 99% without any spatial filtering. Our findings provide valuable insights into the spatial waveform generated in structured SPDC crystals, with implications for applications such as boson sampling.

We report on a scheme for loading dysprosium atoms into a narrow-line three-dimensional magneto-optical trap (3D MOT). Our approach replaces the conventional Zeeman slower with a two-dimensional (2D) MOT operating on the broad 421-nm line to create a high-flux beam of slow atoms. Even in the absence of a push beam, we demonstrate efficient loading of the 3D MOT, which operates on the narrower 626-nm intercombination line. Adding push beams working at either 421 nm or 626 nm, significant enhancement of the loading rate is achieved. We reach the best performance, with an enhancement factor of 3.6, using a push beam red-detuned to the 626-nm line. With loading rates greater than ${10}^8\text{atoms/s}$ achieved at a moderate oven reservoir temperature of ${800}^{\circ }\mathrm{C}$, our method offers similar or greater performance than Zeeman-slower-based systems. Our 2D-MOT-based approach constitutes a promising first step towards state-of-the-art quantum gas experiments with several advantages over the Zeeman-slower-based setup and is readily adaptable to other open-shell lanthanides.

Despite very promising results, capturing the dynamics of complex quantum systems with neural-network ansätze has been plagued by several problems, one of which is stochastic noise that makes the dynamics unstable and highly dependent on some regularization hyperparameters. We present an alternative general scheme that enables one to capture long-time dynamics of quantum systems in a stable fashion, provided the neural-network ansatz is normalized, which can be ensured by the autoregressive property of the chosen ansatz. We then apply the scheme to time-dependent quench dynamics by investigating the Kibble-Zurek mechanism in the two-dimensional quantum Ising model. We find an excellent agreement with exact dynamics for small systems and are able to recover scaling laws in agreement with other variational methods.

Dynamics-based certification of quantumness is an approach to witnessing the nonclassical character of some continuous-variable states, under the assumption that their dynamics is known. Contrary to other tests of nonclassicality for single systems, it does not require sequential measurements. This family of protocols was introduced for harmonic dynamics. In this work we discuss dynamics-based certification for one degree of freedom evolving under a generic time-independent Hamiltonian. We characterize the conditions under which such a certification is possible. Several examples are explicitly studied, some that are approximately harmonic in the limits of low energy (Kerr nonlinearities, the pendulum, and the Morse potential) and one that is not (the particle in an infinite well).