Dynamical decoupling (DD) and bath engineering are two parallel techniques employed to mitigate qubit decoherence resulting from their unavoidable coupling to the environment. Here we present a hybrid DD approach that integrates pulsed DD with bath spin polarization to enhance qubit coherence within the central spin model. This model, which can be realized using GaAs semiconductor quantum dots or analogous quantum simulators, demonstrates a significant extension of the central spin's coherence time by approximately two to three orders of magnitude that compared with the free-induced decay time, where the dominant contribution from DD and a moderate improvement from spin-bath polarization. This study, which integrates uniaxial dynamical decoupling and auxiliary bath-spin engineering, paves the way for prolonging coherence times in various practical quantum systems, including GaAs/AlGaAs, silicon, and Si/SiGe. And this advancement holds substantial promise for applications in quantum information processing.

We present benchmarking results for the nonvariational quantum walk-based optimization algorithm (nonvariational QWOA) applied to the weighted MaxCut problem, using classical simulations for problem sizes up to $n=31$. The amplified quantum state, prepared using a quadratic number of alternating unitaries, achieves a constant average-case measurement probability for globally optimal solutions across these problem sizes. This behavior contrasts with that of classical heuristics, which, for NP-hard optimization problems, typically exhibit solve probabilities that decay as problem size increases. Performance comparisons with two local-search heuristics on the same benchmark instances suggest that the nonvariational QWOA may offer a meaningful advantage by scaling more favorably with problem size. These results provide supporting evidence for the potential of this quantum heuristic to achieve quantum advantage, though further work is needed to assess whether the observed performance scaling persists at larger problem sizes, and to confirm whether similar performance trends are observed for the other problem classes to which the nonvariational QWOA is designed to generalize.

Within a fully relativistic framework, the one-loop self-energy correction for a bound electron is derived and extended to incorporate the effects of external thermal radiation. In a series of previous works, it was shown that in quantum electrodynamics at finite temperature, the description of effects caused by blackbody radiation can be reduced to using the thermal part of the photon propagator. As a consequence of the nonrelativistic approximation in the calculation of the thermal one-loop self-energy correction, well-known quantum-mechanical phenomena emerge at successive orders: the Stark effect arises at leading order in $\alpha Z$, and the Zeeman effect appears in the next-to-leading nonrelativistic correction, accompanied by diamagnetic contributions and their relativistic refinements, among other perturbative corrections. The fully relativistic approach used in this work for calculating the SE contribution allows for accurate calculations of the thermal shift of atomic levels, in which all these effects are automatically taken into account. The hydrogen atom serves as the basis for testing a fully relativistic approach to such calculations. Additionally, an analysis is presented of the behavior of the thermal shift caused by the thermal one-loop correction to the self-energy of a bound electron for hydrogen-like ions with an arbitrary nuclear charge $Z$. The significance of these calculations lies in their relevance to contemporary high-precision experiments, where thermal radiation constitutes one of the major contributions to the overall uncertainty budget.

This paper proposes a scheme to measure atomic parity violation in barium ions at $\le 0.1\%$ precision. The scheme is based on using multiion entangled states to common-mode reject parity-conserving systematic shifts and selectively detect a parity-violating vector light shift. This measurement protocol eliminates the need to suppress a leading systematic by 11 orders of magnitude, as is required in the single-ion measurement scheme [Phys. Rev. Lett. 70, 2383 (1993)]. Furthermore, the protocol can be combined with the use of integrated photonic waveguides in an architecture that is scalable to large ion numbers, with a proportional increase in measurement precision.

The helium hydride ion (${\mathrm{HeH}}^{+}$) represents the simplest molecular system composed of nuclei with unequal charges and serves as a model system of unique importance to molecular structure theory. We present high-precision calculations of the leading relativistic ($m{\alpha }^4$) and QED ($m{\alpha }^5$) corrections for the ground electronic state of ${\mathrm{HeH}}^{+}$, performed within the Born-Oppenheimer approximation and using effective operators in the nonrecoil limit. The use of explicitly correlated Gaussian (ECG) and cusp-enforced $r\mathrm{ECG}$ basis functions, combined with regularization techniques for singular operators, yields a substantial reduction in numerical uncertainty compared to previous calculations. The resulting potentials reproduce rovibrational transition energies with few-megahertz uncertainties (${10}^{-4}–{10}^{-5}{\mathrm{cm}}^{-1}$) and pure rotational transitions with submegahertz accuracy (${10}^{-5}–{10}^{-6}{\mathrm{cm}}^{-1}$), enabling comparison with the most precise spectroscopic data for ${\mathrm{HeH}}^{+}$ isotopologues. These results provide a solid foundation for including higher-order effects and establish ${\mathrm{HeH}}^{+}$ as a primary molecular system alongside ${\mathrm{H}}_2$ for high-resolution spectroscopy, astrophysical modeling, and precision tests of fundamental physics.

We report a 4.9-ppb measurement of the positronium $1^3{S}_1\to 2^3{S}_1$ interval using continuous-wave two-photon laser spectroscopy. The transition is detected via photoionization by the same excitation laser. The resulting positrons are guided to a microchannel plate detector, surrounded by scintillators to detect the annihilation photons in coincidence, thereby reducing the background. A Monte Carlo line-shape simulation, accounting for effects such as the second-order Doppler shift and the AC Stark shift, is used to extract a transition frequency of $1233607224.1\left(6.0\right)\text{MHz}$, consistent with the previous 2.6-ppb determination of this transition and with the most recent QED calculations at order $\mathcal{O}\left[{\alpha }^7{ln}^2(1/\alpha )\right]$, which predict $1233607222.12\left(58\right)\text{MHz}$. Combining the two measurements gives $1233607218.1\left(2.8\right)\text{MHz}$, reducing the tension with QED to about $1.4\sigma$. We also present a semianalytical line-shape model of $1^3{S}_1\to 2^3{S}_1$ of positronium, which shows excellent agreement with detailed simulations and is validated by the experimental data. This expands on previous work with stable atoms by incorporating effects such as limited lifetime of the atoms, photoionization, and AC Stark shift. The line-shape modeling is also applicable to other unstable systems, such as muonium. This provides a powerful tool for optimizing the experimental parameters and gaining deeper insights without the need for computationally intensive simulations.

Recently thermally-assisted-occupation density-functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] has been demonstrated to be an efficient and accurate electronic structure method for studying the ground-state properties of large multireference (MR) systems at absolute zero. To explore the thermal equilibrium properties of large MR systems at finite electronic temperatures, in the present work, we propose the finite-temperature (FT) extension of TAO-DFT, denoted as FT-TAO-DFT. As well, to unlock the dynamical information of large MR systems at finite temperatures, FT-TAO-DFT is combined with ab initio molecular dynamics, leading to FT-TAO-AIMD. In addition, we also develop FT-TAO-DFT-based quantum mechanics and molecular mechanics (QM/MM), denoted as FT-TAO-QM/MM, to provide a cost-effective description of the thermal equilibrium properties of a QM subsystem with MR character embedded in an MM environment at finite temperatures. Moreover, the FT-TAO-DFT, FT-TAO-AIMD, and FT-TAO-QM/MM methods are employed to explore the radical nature and infrared (IR) spectra of $n$-acenes ($n=2–6$), consisting of $n$ linearly fused benzene rings, in vacuum and in an argon (Ar) matrix at finite temperatures. According to our calculations, for $n$-acenes at 1000 K or below, the electronic temperature effects on the radical nature and IR spectra are very minor, while the nuclear temperature effects on these properties are noticeable. For $n$-acene in an Ar matrx at absolute zero, the Ar matrix has minimal impact on the radical nature of $n$-acene, while the codeposition procedure of $n$-acene and Ar atoms may affect the IR spectrum of $n$-acene.

An efficient field-free molecular orientation in the ground electronic state of the LiH molecule is steered by the linearly overlapping two-color laser pulses of the fundamental frequency $\omega$ and its second harmonic $2\omega$ through the quasiresonant (three-photon) hyper-Raman transitions with negligible (final) vibrational excitations, where the vibrational state $v=1$ is selected as the intermediate state. A relatively large positive detuning is needed to trigger such nearly pure rotational excitations, and the required laser intensity becomes larger with the increase of the detuning. Interestingly, it is also found that either the relative phase or the delay time between the two harmonic pulses can be used to control well the degree and direction of the field-free molecular orientation, which is closely related to the periodical variations of the resulting maximal electric fields in the positive and negative directions and indicates the dominated hyper-Raman process near the maximal laser intensity. Of course, since more vibrational excitations may occur when the delay time between the two harmonic pulses becomes larger, a considerable overlap between them is also important. Finally, the effects of the intensity and duration of the second harmonic pulse on the degree of the field-free orientation are also discussed.

For precision atomic magnetometry, inert buffer gas is included in alkali-metal vapor cells to significantly broaden hyperfine transitions, which facilitates optical pumping and reduces diffusive relaxation, while also providing nonradiative excited-state quenching. We show low-buffer gas pressure (below 50 Torr) alkali-metal vapor cells with resolved hyperfine manifolds can also yield high-performance magnetometers. For high polarization in ${}^{87}\mathrm{Rb}$, we optically pump $F=2$ states with narrow linewidth ${\sigma }_{+}$ light, while tuning a probe beam to depopulate $F=1$ states ($\mathrm{\Delta }\nu =6.8\mathrm{GHz}$ from $F=2$). The probe tuning then also provides $F=2$ detection with high optical rotation and low probe broadening; we demonstrate top-bottom gradiometry, within a single 25-Torr, 0.5-${\mathrm{cm}}^3\text{cell}$, that yields an Earth's field free-precession magnetometer sensitivity of 18 $\mathrm{fT}/\sqrt{\text{Hz}}$ with a 1 kHz bandwidth, as well as an RF magnetometer sensitivity of 12 $\mathrm{fT}/\sqrt{\text{Hz}}$ in a small band about 110 kHz.

The cluster Gutzwiller method is widely used to study the strongly correlated bosonic systems, particularly in the context of ultracold bosons in optical lattices, owing to its ability to provide a more precise description of quantum fluctuations. However, its utility is limited by the exponential increase in computational complexity as the cluster size grows. To overcome this limitation, we propose an artificial intelligence-based method known as $\mathrm{\Delta }$ learning. This approach constructs a predictive model by learning the discrepancies between low-precision (small cluster sizes) and high-precision (large cluster sizes) implementations of the cluster Gutzwiller method, requiring only a small number of training samples. By utilizing this predictive model, we can effectively forecast the outcomes of high-precision methods with high accuracy. We demonstrate the effectiveness of $\mathrm{\Delta }$ learning in predicting phase diagrams across various Bose-Hubbard models, achieving a significant reduction in computational resources and time. Furthermore, we compare the predictive accuracy of $\mathrm{\Delta }$ learning with other direct learning methods and find that $\mathrm{\Delta }$ learning exhibits superior performance in scenarios with limited training data. Therefore, when combined with the cluster Gutzwiller approximation, the $\mathrm{\Delta }$-learning approach offers a computationally efficient and accurate framework for exploring phase transitions in nonstandard Bose-Hubbard models within large, complex optical lattices, paving the way for future research in this area.

We investigate dynamical quantum phase transitions (DQPTs) in quantum systems that possess well-defined classical limits, focusing on the spinor Bose-Einstein condensate and the Lipkin-Meshkov-Glick model. We diagnose the DQPTs with the long-time average of the quantum Fisher information (QFI), showing that it abruptly changes at the transition point. Using mean-field and semiclassical approximations, we demonstrate that the long-time average of the QFI reveals universal behavior that persists across different systems.

Rapid modulation of the electromagnetic response in both time and space creates temporal boundaries in the medium and leads to “time reflection” and “time refraction” of light and to the eventual formation of the photonic time crystal within the modulated optical material, offering an alternative regime of light-matter interactions and a potential for practical applications, from nonresonant light amplification to tunable lasing. However, the conventional approach commonly used for the photonic time crystals and related phenomena that relies on the concept of effective time-dependent refractive index is fundamentally unsuitable to this domain of ultrafast modulation at optical timescales. We develop the appropriate theoretical description of the electromagnetic response and the resulting phenomena in this regime, and demonstrate not only quantitative but also qualitative differences from the conclusions obtained using the conventional approach.

In this article we introduce a continuum of families of nondiffracting spatiotemporal optical wave packets that exhibit caustic waveforms in both space and time. We show that their envelopes admit closed form expressions, consistent with conventional spatial caustic beams, when appropriate spatiotemporal spectral correlations and phase excitations are applied. The resulting propagation-invariant wave packets display rich spatiotemporal caustic structures (fold, cusp, and swallowtail) and feature tunable group velocities in free space. The spatiotemporal properties and dynamics of resultant caustic wave packets are accurately captured by catastrophe theory. We demonstrate that these space-time wave packets exhibit diffraction-free propagation in free space, while in an anomalously dispersive regime they undergo characteristic spatiotemporal evolution analogous to that of conventional caustic beams. We further discuss the feasible experimental schemes for synthesizing these wave packets via spatiotemporal holography. Such caustic-structured spatiotemporal waves extend the family of nondiffracting wave packets and may enable applications in micromachining, photonic topological textures, nonlinear spectroscopy, and ultrastable metrology.

This work unveils a novel and fundamental connection between structured light and topological field theory by showing how the natural geometrical setting for paraxial vector beams is that of an $\text{SU}\left(2\right)$ principal bundle over ${\mathbb{R}}^{2+1}$. Going beyond the usual high-order Poincaré sphere approach, we show how the nonseparable structure of polarization and spatial modes in vector beams is naturally described by a non-Abelian Chern-Simons gauge theory. In this framework, we link the Chern-Simons charge to spin-orbit coupling. This new insight on vector beams opens new possibilities for realizing and probing topological quantum field theories using classical optics, as well as laying the foundation for implementing topologically protected classical and quantum information protocols with structured light.

Squeezed states, characterized by the reduction of quantum fluctuations in specific quadratures, represent a vital resource for quantum metrology and information processing. A prominent platform for generating such states is the cavity optomechanical system, where mechanical oscillators can be prepared in squeezed states via tailored control. While periodic driving has served as a foundational technique for producing strong mechanical squeezing in this system, we propose an enhanced method based on deep reinforcement learning (DRL). Using both deep $Q$ network (DQN) and proximal policy optimization (PPO) algorithms, we optimize time-dependent control sequences. As a result, the machine-learning-driven control can surpass fundamental bounds imposed by traditional quantum control strategies due to the suppression of counter-rotating wave terms in the dynamics, with PPO achieving stronger squeezing than DQN. Moreover, our DRL-based scheme demonstrates robustness against both cavity decay and time delay in the control loop. This work presents the mapping of covariance matrix dynamics to reinforcement learning, significantly expanding artificial intelligence applications in continuous-variable quantum systems.

Coupling an emitter to a Fabry-Pérot optical cavity can provide a coherent and strong light-matter interface whose performance in a variety of applications depends critically on the emitter-photon coupling strength. Altering the typically spherical profiles of the cavity mirrors can improve this coupling strength, but directly optimizing the mirror shape is numerically challenging as the multidimensional parameter space features many local optima. Here we develop a two-step method to optimize mirror surface profiles while avoiding these issues. First, we optimize the target cavity eigenmode for the chosen application directly, and, second, we construct the mirror surfaces to retroreflect this optimized target mode at both ends of the cavity. We apply our procedure to different emitter-cavity coupling scenarios. We show that mirror shaping can increase the cooperativity of coupling to a central emitter by a factor of approximately 3 across a wide range of geometries and that, for coupling two or more emitters to a single cavity mode, the improvement factors can far exceed an order of magnitude.

We report the generation of helical electromagnetic radiation in a microwave cavity resonator, achieved by introducing mirror asymmetry, i.e., chirality, through a controlled geometric twist of the conducting boundary conditions. The emergence of this electromagnetic helicity is attributed to a nonzero spatial overlap between the electric and magnetic mode eigenvectors, quantified by $\text{Im}[{\vec{\mathbf{E}}}_i\left(\vec{r}\right)·{\vec{\mathbf{H}}}_i^{*}\left(\vec{r}\right)]$, a feature not observed in conventional cavity resonators. This phenomenon originates from magnetoelectric coupling between nearly degenerate TE and TM modes, resulting in a measurable frequency shift of the resonant modes as a function of the twist angle, $\varphi$. By dynamically varying $\varphi$, we demonstrate real-time, macroscopic manipulation of both electromagnetic helicity and resonant frequency. In addition to the bulk helicity induced by global geometric twist, internal helical corrugations break structural symmetry on the surface, introducing an effective surface chirality ${\kappa }_{\text{eff}}$, which perturbs the resonant conditions and contributes to asymmetric frequency tuning. Furthermore, we investigate the underlying mode coupling dynamics of the system, highlighting strong photon-photon interactions.

Precise control of photon-photon interactions is fundamental to quantum information processing. This study explores the simultaneous manipulation of opposite photon correlations (photon blockade and photon bunching) through optical parametric amplification. The nonlinear pump field, together with the driving field, establishes asymmetric photon-excitation pathways for whispering-gallery modes (WGMs), enabling the concurrent generation of distinct photon-photon interactions over a wide parameter range. Two sets of optimal parameters are derived to selectively induce destructive interference in each WGM: one set for the first WGM and the other for the second. Furthermore, we show the resulting photon correlations can be spatially switched between these modes by tuning the corresponding optimal parameters. This work elucidates the mechanism governing the coexistence and controllable switching of opposite photon correlations, offering another perspective for in-depth studies of quantum correlations and potential applications in switchable chiral quantum technologies.

In this study we investigate the statistical properties and dynamical behaviors of the finite-size Dicke-Stark model. We numerically obtain the energy spectrum and eigenstates within the extended coherent-state space and subsequently utilize the quantum dressed master equation to describe the open-system dynamics under strong coupling. Under thermal equilibrium conditions, analyses of the negativity, zero-time-delay two-photon correlation function, and atom-spin-squeezing parameters reveal that as the coupling strength increases, the light field undergoes a transition from photon bunching to antibunching and then back to bunching. The Stark field can modulate both the extrema of the two-photon correlation function and their corresponding coupling strengths. At low temperatures, the system exhibits entanglement and spin squeezing. As the temperature increases, the entanglement gradually diminishes, while strong coupling facilitates the preservation of the entanglement. The atom-spin squeezing is highly sensitive to thermal fluctuations and vanishes rapidly with increasing temperature. Furthermore, we illustrate the time-evolution properties of the thermodynamic nonequilibrium of the system from a low-temperature state to a high-temperature state. Our results demonstrate that an appropriately tuned Stark interaction can effectively prolong the survival time of quantum entanglement against thermal noise. This work contributes to the fundamental understanding of quantum phenomena in Dicke-Stark systems.

We investigate the lateral and rotary photon drag effects in a Doppler-free and Doppler-broadened duplicated two-level atomic system, focusing on the influence of the controlling field strength, the detuning, and the relative phase of applied fields. The phase of the applied fields plays a crucial role in modulating the absorption and dispersion characteristics in multiphoton resonance, enabling control over the photon drag effect. Beyond the multiphoton resonance condition, adjusting the detuning of the controlling field can influence photon drag based on the Zeeman coherence oscillations. The results indicate that small values of the controlling field strength lead to subluminal light propagation with an absorption doublet, while increasing the strength of the controlling field changes the system to superluminal light propagation with a gain doublet. Eliminating the multiphoton resonance condition significantly enhances the magnitude of photon drag while maintaining very low light absorption in both Doppler-free and Doppler-broadened regimes.