We calculate the parity nonconserving (PNC) electric-dipole ($E1$) transition amplitudes for the $5s\text{–}6s$ and $5s\text{–}4d_{3/2}$ transitions in Rb and ${\mathrm{Sr}}^{+}$. Our results include both the nuclear-spin-independent and nuclear-spin-dependent contributions, with particular emphasis on the potential effects of a hypothetical additional $Z^{\prime }$ boson. We highlight possible advantages of using light atoms in searches for such new interaction. The ratio of the contribution of a low-mass $Z^{\prime }$ boson to the contribution of the Standard Model $Z$ boson to PNC effects increases rapidly (faster than $1/Z^2$) with decreasing nuclear charge $Z$. Another advantage is that theoretical interpretations of experiments in lighter systems may be carried out with a higher accuracy than that in Cs, ${\mathrm{Ba}}^{+}$, Fr, and ${\mathrm{Ra}}^{+}$.

Relativistic calculations for the $g$ factor of the lowest excited states $2p_{1/2}$ and $2p_{3/2}$ of lithiumlike ions over a wide range of the nuclear-charge numbers $Z=10\text{–}92$ are presented. Interelectronic interaction is considered within perturbation theory up to the second order. One-loop QED contributions are calculated to all orders in $\alpha Z$. Leading contributions of the nuclear-recoil effect are taken into account. The quadratic and cubic terms in magnetic field are considered as well. A set of screening potentials is used in all calculations to estimate the unknown higher-order correlation effects. The most accurate theoretical predictions for the $g$ factor of the $2p_j$ states are obtained, with uncertainties at the parts-per-million level.

We investigate strong-field ionization of helium atoms exposed to an intense infrared (IR) laser field assisted by a weak extreme-ultraviolet (XUV) field, where the XUV photon energy is below the ionization potential of helium, prohibiting direct single-photon ionization. Despite its low intensity, the XUV field enhances the ionization probability by nearly 3 orders of magnitude compared to the case with the IR field alone. By varying the XUV intensity, we demonstrate that this enhancement stems from strong-field ionization assisted by single-XUV-photon absorption. Using the strong-field approximation model, we disentangle the contributions of direct and rescattered electrons to the photoelectron energy spectrum. Our results reveal that direct ionization is primarily enhanced near the zero crossing of the IR field, whereas rescattered electron ionization is enhanced near the field maximum.

We show that superficially similar implementations of Stern-Gerlach Interferometers (SGIs) are expected to differ dramatically in their sensitivity to fields transverse to the primary acceleration direction. These transverse fields unavoidably accompany any static magnetic or electric field gradients and have been shown by Comparat [Phys. Rev. A 101, 023606 (2020)] to limit the precision application of SGIs. As a concrete example, we consider SGIs with ultracold rubidium Rydberg atoms accelerated by spatially varying electric fields. We find that the deleterious effect of transverse fields imply that only some implementations (sequences of field gradients and internal state swaps) may exhibit fringes with high visibility.

Energy is a fundamental quantity in characterizing the dynamic evolution of quantum systems, while energy evolution in a nonequilibrium system remains elusive. The realization of a long-lived nonequilibrium state is a favorite method for probing the energy dynamics in the system. Here, we systematically explore the nonequilibrium energy dynamics on the basis of a spherical unitary Fermi gas. The long-lived breathing oscillation, protected by SO(2,1) symmetry, acts as a sensitive probe for precisely measuring energy evolution, enabling quantitative comparisons with theoretical calculations. Unlike in equilibrium systems, the energy evolution in a nonequilibrium system depends on collective motions and is characterized by the dynamic virial theorem. The trapping potential and internal energies increase with the energy injection while oscillating nearly ${\text{180}}^{\circ }$ out of phase. We further theoretically develop and experimentally demonstrate the dynamic virial theorem beyond the harmonic trap. Our work achieves time-resolved observations of energy evolution, providing deep insights into energy injection and redistribution in a nonequilibrium quantum system.

We report a striking $E^4$ energy dependence of transition-radiation (TR) intensity, observed at Brewster's angle in the optical region and emitted by ultrarelativistic charged particles traversing a specially engineered one-dimensional photonic crystal (PhC). This strong scaling—absent in conventional Cherenkov or TR—persists until saturation sets in at Lorentz factors $\gamma \sim \sqrt{N_s}$ (where $N_s$ is the number of unit cells). The effect originates from a Dirac conelike band structure in the dispersion relation of the PhC, analogous to that of graphene, which emerges when the slab thicknesses within each period satisfy the proportion $a_b/a_{\varepsilon }=(\sqrt{\varepsilon +b}-\varepsilon )/(b-\sqrt{\varepsilon +b})$. Remarkably, for both this periodic structure and a complementary class of disordered stacks exhibiting Brewster randomness [Z. Gong et al., Proc. Natl. Acad. Sci. USA 122, e2413336122 (2025)], the radiation problem admits an exact analytical solution at forward and backward Brewster observation angles. In the disordered case, a strong $N_s^2$ dependence of intensity on slab number $N_s$ yielding pronounced directivity either in the forward or backward direction, depending on the type of randomness, was reproduced. The radiation formation zone remains limited ($\sim \lambda /2$) even for ultrarelativistic particles—unlike x-ray TR detectors—making this system a promising platform for compact, energy-sensitive detection of relativistic particles in the optical regime.

The optical spin Hall effect has been extensively observed in various spatially structured beams. In this work we actively break the rotational symmetry of a radially polarized beam carrying an optical vortex through the off-axis phase singularity, thereby systematically investigating the induced optical spin Hall effect. We propose and generate radially polarized beams carrying an off-axis optical vortex, termed radially polarized off-axis vortex beams (RPOffVBs), and study their evolutions of both state of polarization and spin angular momentum (SAM) during the focusing process. By changing the off-axis distance of the phase singularity and/or the position of the relative focus, it is shown that the SAM density distribution of the RPOffVB can be controlled, while their total SAMs remain conserved. Moreover, it is observed that the transverse separation phenomenon of the SAM density distribution in the focal field region, where the separation of left-handed and right-handed circular polarization components—caused by their difference in Bessel function orders—results in asymmetric local SAM density distribution and the emergence of the optical spin Hall effect. This study provides insights into the SAM characteristics of focused off-axis vortex beams with radial polarization and contributes to the development of advanced optical manipulation and polarization imaging technologies.

We present a theoretical analysis of power redistribution among field components when a linearly polarized ordinary Gaussian beam propagates at an arbitrary angle $\theta$ relative to the optical axis of a uniaxial crystal. Closed-form expressions for the fractional power of each Cartesian component are derived as functions of both $\theta$ and the normalized crystal thickness $y_r$. Each power function separates into a thickness-independent asymptotic term and an oscillatory term driven by ordinary-extraordinary eigenmode interference. In the thick-crystal limit, the known on-axis result is recovered $(P_z=25\% \text{at} \theta =0^{\circ })$, but finite-thickness oblique propagation substantially exceeds this ceiling: at $\theta \approx 0.8^{\circ }$ and $y_r\approx 30$, the $z$ component reaches $P_z\approx 36.2\%$ of the total input power, a $45\%$ relative enhancement achievable at a physical crystal length of only $\approx 3.7\mathrm{mm}$. In the small-angle regime $(\theta \lesssim 2.5^{\circ })$, the power distribution is highly sensitive to the propagation angle, with a change of $\approx 1^{\circ }\text{–}{2}^{\circ }$ shifting $P_x$ by up to 0.34. This sensitivity originates from the quadratic dependence of the ordinary-extraordinary phase mismatch on $\theta$ near parallel propagation and grows linearly with crystal thickness. A closed-form characteristic sensitivity angle is derived, providing explicit design rules for engineering the sensitivity window. Three distinct operational regimes are identified, offering quantitative guidelines for optimizing power conversion and polarization control in uniaxial-crystal-based optical systems.

Superradiant lasers are promising candidates for ultrastable atomic clocks, but their frequency stability is fundamentally limited by cavity-pulling effects induced by cavity detuning. Here we propose a scheme to synchronously generate two ultranarrow superradiant lasers with stable frequencies by coupling two cavity modes to an atomic ensemble. We show that destructive interference between the cavity modes and the atomic ensemble suppresses the collective frequency shift. This mechanism enables the superradiant laser to operate precisely at the stable atomic transition frequency, rendering it insensitive to cavity detuning. As the cavity detuning increases, the linewidths of the superradiant lasers are reduced by approximately two orders of magnitude, reaching the microhertz regime under realistic conditions. Meanwhile, increasing the atom number enhances the emission intensity while preserving the ultranarrow linewidth. We further analyze how the emission frequencies and intensities of the two cavity modes depend on the coupling strengths and cavity detunings and we identify the parameter conditions required to generate ultranarrow superradiant lasers whose frequencies are locked to the atomic transition frequency. Our work may play an important role in advancing atomic clocks and a broad range of precision-metrology applications.

We derive a thermodynamically consistent quantum master equation that satisfies locality for quadratic systems coupled to independent and identical baths at each site. We show that the quasilocal Redfield equation coincides exactly with the Davies equation, which satisfies the detailed balance condition, due to cancellation of quantum coherence generated by each bath. This derivation does not rely on the secular approximation, which fails in systems with vanishing energy-level spacings. We discuss generalizations of our result to slowly driven quadratic systems and generic quantum many-body systems. Our result paves the way to a thermodynamically consistent description of quantum many-body systems.

We design a setup for creating almost maximally entangled two-qudit link between distant nodes which are weakly coupled with the interacting spin-$s$ bulk (processor). We exhibit that such a quantum link between spins of arbitrary spin quantum number can be formed when the system is prepared at sufficiently low temperature. We find that the Heisenberg and the bilinear-biquadratic (BBQ) spin-1 models are the potential candidates to obtain long-distance near-maximal entanglement in equilibrium. Beyond the static regime, we further show that initializing the bulk in a fully polarized state and the link in an appropriate qudit state allows the system to dynamically evolve into a highly entangled state under both Heisenberg and BBQ Hamiltonians. Our findings reveal that both the static and the dynamical protocols presented here remain efficient towards creating highly entangled two-qudit states even if the spin quantum numbers of the bulk is lower than that of the link.

We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries that allows for the classification of similar and dissimilar pairs based on global correlations, and enables generalization from just a few samples. Unlike GQML algorithms developed to date, we propose to focus on symmetry-aware measurement adaptation that outperforms unitary parametrizations. We compare GQML for similarity testing against classical deep neural networks and convolutional neural networks with Siamese architectures. We show that quantum networks demonstrate strong empirical performance gains over their classical counterparts in generalization. We explain this difference in performance by analyzing correlated distributions used for composing our dataset. We relate the similarity testing to problems that showcase a proven maximal separation between the bounded-error quantum polynomial time complexity class and the polynomial hierarchy. While the ability to achieve a formal advantage depends on how data are loaded, we discuss how similar problems can benefit from quantum machine learning. Finally, we present a 40-qubit hardware implementation of our quantum model, using a superconducting processor (IBM Kyiv), showing remarkable scalability and resilience to noise.

We study the first detected recurrence time problem of continuous-time quantum walks on graphs. While previous works have employed projective measurements to determine the first return time, we implement a protocol based on weak measurements on a dilated system, enabling minimally invasive monitoring throughout the evolution. To achieve this, we implement a weak measurement protocol theoretically and complement it with both numerical simulations and investigations on an IBM quantum computer. Despite the implementation of a generalized measurement, the proposed protocol provides a description purely within the Hilbert space of the quantum system. Our results reveal that for rank-one monitored, pure initial states, the first hitting timescales inversely with the coupling parameter between the ancilla and the quantum system.

Many years have passed since the conception of the quintessential method of the shortcut to adiabaticity known as counterdiabatic driving (or transitionless quantum driving). However, this method appears to be energetically cost-free and thus continually challenges the task of quantifying the amount of energy it requires to be achieved. This paper proposes that the energy cost of controlling a closed quantum system using the counterdiabatic method can also be assessed using the instantaneous excess work during the process and related quantities, such as the time-averaged excess work. Starting from the Mandelstam-Tamm bound for driven dynamics, we show that the speedup of counterdiabatic driving is linked to the spreading of energy between the eigenstates of the total Hamiltonian, which is necessarily accompanied by transitions between these eigenstates. Nonetheless, although excess work can be used to energetically quantify these transitions, it is well-known that the excess work is zero throughout the entire process under counterdiabatic driving. To recover the excess work as an energetic cost quantifier for counterdiabatic driving, we propose a different interpretation of the parameters of the counterdiabatic Hamiltonian, leading to an excess work different from zero. We illustrate our findings using the Landau-Zener model.

We investigate the effects of the tensor polarizability of a nucleus on the bound-state energy levels and obtain a general formula for the contribution of the tensor polarizability to the energy levels in two-body bound systems. In particular, it is demonstrated that the tensor polarizability leads to mixing between states with different orbital angular momenta. The effect of tensor polarizability is evaluated for the hyperfine-structure components of $P$ states and for the mixing of $S$ and $D$ states in muonic deuterium.

We propose a flexible Raman lattice system for alkaline-earth-like atoms to theoretically investigate localization behaviors in a quasiperiodic lattice with controllable non-Hermiticity. Our analysis demonstrates that critical phases and mobility edges can arise by adjusting the spin dependence of the incommensurate potentials in the Hermitian regime. With non-Hermiticity introduced by spin-selective atom loss, our calculations reveal that critical localization behavior in this system can be suppressed by dissipation. Our work provides insights into the interplay between quasiperiodicity and non-Hermitian physics, offering a different perspective on localization phenomena.

Cavity optomechanics has enabled slow-to-fast light conversion, but traditional optomechanic systems suffer from limited tunability due to fixed mechanical frequencies. To address this constraint, we introduce a magnon degree of freedom into an optomechanical system, constructing a system that integrates photons, phonons, and magnons. We establish the theoretical model of the optomagnonic-Laguerre-Gaussian rotational system and present numerical simulations of Fano resonances and group delay. By manipulating the magnon degree of freedom, we not only achieve slow-to-fast light conversion associated with magnons but also successfully realize such conversion effects associated with mechanical rotation—this achievement effectively overcomes the inherent tunability limitations of pure optomechanical systems and expands the frequency coverage of light conversion effects. Notably, we numerically demonstrate bidirectional tunable conversion between slow and fast light (including both slow-to-fast and fast-to-slow regimes) by continuously modulating the control field frequency to adjust the detuning between the control field and the cavity mode. Additionally, our results show that adjusting optomagnonic parameters enables dynamic switching between slow light and fast light at multiple frequencies. This work provides a flexible platform for multifrequency group velocity control, with potential applications in all-optical networks and quantum communications.

Compressing an ultrafast optical pulse down to a subcycle scale is an essential approach to improving temporal resolution in light-matter interaction. Considering that temporal far-field approaches have a half-cycle limit in generating subcycle pulses, recently we have proposed to break this limit in the temporal near field, and generate sub-half-cycle pulses via inverse Compton scattering in a sub-half-wavelength spatially confined optical driving field, which is generated in a line slit constructed by two sapphire hexagonal waveguides. While in principle one can generate an ultrafast optical pulse with pulse width narrower than 0.1 cycle, the practical fabrication of sapphire hexagonal waveguides and the line-slit-confinement structure is highly challenging. Here, we propose to replace the line slit with a flat slit constructed with two sapphire square waveguides, which can not only simplify the fabrication of the field-confining structure, but also evidently increase the single-pulse energy of the yielded sub-half-cycle pulse. For example, using a 0.4-THz 1-ps optical driving field and a 1-fs 3-MeV 0.1-nC electron bunch, a 0.12-cycle 5.1-fs-width midinfrared femtosecond pulse can be obtained, while the single-pulse energy is increased from 3.3 to 5.2 pJ, due to the increased fraction of the driving-field energy in the flat slit.

We investigate the fundamental properties of the caustic curve associated with an optical beam by performing a kinematic analysis of its spectral phase. By parametrizing the caustic curve in terms of the first and second derivatives of the phase, we characterize the kinematic behavior of the trajectory and identify the conditions under which singularities arise—specifically, when the caustic velocity vector either vanishes or becomes undefined. Our results show that the third derivative of the spectral phase plays a central role: Its roots and discontinuities determine the occurrence of singularities. A detailed analysis distinguishes two classes of singularities: avoidable and unavoidable. Avoidable singularities preserve the smoothness of the caustic trajectory, whereas unavoidable ones disrupt it, giving rise to cusp points. Both classes of singularities strongly influence the mapping from spectral to spatial coordinates that governs the generation of the optical beam. Consequently, the light intensity distribution undergoes pronounced modifications in the vicinity of these points, potentially producing regions of enhanced intensity and steep intensity gradients. These findings provide a kinematic extension to the standard catastrophe classification by introducing the concepts of avoidable and unavoidable singularities, thereby broadening the potential of caustic beams in structured light applications.