We derive a channel-resolved Lee-Huang-Yang correction and construct an extended Gross-Pitaevskii model for one-dimensional polar spin-1 quantum droplets. The fluctuation contribution separates into density and spin channels, which supports self-bound droplets even when the spin-independent mean-field interaction is repulsive. Stationary solutions exhibit a continuous crossover from solitonlike to flat-top droplets, accompanied by saturation of the chemical potential and peak density as the particle number increases. Within the parameter range examined here, linear Bogoliubov analysis together with weak-perturbation dynamics supports the stability of both droplet types. A quadratic-Zeeman quench reveals a finite-size crossover in breathing dynamics and distinct nonequilibrium roles of the density and spin fluctuation channels. Representative head-on collisions further show that the finite-size crossover modulates phase-sensitive nonlinear scattering, with in-phase impact producing coalescencelike central retention and out-of-phase impact favoring quasielastic separation. The analysis clarifies how density and spin fluctuations shape equilibrium structure and nonequilibrium response in low-dimensional polar spinor droplets.

Rotation and quantum tunneling are fundamental concepts in physics, and their interplay in the ultracold atomic systems is of particular interest. In this theoretical work, we investigate the tunneling dynamics of ultracold bosons in a rotating two-dimensional bosonic Josephson junction and show that they offer an alternative pathway for inferring the rotation frequency. Using mean-field and many-body analyses, we demonstrate that rotation strongly modifies the tunneling time period as well as the momentum and angular momentum dynamics. For a double well centered on the rotation axis, these observables exhibit distinct dependences on the rotation frequency, enabling its assessment from the tunneling dynamics. When the double well is displaced from the rotation axis, rotation induces asymmetric tunneling and partial self-trapping, allowing both the rotation frequency and the displacement to be inferred. We further show that an off-centered double well exhibits pronounced orientation-dependent dynamics, making it possible to determine the orientation of the potential. The many-body analysis further shows that the depletion dynamics is strongly influenced by rotation, providing an additional tool for assessing the rotation frequency. Finally, we consider a time-dependent protocol in which the double well is gradually set into rotation in the laboratory frame and identify characteristic signatures that depend on the switching time. Together, these results establish a comprehensive framework for inferring the rotation frequency, radial displacement, and orientation directly from the tunneling dynamics.

Kerr frequency combs in high-Q optical microresonators hold great promise for precision metrology, high-speed communications, and low-noise photonics. Understanding their coherence properties is essential for realizing compact, energy-efficient, and low-noise light sources. The interplay among pulsed injection, intrinsic and external noise, and optical feedback plays a central role in achieving highly coherent microcombs. Here, we study the coherence dynamics of Kerr frequency combs under continuous-wave (CW) and pulsed pumping within the framework of the Lugiato-Lefever equation. Using asymptotic analysis, we quantify the phase noise and timing jitter induced by pump source fluctuations and thermal noise. Numerical simulations further reveal comb degradation due to CW pump noise, while the inclusion of optical feedback restores the comb and narrows the line width through a mechanism analogous to that of external-cavity lasers.

Multimode intracavity frequency-doubled lasers can reach states of intensity-noise suppression orders of magnitude beyond the predictions of independent-mode partition statistics. I show that the ${\chi }^{\left(2\right)}$ coupled-wave dynamics in the doubling crystal obey a dissipation inequality: a fourth-moment functional of the intracavity intensity decreases monotonically under each forward nonlinear pass, driving the mode ensemble toward a constant-intensity manifold. This per-pass result is a strict Lyapunov inequality, and round-trip simulations show attraction to the same low-$M_4$, nearly constant-intensity state under the full cavity dynamics. I confirm the mechanism in an intracavity frequency-doubled ${\mathrm{Nd}\text{:}\mathrm{YVO}}_4$ laser with a lithium triborate (LBO) doubling crystal, observing a $100\times$ contrast between full and Fabry-Perot-filtered output noise at fixed detector bandwidth, well beyond the $\sqrt{N/N_f}$ statistical-averaging baseline. The argument depends only on the algebraic structure of the coupling: a coherent superposition of oscillators that share a quadratic dissipative channel. It therefore points to a general Lyapunov route to intensity-noise suppression in coupled oscillator systems, beyond the intracavity-doubled laser.

The steady final phonon occupation in waveguide optomechanical systems based on backward stimulated Brillouin-Mandelstam scattering has not been established in the strong-coupling regime. In this work, the displacement spectra of anti-Stokes optical modes and acoustic modes in tapered chalcogenide photonic crystal fiber are derived from the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) master equation. By analyzing the full spectral response, we indicate that the system can enter the strong-coupling regime through the emergence of normal-mode splitting and avoided crossings. Within a non-Hermitian framework, the threshold for strong coupling is identified, showing that it can be achieved at relatively low pump power even at room temperature. Furthermore, we derive a unified analytical expression for the final phonon occupation, revealing that quantum backaction and zero-point fluctuations impose additional fundamental limits that hinder the achievement of ground-state cooling. These results redefine the quantum limits of steady-state cooling in continuum optomechanics, motivating the search for new strategies to access the quantum ground-state of macroscopic phonons.

We propose a controllable quantum battery based on a one-dimensional dissipative coupled-cavity array, where the first cavity serves as the charger, the last cavity serves as the battery, and the intermediate cavities form the charger line. The charging process can be actively regulated through two distinct schemes: the frequency-tunable cavity scheme, where quantum-switch-controlled charging is achieved by detuning the frequency-tunable cavity, and the atomic scheme, where quantum-switch-controlled charging is achieved by detuning the two-level atom or by applying an external pump laser to the three-level atom. Both schemes offer effective control over energy transfer. However, as the array length increases, the charging performance degrades, especially in the atomic scheme. To overcome this limitation, we introduce an improvement strategy that enhances the hopping energies along the charger line. This approach significantly restores charging efficiency, enabling high-efficiency charging even over extended distances. Our work provides a deeper understanding of the charging mechanism in quantum batteries and establishes a theoretical foundation for realizing controllable charging in practical quantum devices.

Long-lived waiting-time beatings in two-dimensional electronic spectroscopy remain puzzling in strongly dephasing regimes, where excitonic coherence is expected to decay rapidly. These oscillations are often attributed to environmental memory, typically modeled by resonance with a discrete mode. Here we show that they can instead arise within a Bloch-Redfield framework when bath memory, enhanced by low-frequency spectral weight, is carried across ultrafast pulse boundaries. The resulting three-pulse kernel retains nonsecular population-coherence transfer through the propagation of bath memory across pulse boundaries, generating cross-peak beatings without invoking resonant modes. Benchmarks against a reaction-coordinate master equation, spanning frequencies from small to well above the exciton scale, confirm the predicted low-frequency coherence-revival mechanism. The beatings thus arise from environmental displacements, which drive population-coherence transfer while damping coherence at comparable rates, thereby sustaining a finite coherence amplitude.

Traditional Bell state measurement (BSM) and the product basis measurement (PBM) have been integral to nearly the entire development of quantum computing. Unlike the BSM and the PBM, a recently proposed two-qubit joint measurement called the elegant joint measurement (EJM) exhibits novel tetrahedral symmetry in its single-qubit reduced states. In Tavakoli et al. [Phys. Rev. Lett. 126, 220401 (2021)], a parametrized two-qubit isoentangled basis was proposed, with concurrence between 1/2 and 1, perfectly spanning the original EJM and conventional BSM. We present a two-qubit symmetric joint measurement having concurrence from 0 to 1/2, which is complementary to the parametrized EJM and connects the PBM and the original EJM. We investigate the symmetry of the current structure and its application in triangular networks. The results indicate that the reduced vectors of the current basis states exhibit rotational symmetry rather than mirror symmetry; moreover, the output probability distributions of three parties in the network explicitly demonstrate the expected permutation symmetry. Furthermore, we generalize the two-qubit symmetric joint measurement to the multiqubit systems with an even number of qubits.

Building on the framework developed by Meng et al. [Sci. Adv. 8, eabm7585 (2022)], we present an analytical study of a measurement-record-based state estimation method for a mechanical oscillator serving as one end mirror of a detuned-cavity system. Unlike conventional approaches, this method enables quantum-state verification without requiring the unconditional covariance matrix as an externally provided theoretical input. We construct a relative-estimate operator from causal and anticausal quantum Wiener filters and calculate its variance. The deviation from the causal conditional variance is defined as a reconstruction bias, whose magnitude is evaluated analytically. We show that, within experimentally relevant parameter regimes for typical quantum-state preparation, the reconstruction bias is sufficiently small to be neglected. As applications to state verification, we apply the method to proposals for macroscopic quantum entanglement mediated by electromagnetic interactions and for conditional momentum-squeezed states generated by homodyne detection and clarify the conditions under which the bias remains negligible and when the reconstruction bias becomes significant.

Dipole-dipole interactions in atomic vapors couple the optical responses of nearby atoms and give rise to few-body correlation effects. Earlier nonlinear spectroscopic studies have identified two-atom double-quantum coherences and higher-order multiatom responses, primarily involving sum-frequency combinations of optical transitions. Here we measure the nonlinear response of rubidium vapor under conditions comparable to prior high-order studies and identify previously unreported interaction-enabled correlations. These include ground-excited pair couplings as well as three-atom correlations in which one atom evolves in a zero-quantum coherence while others evolve optically. These results demonstrate that dipole-dipole interactions give rise to more complex collective coherence structures than previously observed.

When a two-level quantum system is driven periodically with a Rabi frequency $\mathrm{\Omega }$ comparable to the driving frequency ${\nu }_s$, the resonant transition frequency deviates from the bare energy gap—an effect known as the Bloch-Siegert shift. Observing sub-Hertz Bloch-Siegert shift is challenging due to its small energy scale and its mixing with other systematic shifts. Using a Floquet-engineered optical lattice clock, we directly observe this sub-hertz shift in ultracold atoms. We tune driving parameters to suppress micromotion and apply a self-comparison stroboscopic method to remove unwanted frequency shifts. Assisted by closed-loop feedback, we achieve high-precision results after one hour of averaging and longer integration will further improve the measurement accuracy.

We investigate the rotational response of confined two-dimensional quantum droplets, which emerge in a binary Bose mixture that is stabilized against collapse by beyond-mean-field effects. We consider both a harmonic and an anharmonic external confining potential. We go beyond the widely employed single-order-parameter model, maintaining separate order parameters for the two components, and calculating the lowest-energy state for various values of the angular momentum. For a population-balanced quantum droplet and sufficiently strong confinement, we find that for certain values of the angular momentum the droplet is excited in a “heterosymmetric” manner, with the two components carrying different vorticities. We additionally investigate the effects of a small population imbalance in the droplet. Apart from an energy increase associated with the population difference, the imbalance also lifts the double degeneracy of the heterosymmetric states, which characterizes the ${\mathbb{Z}}_2$-symmetric balanced droplet. The heterosymmetric mode is found to be favored by the energy term that captures the beyond-mean-field effects in the mixture.

We investigate the suppression of matter-wave Talbot interference under environmentally induced decoherence. The system is modeled as an atomic beam diffracted by a periodic grating whose transverse dynamics is described within the paraxial approximation. Environmental coupling is introduced through an effective open-system model that exponentially damps spatial coherences between diffracted components, allowing a continuous interpolation between the coherent Talbot regime and the incoherent far-field diffraction limit. In addition to the usual intensity and transverse-momentum distributions, we analyze the local probability flow associated with the diffracted matter wave. The corresponding Bohmian, or hydrodynamic, representation is used here as a diagnostic tool fully equivalent to the standard quantum description, with no additional assumptions beyond the probability current of the paraxial wave field. In the present Talbot geometry, this analysis shows how decoherence progressively suppresses the carpet structure and smooths the transverse-momentum distribution, while the flow may remain organized into channels determined by the grating periodicity. The results illustrate, in a periodic matter-wave Talbot geometry, that the loss of visible interference and the degradation of the grating-defined flow-domain organization need not occur simultaneously. In particular, flux-channel structures can persist in parameter regimes where multislit interference features have already been strongly reduced. This distinction provides a local characterization of decoherence in matter-wave Talbot interferometry and complements previous trajectory-based analyses of coherence loss in simpler interference and confined geometries.

We study one-dimensional quantum gases in continuous space with cavity-mediated infinite-range interactions using the Variational and the Diffusion Monte Carlo methods. Starting from the exact two-body solution, we construct a nontranslationally invariant Jastrow wave function that accurately captures the spatial structure induced by the cavity field and provides an efficient many-body ansatz for both bosonic and fermionic systems. We analyze properties of three characteristic quantum systems, subject to long-range interactions: (i) ideal Bose gas, (ii) interacting Bose gas, (iii) ideal Fermi gas. In the absence of short-range interactions, we identify a crossover from a stable, weakly modulated phase realized at finite particle number for repulsive interactions to a self-organized state for attractive interactions, marked by clustering, loss of superfluidity, and, at fixed interaction strength, the absence of a thermodynamic limit. Introducing short-range repulsion, either through contact interactions or fermionic statistics, leads to the formation of a mesoscopic gas-like regime that disappears in the thermodynamic limit. A qualitative phase diagram is proposed to illustrate the combined effects of short- and long-range interactions, highlighting the emergence of distinct regimes with characteristic structural properties. Applying the Kac prescription, we obtain a well-defined thermodynamic limit and show that the periodic modulation found for a finite number of particles in the repulsive regime is a finite-size artifact, while the self-organized state survives with its onset shifted to substantially stronger coupling.

Nonreciprocal conversion is essential for protecting sources and enabling unidirectional signal routing in photonic, phononic, electronic, and quantum systems, yet conventional implementations often rely on magnetic bias that can be difficult to integrate on chip. We propose a magnet-free scheme for frequency-domain nonreciprocity based on sequential, time-gated modulation in a three-mode system. By activating interactions in a fixed temporal order, the forward and reverse frequency-conversion pathways acquire unequal dwell times in a lossy intermediate mode, producing strong nonreciprocity without requiring nonlinearities or magnetic materials. Using harmonic-balance and Dyson-Born expansions, we derive an analytical expression for the isolation ratio and show that breaking time-reversal symmetry alone is insufficient to produce isolation in this scheme: Dissipation in the intermediate mode is necessary, and the isolation is maximized at a finite loss. The resulting framework identifies how duty cycles, modulation frequency, relative delay, coupling strength, and loss control the isolation, in agreement with direct time-domain simulations. The approach is general and applicable to integrated photonic, phononic, microwave, and superconducting-circuit platforms.

We investigate the role of magnetic sublevels in Autler-Townes spectra of Rydberg atoms driven by radio-frequency (rf) fields with arbitrary polarization. While conventional treatments predict two symmetric sidebands from independent $m_J$ transitions, experiments have reported additional unexplained spectral features. We show that these arise from elliptical rf polarization, which coherently couples multiple magnetic sublevels and requires a full multilevel treatment. We develop and diagonalize a Hamiltonian including all coupled $m_J$ sublevels, predicting polarization-dependent degeneracies that produce varying numbers of resolved peaks. Using long-wavelength transitions and an anechoic environment we realize homogeneous rf fields that enable complete resolution of the $m_J$-dependent dressed states. We observe excellent agreement with theory as the rf ellipticity is varied. These results demonstrate that rf polarization fundamentally modifies Autler-Townes spectra and provide a consistent framework for interpreting magnetic-sublevel structures, with implications for Rydberg-based rf electrometry and polarimetry.