We propose a protocol to measure three-dimensional impulses beyond the standard quantum limit. The protocol reduces noise in all three spatial dimensions and consists of squeezing a mechanical system's state via a series of jumps in the frequency of the harmonic potential. We quantify how decoherence in a realistic system of an optically levitated, dielectric nanoparticle limits the ultimate sensitivity. We predict that $\sim 10\mathrm{dB}$ of squeezing is achievable with current technology, enabling quantum-enhanced detection of weak impulses.

This paper demonstrates a scheme that combines a linear quantum scissor (LQS) with weak cross-Kerr nonlinearity (CKN) to perform quantum nondemolition (QND) measurements. Performing the postselection on an input coherent state in the LQS, a superposition of vacuum and a single-photon component is truncated. The truncated state is coupled with a Fock state $|N\rangle$, via the CKN. The combination provides more flexibility for generating a nonclassical phase-labeled truncated state (PLTS). The phase shift of the PLTS is proportional to the photon number $N$. Here, we examine the nonclassical properties of the PLTS. By applying beam-splitter interference and detecting the outputs, the QND measurement of the photon number takes place. In this approach, the photon-number information which is imprinted as a phase shift on the PLTS is converted into detectable intensity differences between output ports. For low-photon-number regimes, the scheme outperforms the conventional coherent-state-based QND scheme due to the non-Gaussian nature of the PLTS, which reduces phase diffusion and increases the visibility of interference fringes. Thus, the scheme offers a clear advantage in realistic, low-photon-number conditions, particularly in weakly nonlinear media, where the conventional coherent-state-based QND scheme faces limitations. However, the non-Gaussian features of the PLTS still provide unique advantages in terms of heralding and robustness to experimental imperfections.

Subwavelength atomic arrays are a leading platform for engineering light-matter interactions, enabling near-perfect single-photon mirrors and robust quantum memories based on long-lived dark spin waves. However, a comprehensive theory of their nonlinear, multi-excitation dynamics has remained a significant challenge. We present a unified quantum scattering theory that treats both photons and collective atomic spin waves as distinct propagating excitations interacting across different spatial dimensions. Our central result is a powerful analytical reduction: we demonstrate that the complete multichannel $S$-matrix and the associated scattering cross sections are exactly determined by the effective scattering dynamics solely within the atomic spin-wave subspace. This maps the complex physical problem of photon-atom interactions to a conceptually simpler one involving only atomic modes. We apply this formalism to the two-excitation case, deriving the complete analytical $S$-matrix and scattering cross sections for systems with two-level nonlinearities. Our work provides a versatile analytic tool for analyzing and engineering complex quantum nonlinear phenomena, including multi-excitation subradiance, in large-scale atomic systems.

The quadrature squeezing and quantum Fisher information in a driven non-Hermitian Swanson oscillator coupled to a thermal bath are studied. Analytically solving the master equation, we find that the system reaches a Gaussian steady state in the $\mathcal{PT}$-symmetric regime. Quadrature squeezing as a resource for parameter estimations of temperature and frequency is extensively investigated. Due to the asymmetric two-photon annihilation and creation processes, the positivity of quadrature variances provides a stricter constraint depending on the temperature compared with its Hermitian counterpart. This leads to the absence of exceptional points. However, in certain parameter regimes, quadrature squeezing remains robust and exceeds its Hermitian counterpart, while the variances are more sensitive to temperature and frequency. These advantages lead to the enhancement of temperature and frequency estimation. Importantly, when the Swanson oscillator is coherently driven off resonantly, the non-Hermiticity results in the encoding of temperature information in one of the first-order moments. This distinctive difference from its Hermitian counterpart provides a different way to design a quantum thermometer. Our work establishes the non-Hermitian Swanson oscillator as a viable platform for high-precision Gaussian quantum metrology.

We investigate bipartite entanglement and prove that in constrained energy subspaces, the entanglement spectra of multiple bipartitions are the same across the whole subspace. We show that in quantum many-body systems the bipartite entanglement entropy is affected in such a way that it forms “bundles” under unitary time evolution. Leveraging the structure of the subspace, we present methods to verify whether the entanglement spectrum of two bipartitions is identical throughout the entire subspace. For the subspace defined by the parity embedding, we further provide an algorithm that can determine this in polynomial time.

Quantifying genuine multipartite entanglement remains a significant challenge due to the exponential scaling of computational complexity. In this paper, we propose a multipartite entanglement monotone defined by the minimum entanglement drop—the reduction in global one-to-group entanglement when a single constituent particle is traced out. While analytically rooted in the generalized monogamy inequality, we formulate a computationally efficient variant based on tangle and negativity to ensure nonvanishing values for $W$-class states. We rigorously prove that this quantity constitutes a valid entanglement monotone under local operations and classical communication. In the tripartite regime, we demonstrate that the minimum tangle drop is physically equivalent to the minimum pairwise concurrence. Furthermore, we establish a proof-of-principle operational framework where the entanglement drop serves as a structural heuristic probe: by evaluating the sensitivity of the system to qubit loss, we identify inseparable clusters within certain classes of multipartite states, effectively extracting their connectivity fingerprints, which can uniquely differentiate graph topologies even within the same local Clifford equivalence class. Building on this localized mapping, we highlight its practical utility by integrating it with the classical shadows formalism for efficient experimental estimation and demonstrate its unique capability to dynamically track the spatiotemporal evolution of entanglement networks. To further validate its scalability, we derive exact analytical solutions for $n$-qubit $W$ states under environmental noise, revealing the robust scaling behaviors of the proposed measure. Finally, to ensure a balanced assessment, we candidly acknowledge the fundamental limitations of this heuristic probe, noting that its diagnostic sensitivity strictly vanishes for highly robust, symmetrically correlated states, such as the five-qubit error-correcting code.

Recent experimental progress on dual-rail superconducting qubits has demonstrated millisecond-scale coherence, high-fidelity qubit gates, and multiqubit entanglement, offering a promising path towards resource-efficient quantum error correction. Fast reset and rapid state preparation are becoming critical requirements as dual-rail quantum processors scale up. In this work, we introduce the technique of applying dual driving fields with in-phase and out-of-phase configurations to both physical qubits of the dressed two-qubit system, which aligns with the dual-rail logical subspace structure defined as the symmetric and antisymmetric combinations of $|10\rangle$ and $|01\rangle$. We show that the desired (unwanted) transitions of the dressed two-qubit system can be selectively opened (suppressed) by dual external fields and used to synthesize a three-level system with all transitions controllable by qubit frequency modulation. Our work bridges fundamental quantum control theory with immediate experimental relevance to dual-rail encoding for a general physical system.

We propose a scheme for achieving nonreciprocal phonon blockade in a quadratic optomechanical system consisting of two spinning resonators near-field coupled to a nanomechanical oscillator. Due to the Sagnac-Fizeau effect, pump fields propagating in opposite directions experience distinct effective detunings, thereby leading to asymmetric intracavity intensities. Through the optical spring effect, this intensity imbalance gives rise to direction-dependent shifts in the effective mechanical frequency, providing the core mechanism for nonreciprocal phonon blockade. By judiciously setting parameters, single-phonon resonant excitation leads to conventional phonon blockade for one pump direction, whereas two-phonon resonance facilitates phonon-induced tunneling for the other. The pronounced nonreciprocity is quantified by a contrast ratio in the phonon second-order correlation function exceeding 55 dB. To elucidate the nonreciprocal statistics, the phonon blockade is further analyzed in terms of interference between the coherent component and squeezed fluctuations. Incorporating thermal phonons, we reveal an extended nonreciprocal thermal effect, where increasing thermal noise degrades antibunching toward Poissonian statistics in one direction yet reverses the statistics from bunching to antibunching in the opposite direction. Our work provides a pathway toward nonreciprocal phonon devices and directional phonon switches, with potential applications in chiral networks and phononic information processing.

Generating long-distance quantum entanglement is crucial for advancing quantum information processing. In this work, we propose a protocol for generating remote magnon-phonon entanglement in a hybrid waveguide magnomechanical system, where multiple spatially separated magnon modes couple to a common waveguide while interacting with their respective phonon modes. By applying tailored pulsed drives and engineering the magnomechanical interactions, our scheme enables the creation of diverse long-distance and dynamically stable entanglement. Beyond basic magnon-phonon two-mode entanglement, it supports genuine multimode entanglement between a single phonon and multiple magnons, bipartite entanglement between a single magnon and multiple phonons, as well as genuine four-mode entanglement involving two magnons and two phonons. Moreover, we show that dissipative magnon-magnon interactions mediated by traveling photons can generate substantially stronger remote entanglement than coherent couplings. Our work provides an experimentally feasible scheme for the remote generation of magnon-phonon entanglement.

Quantum thermometry aims to measure temperature in nanoscale quantum systems, paralleling classical thermometry. Nonequilibrium quantum thermometry, emerging as a complement to its equilibrium counterpart, addresses scenarios where thermalization is prohibitively slow or real-time temperature monitoring is required. Since temperature is not well defined for nonequilibrium states, a direct inference of temperature values might seem impossible in nonequilibrium quantum thermometry, unlike in the thermal equilibrium case. Here we show that direct temperature inference from the nonequilibrium dynamics of a thermometer is achievable by developing a thermodynamic inference scheme. The scheme integrates two conceptual developments. (i) By applying the maximum-entropy principle with the thermometer's mean energy as a constraint, we assign a reference temperature to the nonequilibrium thermometer. We demonstrate that this reference temperature outperforms a commonly used effective temperature defined through equilibrium analogy. (ii) We obtain positive-semidefinite error functions that lower bound the deviation of the reference temperature from the true temperature and vanish upon thermalization with the sample. Combining the reference temperature with these error functions, we introduce a notion of corrected dynamical temperature which furnishes a postprocessed temperature inference under nonequilibrium conditions. This corrected dynamical temperature can be evaluated adaptively without prior knowledge of the actual temperature. We validate the corrected dynamical temperature in a qubit-based thermometer under a range of nonequilibrium initial states, confirming its capability to estimate the true temperature. Importantly, we find that increasing quantum coherence can enhance the precision of this readout. Our findings complement existing research on nonequilibrium quantum thermometry and help bridge the gap between prevailing theoretical analysis on precision limit and the practical need of direct temperature inference.

Optical backflow in paraxial Gaussian beams is investigated within the Maxwell framework. Scalar potential representations are employed to identify conditions under which the longitudinal Poynting component becomes negative, showing that backflow is enabled by local suppression of the leading-order transverse field and the dominance of higher-order vectorial contributions. The spatial topology of backflow regions is shown to be governed by polarization through the number of independent local constraints on the transverse field. When the local polarization phase is free, as in the generic case of circular polarization, the leading-order field vanishes only at isolated points, giving rise to pointlike backflow regions (extended curves may arise if an additional global phase constraint is imposed). In contrast, when the polarization phase is locally fixed, as for linear, radial, or azimuthal polarization, the suppression condition reduces to a single real constraint, resulting in extended backflow curves. Analytical Gaussian-polynomial solutions explicitly illustrate these effects. These results clarify the role of vectorial interference, establish a polarization-controlled backflow geometry, and provide a foundation for further studies of optical backflow in structured and nonparaxial beam configurations, as well as potential applications in optical manipulation and structured light design.

Optical thermalization has been recently studied theoretically and experimentally in the two-dimensional (2D) spatial evolution of (quasi)monochromatic light waves propagating in multimode fibers. In this work, we investigate the spatiotemporal equilibrium properties of incoherent multimode optical waves through the analysis of the ($2+1$)D Bose-Einstein thermal distribution and the corresponding classical Rayleigh-Jeans approximation. In the classical regime, we perform numerical simulations of the nonlinear Schrödinger equation and demonstrate relaxation toward the spatiotemporal Rayleigh-Jeans equilibrium state, as described by the corresponding wave turbulence kinetic equation. Remarkable adiabatic cooling phenomena stemming from the high-frequency tails of the Rayleigh-Jeans distribution are discussed and the consequent limitations of the classical approximation are highlighted. To overcome these issues and properly include quantum effects, we make use of a quantum version of the nonlinear Schrödinger equation that is obtained from the general quantum theory of light propagating in nonlinear waveguides. The associated kinetic equation describes relaxation toward the spatiotemporal Bose-Einstein equilibrium distribution with a fully regular ultraviolet behavior. The analysis of thermodynamic equilibrium properties reveals a strong dependence on the specific dispersion regime under consideration. In the anomalous dispersion regime, the system relaxes to positive-temperature equilibrium states: as the number of modes of the waveguide increases, the fundamental spatial mode becomes macroscopically populated, while its temporal spectrum undergoes significant narrowing, ultimately leading to complete ($2+1$)D spatiotemporal condensation in the thermodynamic limit. By contrast, in the normal dispersion regime the system evolves toward negative-temperature equilibrium states characterized by a hybrid structure: the spatial equilibrium displays an inverted modal population, whereas the temporal spectrum remains peaked around the fundamental (carrier) optical frequency. In this regime, we predict that spatiotemporal light waves exhibit a phase transition to Bose-Einstein condensation at negative temperatures, which occurs by increasing the temperature above a negative critical value. Our work opens new avenues for future research, including the possibility for a dual spatiotemporal beam cleaning through full spatiotemporal light condensation, and lay the groundwork for the development of spatiotemporal optical thermodynamics.

Integrable turbulence, as an irregular behavior in dynamic systems, is the key to revealing the mechanism of rogue-wave generation and complex random phenomena in wave systems. In this paper we numerically and statistically investigate the integrable turbulence of a coupled nonlinear Schrödinger system with four-wave mixing effects, which describes optical wave propagation in multimode fibers. Different from prior studies of scalar integrable turbulence, our work deals with two coupled polarization components whose nonlinear evolution is modulated by a shared potential containing cross-phase modulation and four-wave mixing. It reveals that an increase in the initial perturbation standard deviation leads to a transition from breather turbulence to soliton turbulence, significantly enhancing the occurrence probability of rogue waves. This can be reflected in an enhanced heavy-tailed feature of the probability density function and an increase in the asymptotic values of the stable state for skewness and kurtosis. Moreover, the change of the correlation length mainly affects the ratio of solitons to breathers, with a relatively minor impact on the probability distribution. It also indicates that the four-wave mixing effect drives the redistribution of spectral energy, further modulating the generation dynamics of rogue waves. These findings deepen the understanding of integrable turbulence and rogue-wave generation in coupled nonlinear systems with four-wave mixing effects.

A mathematical formalism of the generalized Stokes field is developed to characterize the propagation properties of partially coherent higher-order vector vortex beams (PC-HOVVBs) in two configurations: (1) without double-slit and (2) with double-slit. Unlike the usual Stokes field, which solely characterizes the polarization of the beam, the generalized Stokes field is a unified representation that encodes both the polarization and coherence properties of the PC-HOVVBs. The generalized Stokes phase is shown to exhibit an explicit dependence on the choice of spatial coordinates. In the far-field interference patterns of PC-HOVVB, the emergence of new generalized Stokes vortices ($N$) is observed, revealing the information of the index ($\left|\eta \right|$) of the input beam as $N=2\left|\eta \right|$. The separation between these generalized vortices increases with decreasing source spatial correlation. This interdependence can be used to determine the spatial coherence width of the input beam. Furthermore, during propagation, these vortices undergo rotation, creation, and annihilation. The experimentally measured generalized Stokes intensity and phase at the double-slit plane were in good agreement with the theoretical predictions. The generalized Stokes field formalism developed in the article may find potential wherever the coherence and polarization properties are crucial, including polarization metrology, free-space optical communication, beam shaping, and quantum communication.

Optical topologies in the form of Skyrmions have attracted significant interest of late, where their integer Skyrmion number has been shown to be robust to complex media. Here we create fractional Skyrmions with noninteger topological numbers by structuring light as a vectorial superposition of fractional (noninteger) orbital angular momentum. We reveal a nonlinear evolution of the skyrmion number with abrupt transitions toward the nearest integer values. Furthermore, during propagation, the topological transition occurs slightly before the half-integer values, indicating their instability, while the topology becomes stable as it approaches integer values. Our experimental demonstration agrees well with simulations, opening a spectrum of optical topologies to explore, with exciting possibilities in optical communication and sensing.