Coherent quantum noise cancellation (CQNC) suppresses radiation-pressure backaction noise by introducing an auxiliary oscillator with an effective negative mass. In this context, once shot noise is further reduced by increasing the intracavity field intensity, the noise associated with the auxiliary system ultimately limits further improvements in sensitivity. To overcome this limitation, we propose and investigate a hybrid cavity-optomechanical weak-force sensing scheme that combines CQNC and mechanical-mode softening. We show that mechanical-mode softening exponentially increases the mechanical zero-point displacement scale, thereby enhancing the mechanical response to an external force and further amplifying the corresponding weak-force-induced optical output signal. As a result, the signal-to-noise ratio is substantially improved, enabling the limitation imposed by the auxiliary-system noise on the sensing sensitivity to be overcome. Meanwhile, mechanical-mode softening strengthens the effective optomechanical coupling, and the synergistic interaction between the enhanced optomechanical coupling and the signal-amplification effect leads to a dual suppression of optical shot noise. Therefore, unlike conventional CQNC schemes that rely on strong driving to reduce shot noise, our scheme can efficiently suppress shot noise over a broad frequency range even at relatively low intracavity field intensities. As a result, it achieves force sensitivities far exceeding the standard quantum limit (SQL) over a broad bandwidth. These results establish a practical route toward broadband optomechanical weak-force sensing beyond the SQL.

Quantum reference frame transformations have been proposed to provide a means by which to translate descriptions of quantum systems relative to each other. At present, there are several differing frameworks for describing quantum reference frames, with concomitantly different transformation rules. Here we investigate a simple example of three qubit systems with ${\mathbb{Z}}_2$ symmetry in order to analyze physical and conceptual distinctions between three contemporary approaches to quantum reference frames—dubbed perspective-neutral, extra particle, and operational. By constructing two three-qubit states that are indistinguishable by observables relative to one frame but are distinguishable by observables relative to another, we show that each of the three approaches provides a distinct transformation rule, which may be understood to reflect differing attitudes towards the global state and the information that can be accessed by each frame. This helps us to shed light on the physical meaning of each approach and the contexts in which they may be most naturally applied.

We address the task of converting $n$ uses of an unknown unitary transformation into a quantum state (i.e., storage) and later retrieval of the transformation. Specifically, we consider the case where the unknown unitary is selected with equal prior probability from two options. First, we prove that the optimal storage strategy involves the sequential application of the $n$ uses of the unknown unitary, and it produces the optimal state for discrimination between the two possible unitaries. Next, we show that incoherent “measure-and-prepare” retrieval achieves the maximum fidelity between the retrieved operation and the original (qubit) unitary. We then identify the retrieval strategy that maximizes the probability of successfully and perfectly retrieving the unknown transformation. In the regime in which the fidelity between the two possible unitaries is large the probability of success scales as $P_{\text{succ}}=1-O\left(n^{-2}\right)$, which is a quadratic improvement with respect to the case in which the unitaries are drawn from the entire unitary group $U\left(d\right)$ with uniform prior probability. Finally, we present an optical experiment for this approach and assess the storage and retrieval quality using quantum tomography of states and processes. The results are discussed in relation to nonoptimal measure-and-prepare strategy, highlighting the advantages of our protocol.

We study a modified fixed-point version of the quantum approximate optimization algorithm (fpQAOA), where parameters are trained classically on small instances and then transferred to larger problems. Our scheme combines three ingredients: (i) targeting approximate solutions via a prescribed approximation ratio (AR), (ii) scaling the circuit depth linearly with the problem size using a two-parameter sin-cos angle encoding, and (iii) normalizing quadratic unconstrained binary optimization (QUBO) Hamiltonians by their Frobenius norm. Noiseless numerical simulations (for system sizes up to 30 qubits) across a variety of random QUBO ensembles show that with these modifications the median number of quantum circuit runs (“shots”) required to achieve AR = 0.95 counterintuitively decreases towards a nearly constant value as the problem size increases, while the per-shot time remains polynomial. Extrapolation of this finite-size behavior is consistent with an effectively constant sampling complexity. Moreover, removing any single component of the scheme restores rapid growth of the required number of shots, highlighting the synergistic nature of the three modifications. These empirical findings suggest that fpQAOA, equipped with the proposed protocol, may achieve scalable approximate performance with polynomial-depth circuits for the considered problem classes.

The Casimir-Polder force acts on polarizable particles due to quantum fluctuations of the electromagnetic field that are modified by the presence of material bodies. We investigate the Casimir-Polder interaction for atoms near cylindrical fibers with hollow cores. This geometry represents one of the archetypal configurations encountered in numerous experimental setups designed to control and manipulate atoms in fundamental and quantum technological applications. Specifically, we analyze how the interplay of both geometrical and material-related length scales characterize the interaction, emphasizing the impact of the shell thickness. We develop a flexible and fast-converging numerical scheme for evaluating the interaction over a wide range of atom-cylinder separations at both zero and finite temperature. Furthermore, we provide a detailed analytical investigation of how various material properties modify the Casimir-Polder potential. Finally, we analyze and discuss a number of limiting cases and compare numerical computations with corresponding analytical asymptotic expressions. In particular, in this geometry the Casimir-Polder potential is able to distinguish between an Ohmic and non-Ohmic description of conductors. One of the most significant outcomes of our work is that the shell thickness emerges as a useful parameter for controlling the interaction, opening avenues for both fundamental physics and applications in quantum technologies.

The energy correction associated with the self-energy diagram is the leading (in magnitude) and fundamental (in significance) contribution to the Lamb shift in few-electron atoms and ions. Conventional approaches to this correction rely on partial-wave expansion, which is a major limitation on the achievable accuracy. To elucidate the issue, we perform a comprehensive comparative analysis of partial-wave-expansion convergence between the Feynman and Coulomb gauges. We also implement and discuss several techniques for improving the convergence. Both the Green's function and finite basis set are employed in the calculations.

We theoretically investigate the physical principles underlying the attoclock method in strong-field ionization, with particular emphasis on the interpretation of the offset angle and the role of the Coulomb potential. Our analysis is based on the numerical solution of the time-dependent Schrödinger equation (TDSE) and several variants of the strong-field approximation (SFA) combined with quantum-orbit theory. Among the investigated models, the best agreement with the TDSE is obtained when the ionization probability and the initial conditions for the electron trajectory are determined using the SFA together with the saddle-point method. The corresponding final electron momentum is then calculated by classical propagation in the combined laser and Coulomb fields.

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.