The effective Hamiltonian of $m{\alpha }^6$- and $m{\alpha }^6(m/M)$-order corrections for hydrogen molecular ions has been derived by Zhong et al. [Z.-X. Zhong, W.-P. Zhou, and X.-S. Mei, Phys. Rev. A 98, 032502 (2018)]; in this work we express the energy correction in the form of finite-value effective operators. The cutoff regularization scheme is used to determine the finite part of divergent operators of the leading-order recoil corrections. Numerical calculations of first-order contributions are performed in the Hylleraas basis set. Combining the second-order terms calculated in recent work [V. I. Korobov, J.-P. Karr, and Z.-X. Zhong, Mol. Phys. e2563023 (2025)], the $m{\alpha }^6$-order corrections for the fundamental rovibrational transition are obtained with an uncertainty three times smaller than in previous calculations.

Superradiance is an extensive cooperative spontaneous emission phenomenon, exhibited by some atomic collective-spin states. However, distinct initial states differ in their decay dynamics. Dicke states $|j,m\rangle$ with distinct numbers of excitations $n=m+j$, driven by vacuum fluctuations, have their peak emission intensity shifted in time. Rotating Dicke states relative to the decay axis introduces an interesting parity structure that affects the pulse profile and photon correlations. Squeezed-bath prepared states undergo a squeezing-controlled crossover to the rotated Dicke states, making the emission character dependent on the amount of squeezing transferred from light to the atomic state. For semiclassical states with a macroscopic dipole moment, like the atomic coherent state, the emission intensity depends on their polarization. We present detailed results on the superradiant dynamics of a representative selection of states expanded in Dicke states to highlight the initial state as an independent dynamical control parameter. For large-$N$, we are able to predict fairly accurately the pulse profile in each case using the mean-field approximation, an approach based on the Fokker-Planck equation. We also present comparative results on the intensity correlation function, quantify the coherent and incoherent contributions of the emission, and contrast between small and large ensembles.

Doppler broadening presents a major limitation for high-resolution spectroscopy and nonlinear optics in room-temperature atomic vapors. Here, we demonstrate the suppression of Doppler broadening accompanied by pronounced absorption on the upper transition of a three-level ladder system, achieved by dressing the intermediate state with a strong control field. As a concrete realization, we study a hot vapor of ${}^{87}\mathrm{Rb}$ where the lower transition is driven by a strong control field resonant with the $D_2$ line at a wavelength of 780 nm, while a weak counterpropagating probe field at the telecom C-band wavelength of 1529 nm $(5P_{3/2}\leftrightarrow 4D_{5/2})$ interrogates the dressed states. We observe absorption features with a resonant optical depth of approximately 4 and a full width at half maximum of about 17 MHz. Remarkably, this corresponds to an order-of-magnitude reduction relative to the Doppler width, while the optical depth on the upper transition of the ladder scheme exceeds that of the Doppler-broadened lower transition. The measured spectra are in good agreement with theoretical modeling. Combining high optical density with sub-Doppler-width absorption lines typically requires laser-cooled atoms, while our approach profits from the experimental simplicity of a hot-vapor platform.

Interference provides a fundamental mechanism for generating and manipulating entanglement in many-body quantum systems. Here, we develop an interference framework in which the nonlinear dynamics of collective spin-$\frac{1}{2}$ ensembles are mapped onto phase accumulation and self-interference in phase space, providing a direct and physically transparent description of entanglement formation. Within this framework, one-axis twisting produces Greenberger-Horne-Zeilinger (GHZ) states, while two-axis twisting generates multicomponent GHZ superpositions relevant for multiparameter quantum metrology. Building on this interference-based description, we analyze metrological performance under realistic Markovian noise, including local and collective emission, pumping, and dephasing, and examine the role of Hamiltonian control based on linear and nonlinear interactions. We show that the optimal control enhances sensitivity in both single- and multiparameter estimation across noise-dependent regimes. These results establish interference as a unifying principle linking nonlinear dynamics, entanglement generation, and metrological performance. This framework offers a broadly applicable route to robust quantum-enhanced sensing in noisy many-body systems.

Bell measurements (BMs) are ubiquitous in quantum information and technology. They are basic elements for quantum commmunication, computation, and error correction. In particular, when performed on logical qubits encoded in physical photonic qubits, they allow for a read-out of stabilizer syndrome information to enhance loss tolerance in qubit-state transmission and fusion. However, even in an ideal setting without photon loss, BMs cannot be done perfectly based on the simplest experimental toolbox of linear optics. Here we leverage that any logical BM on stabilizer codes can always be mapped onto a single physical BM perfomed on any qubit pair from the two codes. As a necessary condition for the success of a logical BM, this provides a general upper bound on its success probability, especially ruling out the possibility that the stabilizer information obtainable from only partially succeeding, physical linear-optics BMs could be combined into the full logical stabilizer information. We formulate sufficient criteria to find schemes for which a single successful BM on the physical level will always allow to obtain the full logical information by suitably adapting the subsequent physical measurements. Our approach based on stabilizer group theory is generally applicable to any stabilizer code, which we demonstrate for quantum parity, five-qubit, standard and rotated planar surface, tree, and seven-qubit Steane codes. Our schemes attain the general upper bound for all these codes, while this bound had previously only been reached for the quantum parity code.

Discrete time crystals are nonequilibrium states of periodically driven quantum matter characterized by robust subharmonic responses. We investigate how such temporal order behaves in the presence of stochastic measurements. Using trajectory-resolved simulations of a monitored Floquet-Ising model, we identify an intermediate regime in which the local subharmonic response survives only intermittently in time. The dynamics develops finite-lived temporal plateaus of locally coherent subharmonic response punctuated by stochastic disruptions correlated with projective measurements. While local temporal staggering remains robust over broad intervals, the spectral coherence of the subharmonic response exhibits substantially stronger fluctuations, revealing a temporally fragmented dynamics not fully captured by global long-time observables alone. The resulting plateau statistics are further consistent with an effective two-state kinetic description based on finite-rate stochastic disruption events. These results show that monitored dynamics can support fluctuating local synchronization in which finite temporal domains repeatedly emerge and disappear along individual quantum trajectories, without establishing globally persistent discrete time-crystalline order under stochastic monitoring.

Quantum information masking (QIM) encodes single-qubit information into bipartite entanglement, but the absence of a universal masker restricts standard bipartite implementations to specific Bloch sphere disks. Here, we experimentally demonstrate an automated quantum masking machine that can be reconfigured for target disks of different orientations. Driven by a machine-learning-assisted feedback algorithm, a self-calibrating adapter determines the required rotation directly from photon-count measurements for a fixed base masker and maps a selected target disk to a maskable latitudinal configuration. Leveraging this framework, we experimentally demonstrate a proof-of-principle quantum secret sharing scheme. For the tested states, quantum state tomography shows that the encoded information is retained in the global entanglement, while the corresponding marginal states exhibit no resolvable input dependence within experimental uncertainty. Rather than altering the no-masking principle, this closed-loop architecture broadens the input compatibility of a fixed masker and provides a reconfigurable platform for masking-based quantum communication.

Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for nonadditive codes that lack a stabilizer description. We present a general learning-based framework that, given only an encoding circuit, constructs physical implementations of logical operations while enforcing structural properties such as transversality or shallow depth. Our approach is validated by rediscovering known logical operations of standard stabilizer codes. We then extend it to a codesign procedure, dubbed variational early fault-tolerant quantum computing (VarEFTQC), which tailors nonadditive encodings to a given noise model and enforces desired logical gate sets, such as transversal IQP-type families or low-depth universal sets. A software library implements the complete learning pipeline, including loss-function variants, ansatz families, and optimization routines. Together, these results position VarEFTQC as a proof-of-concept framework for discovering hardware-adapted logical gadgets for early fault-tolerant quantum computing.

Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required computational resources. A standard approach to controlling Trotterized time evolution doubles the number of single-qubit arbitrary rotations. Here, we describe a compilation scheme to control a symmetric Trotterization that does not increase the number of arbitrary rotations. This halves the number of arbitrary rotations required to implement controlled, Trotterized time evolution compared to the standard approach. Arbitrary rotations contribute significantly to $T$ cost in a fault-tolerant architecture due to the number of required magic states. Therefore, arbitrary rotations often dominate resource estimates for fault-tolerant implementations of quantum simulation algorithms. This construction reduces the number of arbitrary rotations for controlled Trotter evolution to that of uncontrolled Trotter evolution, thereby reducing the cost of fault-tolerant quantum simulation.

The standard stimulated Raman adiabatic passage (STIRAP) protocol enables high-fidelity quantum state transfer in an ideal three-level system via adiabatic following of a dark state. However, in practical systems with more energy levels, control pulses with finite spectral selectivity often couple the three-level subspace to the remaining subspace, introducing leakage that fundamentally limits the transfer performance. Here, we adopt a multilevel chain model for STIRAP that explicitly incorporates this leakage subspace. Using Pontryagin's maximum principle, we formulate a leakage-penalized quantum optimal control problem with the control pulses constrained to experimentally feasible Gaussian pulse families. We derive explicit gradients of the objective functional with respect to the pulse parameters, enabling efficient low-dimensional optimization that suppresses leakage while preserving the counterintuitive STIRAP pulse ordering. Numerical simulations for a superconducting transmon platform demonstrate that the optimized control pulses significantly enhance the target-state transfer fidelity and improve robustness against amplitude miscalibration and detuning drifts.

In this article we report on an experimental study of the polarization of atoms in magnetized plasma (PAMP) in ${}^3\mathrm{He}$ gas under various conditions of radio-frequency (rf) excitation of plasma. Among parameters influencing the plasma dynamics are frequency, average and peak rf powers. Our data strongly indicate a significant influence of electron density in the plasma on the polarization value and buildup rate. In particular, it was found that polarization scales as $U^{\beta }$, where $U$ is the voltage across the coil in the tank circuit generating the plasma and $\beta$ is in the range of 1.3–1.5, similar to what is expected for the electron density. Experiments with the modulation of rf power show that the peak rf power governs the polarization rather than the average power. An unexpected increase in polarization related to the appearance of a small amount of impurities in the ${}^3\mathrm{He}$ gas at room temperature is found. Strong correlations between polarization and amount of oxygen impurity, which is desorbed as the temperature rises, support the hypothesis that polarization is proportional to electron density because it is expected that electron density linearly increases with impurity concentration. It was also found that the polarization and buildup rate are proportional to each other, a behavior that is common for all rf plasma frequencies. We propose a scenario that can explain the experimental observations: The polarization is limited by nuclear magnetic relaxation, while the growth rate associated with the intrinsic polarization process depends quadratically on the electron density. Our study identifies the ways to increase the efficiency of the PAMP method by maximizing electron density using different means.

One-dimensional (1D) superlattices provide one simplified platform for exploring moiré physics from a low-dimensional perspective, with the ratio of lattice constants playing a role analogous to the twist angle in two-dimensional bilayers. Here we propose a 1D $\mathcal{PT}$-symmetric bichromatic optical lattice for a weakly repulsive Bose-Einstein condensate and investigate how the interplay of dissipation and interaction impacts the lowest moiré flat band. Without interaction, we find that the lowest-band flatness induced by commensurate ratios exhibits a parity-dependent response to the $\mathcal{PT}$-symmetric imaginary potential due to the distinct $\mathcal{PT}$ pairing mechanism for the energy spectrum. For ratios with even denominators (i.e., even parities), the level attraction and thus the $\mathcal{PT}$-symmetry breaking occur within the lowest two bands, leading to a monotonic broadening of the lowest flat band, whereas odd denominators (i.e., odd parities) yield a nonmonotonic response due to the $\mathcal{PT}$-symmetry breaking within the second and the third lowest bands instead while the lowest band remains purely real. This parity-dependent phenomenon can be understood by the perturbation theory. Furthermore, by solving the Gross-Pitaevskii equation, we also find that although the weak repulsive interaction can broaden the moiré bands alone, the combined effects of interaction and imaginary potential also lead to parity-dependent behaviors. For even parities, band flattening is consistently diminished, whereas for odd parities, the imaginary potential can either enhance or reduce the degree of flattening. These results pave the way for experimental studies of dissipation and interaction effects on band flatness in moiré systems.

We study the effective $s$-wave scattering of two heteronuclear atoms harmonically confined in quasi-low dimensions, where the atoms have unequal masses and are subject to different confinement frequencies. The resulting effective scattering parameters in low dimensions, including scattering length and effective range, are derived as functions of three-dimensional scattering parameters and confinement strengths. Using realistic Li-K and Li-Cr mixtures as examples, we further compute the binding energies of universal $(1+N)$ clusters in quasi-low dimensions using the effective scattering parameters. Our findings suggest a promising pathway for practically observing universal clusters and their associated many-body phases in low-dimensional ultracold heteronuclear systems.

The three- and four-boson systems with a large scattering length and a short effective range in the two-body sector are studied in the framework of Short-Range Effective Field Theory (SREFT). The starting point (leading order) of the EFT is taken to be the universal unitarity limit, where the two-body sector is parameter-free and only one three-body parameter enters. In this limit, physical systems manifest discrete scale invariance. Deviations from universality arising from finite scattering-length and effective-range corrections, as well as a four-body force required by renormalization, are included perturbatively at next-to-leading order. The three-body ground state and its associated four-body ground and first-excited states are studied using the Faddeev-Yakubovsky (FY) formalism and a complementary diagrammatic approach. By employing techniques to remove contributions from deep trimers in tetramer calculations, we extend our analysis to larger cutoffs than previously accessible within the FY approach to SREFT. Our results for binding energies and radii of ${}^4\mathrm{He}$ three- and four-atom systems converge well to results obtained with sophisticated phenomenological potentials. These successes suggest that the physics of ${}^4\mathrm{He}$ atomic clusters is governed by only small deviations from discrete scale invariance.

We show that the supercurrent properties of a superfluid or superconducting junction are significantly modified by single-particle losses in a conduction channel. In the presence of a spin-independent particle loss, we find regimes where the Josephson current $I_N\left(\varphi \right)$ can develop additional zeros within $0<\varphi <\pi$ and the direction of the supercurrent is reversed. Although the region is narrow, we also find a regime in which the critical current is enhanced by dissipation. Such anomalous behaviors in the Josephson current are attributed to a subtle interplay between the contribution that is present regardless of dissipation and the unconventional one that is absent without dissipation and is associated with the quantum jump term of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. In the presence of a spin-selective particle loss, it is shown that a dissipation-induced spin supercurrent and its reversal occur. The proposed system is analyzed by means of the Keldysh field-theory approach based on the GKSL master equation and may be realized in ultracold atomic gases and solid-state systems.

We theoretically investigate the rare-earth ${}^{163}\mathrm{Dy}{}^{107}\mathrm{Ag}$ molecule as a quantum sensor to amplify weak symmetry-breaking interactions not included in the standard model of physics. We focus on parity-breaking interactions from the octupole-deformed ${}^{163}\mathrm{Dy}$ nucleus. To characterize key properties for this molecule, we have performed relativistic electronic configuration-interaction and rovibrational coupled-channels calculations. We show that near the equilibrium geometry, the bond is ionic with the Dy atom losing an electron from its open, submerged 4f electron shell to Ag. In fact, the ${}^{163}\mathrm{Dy}{}^{107}\mathrm{Ag}$ ground-state configuration corresponds to a Dy ion with a large electronic angular momentum of $j_{{\mathrm{Dy}}^{+}}=15\hslash /2$ and a spinless silver ion. Here, $\hslash$ is the reduced Planck constant. We also observe that the crystal-field splittings among states with projections $\mathrm{\Omega }$ of $j_{{\mathrm{Dy}}^{+}}$ along the internuclear axis are on the order of the vibrational spacings in ${}^{163}\mathrm{Dy}{}^{107}\mathrm{Ag}$ and orders of magnitude larger than the rotational spacings, Coriolis-induced $\mathrm{\Omega }$-type doubling, the hyperfine interactions between the spins of the electrons and the ${}^{163}\mathrm{Dy}$ nucleus, and Zeeman interactions when an external magnetic field is applied. The spin-stretched state with $\left|\mathrm{\Omega }\right|=j_{{\mathrm{Dy}}^{+}}$ is the ground state. The splittings between the $\mathrm{\Omega }$-doublets, a pair of states with opposite parity, dramatically depend on $\mathrm{\Omega }$. We predict values on the order of $h\times 10\mathrm{GHz}, h\times 10\mathrm{MHz}$, and $h\times 1\mathrm{kHz}$ for $\mathrm{\Omega }=\hslash /2, 3\hslash /2$, and $5\hslash /2$, respectively, with Planck constant $h$. For larger values of $\mathrm{\Omega }$, the splittings decrease by additional orders of magnitude. Parity violations and thus the mixing of the $\mathrm{\Omega }$-doublets can be achieved by simply applying external electric fields or by interactions induced by the octupole-deformed ${}^{163}\mathrm{Dy}$ nucleus through coupling of its nuclear spin to molecular rotation. The actual energy shifts from the latter contribution are not known as they originate from nuclear forces.

Efficient measurement of center-of-mass motion is fundamental to force sensing and quantum control in levitated optomechanics. While scattering theories predict the spatial distribution of displacement information, direct experimental mapping of this information remains undemonstrated, leaving uncertainties regarding the impact of real-world optical imperfections. Here, we introduce a spatial-scanning technique to experimentally visualize the three-dimensional displacement information distribution of a levitated nanoparticle. By decomposing the scattered field into independent motional axes, we reconstruct the information radiation patterns, which reveal the angular density of detectable information. The measured patterns agree well with theoretical calculations while capturing minor distortions attributed to experimental imperfections. Furthermore, we demonstrate that the integrated displacement information remains robust against variations in the detection plane position along the optical axis. This work establishes a direct approach to characterizing information flow in scattered light, providing a practical framework for optimizing detection efficiency in complex or nonstandard optomechanical systems.

Intermittent chaos is a particular nonlinear phenomenon representing a transitional state in the route to chaos. It alternates between periodic and chaotic motions over time, different from the conventional period-doubling bifurcation. Here we qualitatively and quantitatively analyze this specific bifurcation process in a high-Q optomechanical whispering-gallery-mode microtoroidal resonator, where the dynamical process transits from a periodic state into a fully chaotic state via intermittent chaos. Specifically, we show the trajectories in phase space, the evolution of the Poincaré section, and the characteristic patterns of the corresponding Poincaré map, to reveal the unique dynamical features of intermittent chaos in contrast to purely periodic or chaotic behaviors. Moreover, by employing the maximal Lyapunov exponent, Kolmogorov entropy, autocorrelation function, and box-counting dimension, which quantify the trajectory divergence, information generation ability, temporal memory decay, and spatial occupancy in the phase diagram, respectively, we demonstrate a continuous increase in the degree of chaos. This phenomenon observed in an optomechanical resonator may promote further research on intermittent chaos in cavity optomechanics and provide support for the design and utilization of chaotic devices based on such systems.

We investigate the steady-state dynamics of two coupled cavities with balanced gain and loss in the presence of parametric driving using the Schwinger-Keldysh functional formalism. This approach allows us to analyze the non-Hermitian dynamics and evaluate steady-state observables associated with nonclassical behavior. We show that a parametric drive breaks the exact $\mathcal{PT}$ symmetry of the system and acts as a control parameter that induces a population imbalance between the cavities. The interplay of coherent tunneling, balanced loss and gain, and two-photon driving gives rise to a pronounced population imbalance between the cavities that tends to a limiting value for strong dissipation. This signals a drive-induced localization and Zeno-like suppression of photon distribution. Intermode quantum correlations are characterized using entanglement negativity, revealing a drive-dependent threshold for entanglement generation and the occurrence of entanglement sudden death at finite dissipation. In addition, near the exceptional points the system becomes sensitive to fluctuations, resulting in the minimum of the steady-state purity. The presence of the parametric drive modifies this behavior by lifting the non-Hermitian spectral degeneracy and altering the steady-state coherence properties of the system. Our results demonstrate how parametric driving provides a versatile mechanism for controlling localization, quantum correlations, and fluctuation properties in driven-dissipative non-Hermitian systems.