We investigate the information distribution among different entities in the weak-measurement protocol. Focusing on multilevel, decaying systems under continuous (no-click) monitoring, we derive exact, conservation-type information relations that hold for each outcome in the record. Analogous relations hold when an explicit reversal is applied, with the reversal success probability entering the relation. We extend the framework to finite-count outcomes (arbitrary photon numbers), obtaining quantitative trade-offs that link information change in the weak-measurement process to the entities to which the information is distributed. These results provide a unified, outcome-resolved account of information flow in monitored open quantum dynamics and provide insight into a deeper understanding of open-system dynamics and its control.

We demonstrate that periodically driven quantum rotors provide a promising and broadly applicable platform to implement multigap topological phases, where groups of bands can acquire topological invariants due to non-Abelian braiding of band degeneracies. By adiabatically varying the periodic kicks to the rotor we find nodal-line braiding, which causes sign flips of topological charges of band nodes and can prevent them from annihilating, indicated by nonzero values of the patch Euler class. In particular, we report on the emergence of an anomalous Dirac string phase arising in the strongly driven regime, a truly out-of-equilibrium phase of the quantum rotor. This phase emanates from braiding processes involving all (quasienergy) gaps and manifests itself with edge states at zero angular momentum. Our results reveal direct applications in state-of-the-art experiments of quantum rotors, such as linear molecules driven by periodic far-off-resonant laser pulses or artificial quantum rotors in optical lattices, whose extensive versatility offers precise modification and observation of novel non-Abelian topological properties.

Quantum annealing (QA) encounters limitations when the energy gap along the annealing path becomes exponentially small, leading to impractically long run-times. In contrast, the success of hybrid digital methods [like the quantum approximate optimization algorithm (QAOA)], which operate via discrete unitary operations, relies on the optimization of the variational parameters appearing in the state. We analyze a class of transverse-field Ising models which includes problems with exponentially small spectral gaps, but whose dynamics is described in terms of fermionic Gaussian states after Jordan-Wigner mapping. We show that, for digital alternating QAOA-like states, the number of unitaries required to reach the exact ground state scales quadratically with system size and is independent of the annealing gap. This number can be exactly computed from the algebraic properties of the Ansatz, revealing a fundamental distinction between digital methods and their analog counterpart.

High-precision measurements of the fine-structure splittings in helium high Rydberg states have been reported, yet corresponding ab initio benchmarks for direct comparison remain unavailable. In this work, we extend the correlated B-spline basis function (C-BSBF) method to calculate the fine-structure splittings of high Rydberg states in ${}^4\mathrm{He}$. The calculations include the $m{\alpha }^4$- and $m{\alpha }^5$-order contributions, the singlet–triplet mixing effect, and the estimated spin-dependent $m{\alpha }^6$-order corrections obtained using a $1/n^3$ scaling approximation. High-precision ab initio results are obtained for principal quantum numbers $n=24–37$ with kilohertz-level accuracy and further extended to $n=45–51$ by extrapolation and fitting. The theoretical results show excellent agreement with quantum-defect theory (QDT) predictions and allow direct comparison with experimental measurements. Additionally, the discrepancy observed at $n=34$ is expected to be clarified with improved experimental precision.

The effects of the finite nuclear mass are investigated in high-accuracy calculations of the electronic spectra corresponding to the lowest ten ${}^{1}D$ states of beryllium $\left({}^9\mathrm{Be}\right)$. In the first step of the calculations, the nonrelativistic energies of the considered states are calculated using the standard variational approach with the Hamiltonian obtained by rigorously separating out the kinetic energy of the center-of-mass motion (CMM) from the laboratory-frame Hamiltonian. Large basis sets of up to $16200$ well-optimized all-particle explicitly correlated Gaussian functions are used to expand the nonrelativistic wave functions in the calculations. The wave functions are subsequently used to calculate the leading relativistic corrections using first order of the standard perturbation theory and the Breit-Pauli Hamiltonian (BPH). This Hamiltonian is derived by transforming the laboratory-frame BPH to the internal-coordinate system used to separate out the CMM in the nonrelativistic Hamiltonian. The results indicate that it is mandatory to include the finite-mass effects in the calculations to obtain the transition energies between ${}^{1}D$ states of beryllium with accuracy of below 1 ${\mathrm{cm}}^{-1}$. The major part of the effects comes from the nonrelativistic energy obtained within the finite-nuclear-mass approach.

We propose a scheme to transfer molecules from a slow beam into an optical trap using only a single-photon absorption and emission cycle. The efficiency of such a scheme is numerically explored for BaF using realistic experimental parameters. The technique makes use of the state-dependent potential in an external electric field to trap molecules from an initial velocity of order $10\text{m}/\text{s}$. A rapid optical transition at the point where the molecules come to a standstill in the electric field potential irreversibly transfers them into a $\sim 7\text{mK}$ optical lattice trap. For a pulsed Stark decelerated beam, we estimated the per-shot efficiency to be $\sim 0.52\%$ or up to $\sim {10}^4\text{molecules}$, with a potential factor of 2 improvement when the fields are synchronously modulated with the arriving velocity components. The irreversibility of the scheme allows for larger numbers to be built up over time. Since this scheme does not rely on a closed cycling transition for laser cooling, it broadens the range of molecules that can be used for research on cold molecular chemistry, quantum information, and fundamental interactions in optical traps.

Solitons are striking manifestations of nonlinearity, encountered in diverse physical systems such as water waves, nonlinear optics, and Bose-Einstein condensates (BECs). In BECs, dark solitons emerge as exact stationary solutions of the one-dimensional Gross-Pitaevskii equation. While they can be long lived in elongated traps, their stability is compromised in higher dimensions due to the snake instability, which leads to the decay of the soliton into vortex structures among other excitations. We investigate the dynamics of a dark soliton in a Bose-Einstein condensate confined in an anisotropic harmonic trap. Using a variational ansatz that incorporates both the transverse bending of the soliton plane and the emergence of vortices along the nodal line, we derive equations of motion governing the soliton's evolution. This approach allows us to identify stable soliton-vortex oscillation modes as well as the growth rates of the unstable perturbations. In particular, we determine the critical trap anisotropy required to suppress the snake instability. Our analytical predictions are in good agreement with full numerical simulations of the Gross-Pitaevskii equation.

We investigate the superradiant phase transition in a two-component Bose-Einstein condensate with distinct atomic detunings, confined in an optical cavity and driven by a transverse pump laser. By combining perturbation theory and numerical simulations, we demonstrate that the phase transition is dominated by the red-detuned component, resulting in a phase diagram completely different from that of a single-component case under blue-detuned condition. The system exhibits spontaneous phase separation between the two components, manifested as alternating stripe patterns in the normal phase and distinct Bragg gratings in the superradiant phase. Furthermore, the Bogoliubov excitation spectrum reveals roton-type mode softening, indicating that the phase transition also corresponds to the superfluid-to-lattice supersolid transition. Our findings provide insights into the interplay between atomic detunings and collective quantum many-body phenomena, offering potential applications in quantum simulation and optical switching technologies.

Spinor lattice atomic gases, composed of ultracold spinor atoms in optical lattices, have been well investigated in the strong and weak interaction regimes, between which an intermediate regime still exists. We focus on the low-filling spin-1 lattice gas in the intermediate interaction regime for low-lying eigenstates and demonstrate that, for one thing, the system can still be decomposed into the spin and charge sectors like in the strong interaction regime and, for another, the energy detuning between the two sectors is lowered, which activities the intersector coupling. The two-sector decomposition endows the system with emergent inversion symmetry in the spin and charge sectors for the low-lying eigenstates, as well as a multimanifold structure in the eigenenergy spectrum. The intersector coupling introduces the energetic overlap between different manifolds in the eigenenergy spectrum, as well as the intermanifold avoided crossings, which take place between accidentally degenerate eigenstates from different manifolds. The emergent symmetry can further affect the dynamics at the avoided crossings and holds the potential for controlling spin dynamics in spinor lattice gases.

We obtain the ground-state phase diagram of two spin chains consisting in a set of two-level systems asymmetrically coupled to an XX chain through a chiral interaction. The interaction is parametrized by its magnitude and an angle defined by the relative orientation of the spins in different chains. From the entanglement spectrum, we identify the critical lines separating distinct magnetically ordered phases, with the interaction angle able to shift or fully suppress the transition. By increasing the coupling strength, the system is driven through a quantum phase transition, leading to the formation of two types of in-plane antiferromagnetic stripes. The interaction strength sets stripe formation, while the angle controls the spins' orientations. The chiral interaction also induces a nontrivial finite vector spin chirality with opposite orientation on the chains. We show that the vector spin chirality emerges smoothly from the decoupled limit and occurs for angles different from zero and $\pi /2$, where collinear order is favored instead.

In this study, we report the experimental demonstration of optical pulse compression with a gradual refractive index front comoving in a periodically modulated silicon waveguide. This spatiotemporal effect, also called optical push broom, captures and confines the input signal pulse inside a faster propagating refractive index front, driven by a pump pulse. The signal is accelerated by the approaching front until its velocity matches the front's velocity, effectively stopping the light relative to the front. In contrast with the previous experiment where we used a cw signal, we now utilized a pulsed signal and thus can vary the initial delay between the signal and the pump. We employ the slowly varying envelope approximation to model the effect and successfully reproduce the experimental frequency shift at the output corresponding to the temporal delay at the input.

We experimentally demonstrate the extension and energy redistribution of a high-order harmonic spectrum generated by the near-IR 1.24-µm 100-fs laser pulse coherently combined with the long-wavelength 4.5-µm 200 fs field. This synthesized multicycle field allows formation of up to 200 eV soft-x-ray continuum in He gas under moderate driving field intensity at the level of ${10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. The observed extension is caused by the activation of the cutoff trajectory of the second return while maintaining high photoemission efficiency via the enhanced ionization probability. The decrease in the driving pulses duration and the increase of a long-wavelength field strength will allow further extension of the harmonic spectrum, opening opportunities for the time-resolved K-edge absorption spectroscopy in the water window and keV spectral ranges.

Chirality symmetry breaking (CSB) in Kerr nonlinear whispering-gallery-mode (WGM) microcavities is essential to advance nonlinearity-based nanophotonic devices. Normally, a high chirality in such platforms usually requires a high input power. However, a high input power will induce complicated nonlinear responses that may in turn weaken the chirality. Here, we propose a CSB strategy based on the Kerr nonlinearity, in which the add-drop microring (ADM) is driven by a dual-mirror system. The linear and nonlinear mode dynamics of the clockwise and counterclockwise modes in the microring are described by coupled mode theory. Both the total intracavity energy and the energy imbalance in the proposed configuration with bidirectional inputs can be synchronously varied by the reflection amplitudes and phase delays of the dual-mirror system. It is found that the input power threshold required to excite chiral states can be effectively reduced. Meanwhile, a higher chirality can be achieved under the same level of input power compared with a mirror-free ADM configuration. Furthermore, the proposed strategy can be potentially applied to nanoparticle sensing with robustness, higher sensitivity, and a broader operational power range. In addition, the low power thresholds of the multistage CSB and the distribution of exceptional points in the proposed configuration are also analyzed. The theoretical results are expected to be further applied to high-performance sensors and other low-power on-chip photonic devices.

The study of giant atoms goes beyond the local interaction paradigm in conventional quantum optics and predicts novel phenomena, such as oscillating bound states in the continuum (BICs) and decoherence-free interaction, which do not exist in small atoms, for some particular parameter settings of coupling positions and strengths. However, in realistic experiments to implement giant-atom systems, there is always some level of disorder both in coupling positions and strengths. In this work, we investigate the effects of disorder on the phenomena related to giant atoms. We find that the giant-atom-related phenomena are robust to disorders of both coupling positions and strengths in the Markovian regime but more sensitive to the disorder of coupling positions in the non-Markovian regime. Our work shows that, to observe non-Markovian phenomena such as (oscillating) BICs in giant-atom systems, more precision is needed to control the disorder of coupling positions than that of the coupling strengths in the experiments.

Gaussian states are an essential building block for various applications in quantum optics and quantum information science, yet the precise relation between their second- and third-order correlation functions remains not fully explored. We discuss connections between these correlation functions by constructing an explicit decomposition formula for arbitrary sixth-order moments of ladder operators for general Gaussian states and demonstrate how the derived relations enable state classification from correlation data alone. Whereas violating these relations certifies non-Gaussianity, satisfying them provides evidence for a Gaussian-state description and allows a direct distinction among nondisplaced, nonsqueezed, and displaced-squeezed sectors of the Gaussian state space. Furthermore, we show that it is not possible to uniquely extract state parameters solely from correlation-function measurements without prior assumptions about the Gaussian state. Resolving this ambiguity requires additional loss-sensitive information, e.g., measuring the mean intensity or the vacuum overlap of each mode. In particular, we show under which circumstances these measurements can be used to reconstruct a generic Gaussian state.

Embedding quantum-dot circuits into microwave cavities has emerged as a promising platform for controlling photon-emission statistics by electrical means. With such a circuit version of the Rabi model, we reveal previously unexplored quantum phase transitions in electrically driven lasing regimes. For one-photon interactions, the scaling analysis indicates that the system undergoes a continuous phase transition from thermal to coherent photon emissions. Going beyond this, a discontinuous quantum phase transition from superbunched to coherent states in two-photon processes, accompanied by the bistability within a mean-field theory, is predicted. Both the order of phase transitions and the critical electron-photon coupling can be easily controlled by an electric field, while the tunneling current can be used as a fingerprint of such transitions. Our prediction, along with its extension to multiphoton processes, represents a key step towards accessing lasing phase transitions.

We theoretically investigate the quantum coherence and its nonreciprocity in a cavity magnomechanical system, which consists of a rotating yttrium iron garnet sphere embedded in a microwave cavity and subjected to an external bias magnetic field. By adjusting the direction of the magnetic field, the frequency shift of a magnon mode can be tuned from positive to negative due to the Barnett effect. This effect leads to a significant difference in the system stability and is responsible for the nonreciprocal quantum coherence. We examine how the input power, magnomechanical and magnon-photon coupling rates, decay rates of both the cavity photon mode and the magnon mode, and environmental temperature influence the quantum coherence. Through careful tuning of system parameters, nearly perfect nonreciprocity can be achieved. Our work provides a controllable mechanism for direction-dependent quantum coherence, with potential applications in nonreciprocal quantum devices and information processing.

We investigate a Stern-Gerlach type matter-wave interferometer where an inhomogeneous magnetic field couples to an embedded spin in a nanoparticle to create spatial superpositions. Employing a sequence of harmonic and inverted harmonic-oscillator potentials created by external magnetic fields, we aim to enhance the one-dimensional superposition of a nanodiamond with mass $\approx {10}^{-15}\mathrm{kg}$ to $\approx 1\mu$m. However, random fluctuations of the magnetic field stochastically perturbs the interferometer paths and induce dephasing. We quantitatively estimate the susceptibility of the interferometer to white noise arising from magnetic-field fluctuations. Constraining the dephasing rate $\mathrm{\Gamma }$ to be low enough that the final coherence $e^{-\mathrm{\Gamma }\tau }\ge 0.1$ (where $\tau$ is the experimental time duration), we obtain the following bounds on the noise to signal ratios: $\delta {\eta }_{\text{IHP}}/{\eta }_{\text{IHP}}\lesssim {10}^{-13}$, where ${\eta }_{\text{IHP}}$ is the magnetic-field curvature that gives rise to the inverted harmonic potential, and $\delta {\eta }_{\text{HP}}/{\eta }_{\text{HP}}\lesssim {10}^{-6}$, where ${\eta }_{\text{HP}}$ is the linear magnetic-field gradient that gives rise to the harmonic potential. For such tiny fluctuations, we demonstrate that the Humpty-Dumpty problem arising from a mismatch in position and momentum does not cause a loss in contrast of the interferometer. Furthermore, we show that constraining the dephasing rate leads to stricter bounds on the noise parameters than enforcing a contrast threshold, indicating that good dephasing control ensures high interferometric contrast.

We demonstrate how a single heat exchange between a probe thermal qubit and multiqubit thermal machine encoding a Boolean function can determine whether the function is balanced or constant, thus providing a thermodynamic solution to the Deutsch-Jozsa problem. We introduce a thermodynamic model of quantum query complexity, showing how qubit thermal machines can act as oracles, queried via heat exchange with a probe. While the Deutsch-Jozsa problem requires an exponential encoding in the number of oracle bits, we also explore a restricted Bernstein-Vazirani problem, which admits a linear thermal oracle and a single thermal query solution. We establish bounds on the number of samples needed to determine the probe temperature encoding the solution for the Deutsch-Jozsa problem, showing that it remains constant with problem size. Additionally, we propose a proof-of-principle experimental implementation to solve the three-bit Bernstein-Vazirani problem via thermal kickback. This work bridges thermodynamics and complexity theory, suggesting that quantum thermodynamics could provide an unconventional route to computing beyond classical computation.

We develop the theory of dissociative electron attachment (DEA) to ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ molecules in the 14–18 eV region where attachment is driven by two resonances of ${}^2{\mathrm{\Sigma }}_g{}^{+}$ and ${}^2{\mathrm{\Sigma }}_u{}^{+}$ symmetries. Special attention is given to the description of angular asymmetry in this process due to the coherent superposition of the two resonances. The fixed-nuclei calculations of the resonance potential energy curves and their widths are carried out by the R-matrix method. Vibrational dynamics is then included within the framework of the local complex potential model. Our attempt to describe the angular asymmetry observed in the DEA process [E. Krishnakumar et al., Nat. Phys. 14, 149 (2018).] leads only to a qualitative description of this experiment because of insufficient accuracy of R-matrix calculations at large internuclear separation. This also leads to a large uncertainty in the ungerade resonance contribution to the total cross sections. On the other hand, we show that the major contribution to the DEA peak is due to the ${}^2{\mathrm{\Sigma }}_u{}^{+}$ resonance. Results for the total integrated cross sections are in agreement with existing experiments within the uncertainty of the theoretical calculations.