This paper examines a quantitative and optimal lower bound on the detector efficiency in a (2,2,2) Bell experiment within a fully device-independent framework, whereby the detectors used in the experiment are uncharacterized. We provide a tight lower bound on the minimum efficiency required to observe a desired Bell-CHSH violation using the Navascués-Pironio-Acín hierarchy, confirming tightness up to four decimal places with numerical optimization over explicit quantum realizations. We then introduce the effect of dark counts and demonstrate how to quantify the minimum required efficiency to observe a desired Clauser-Horne-Shimony-Holt (CHSH) violation with an increasing dark count error. Finally, to obtain an analytical closed-form expression of the minimum efficiency, we consider the set of no-signaling behaviors that satisfy the Tsirelson bound, which are easier to characterize than the quantum set. Using such behaviors, we find a simple closed-form expression for a lower bound on the minimum efficiency which is monotonically increasing with the CHSH violation, though the analytically obtained lower bounds are meaningfully below the numerically tight lower bound.

Recently, Xu et al. [Phys. Rev. A 111, 022416 (2025)] have constructed minimal nonlocal orthogonal product states (OPSs) on $n$-partite systems ($n\ge 3$), as well as minimal nonlocal orthogonal entangled states (OESs) on both bipartite and $n$-partite systems ($n\ge 3$). A meaningful question is whether entanglement-assisted discrimination protocols with less entanglement than teleportation can be designed for the above OPSs and OESs. This paper provides an affirmative answer to this question and diagrammatically illustrates the entanglement-assisted local discrimination protocols through geometric shapes. First, we present two efficient entanglement-assisted local discrimination protocols for nonlocal OPSs on tripartite systems, and extend both protocols to general $n$-partite systems ($n\ge 3$). Furthermore, we implement the efficient local discrimination of nonlocal OESs on both bipartite and tripartite systems by using auxiliary entanglement, and the discrimination method is generalized to $n$-partite systems ($n\ge 3$). In particular, when distinguishing tripartite nonlocal OESs, we construct local discrimination protocols with less entanglement resource for $d=4$ and $d=5$. Our results highlight the essential role of entanglement in identifying minimal nonlocal sets on multipartite systems, revealing the phenomenon of less nonlocality with more entanglement.

An octant representation of higher-order optical modes that includes Laguerre-Gaussian and Hermite-Gaussian modes is presented. The octant picture captures the high-dimensional nature of three-state optical systems and beyond, with standard Poincaré spheres for orbital angular momentum forming subspaces of the entire state space. This representation enables intuitive manipulation of both classical modes and optical qudits and provides a framework for extending Berry phases and topological invariants to high dimensions.

Advances in experimental control of interacting quantum many-body systems with multiple tunable parameters—such as ultracold atomic gases and trapped ions—are driving rapid progress in quantum thermodynamics and enabling the design of quantum thermal machines. In this work, we utilize a sudden quench approximation as a means to investigate the operation of a quantum thermodynamic Otto cycle in which multiple parameters are simultaneously controllable. The method applies universally to many-body systems where such control is available, and therefore provides general principles for investigating their operation as a working medium in quantum thermal machines. We investigate the application of this multiparameter quench protocol in an experimentally realistic one-dimensional Bose gas, as well as in the transverse-field Ising model. We find that such a multiparameter Otto cycle, when operating as an engine, outperforms not only its constituent single-parameter Otto cycles in terms of the net work and efficiency, but also the combined net work of its constituent engine cycles when added together independently. We also find that a similar multiparameter enhancement applies to the coefficient of performance when the Otto cycle operates as a refrigerator.

Lasing and coherent perfect absorption (CPA) are time-reversed manifestations of non-Hermitian light-matter interactions. While exceptional points (EPs) have been extensively explored for controlling lasing dynamics, their role in the concurrent manipulation of lasing and absorption remains largely unexplored. Here, we demonstrate the emergence of a pair of conjugate second-order EPs (EP2s) in a gain-loss-engineered Fabry-Pérot microcavity that enables dual-state operation involving both coherent amplification and absorption. By spatially tailoring gain and loss, we realize two such EP2s: one associated with the coalescence of coupled scattering-matrix poles and the other, its conjugate, arising from the coalescence of corresponding zeros, thereby directly linking the amplifying and absorbing branches of the system. Leveraging the branch-point topology of these conjugate EP2s, we adiabatically encircle them in the gain-loss parameter space and achieve deterministic state permutation, enabling multiple reconfigurable switching schemes for the controlled generation and manipulation of threshold lasing and CPA. Notably, simultaneous encirclement of these conjugate EP2s yields a coordinated dual-state switching protocol, resulting in a frequency-matched coexistence of lasing and absorption responses within the same cavity. Our results establish an EP-based framework for unified and flexible control of lasing and absorption in non-Hermitian photonic systems.

Highly excited Rydberg states of lanthanides are a promising, yet largely unexplored, playground for quantum studies. Here we report on the first high-resolution spectroscopy of ${}^{162}\mathrm{Dy}$ obtained by two-color trap depletion spectroscopy in a magneto-optical trap. The absolute excitation frequency of over 700 states with effective principal quantum number $21\le n\le 130$ is measured with an accuracy of 20 MHz. Most states are assigned to the eight different series converging to the first $4{\mathrm{f}}^{10}{(}^5{\mathrm{I}}_8)6\mathrm{s}{(}^2{\mathrm{S}}_{1/2}){}^6{\mathrm{I}}_{17/2}$ ionization potential. This energy is measured at $E_{\mathrm{IP}}=47901.8265\pm 0.0008{\mathrm{cm}}^{-1}$, improving the precision of the literature value by over an order of magnitude. A multichannel-quantum-defect-theory approach is used to benchmark and refine the assignments and to characterize six observed perturbing states belonging to higher ionization limits. These results pave the way for using dysprosium in Rydberg-based quantum architectures, leveraging the unique properties arising from its complex electronic structure. They also represent a compelling benchmark for ab initio calculations of open-shell atomic systems.

We reveal that the entropic uncertainty relation with a quantum memory is able to intrinsically connect local generic contextuality addressed in the pioneering work by Spekkens [Phys. Rev. A 71, 052108 (2005)] and nonlocal quantum resources such as entanglement and Bell nonlocality. Based on the constructed optimal set for any given single-qubit state, we prove rigorously a faithful criterion to witness the generic contextuality in the scenario of local quantum state preparation. Furthermore, within the framework of quantum resource distribution, it is proved that there exist quantitative trade-off relations between local preparation contextuality and bipartite entanglement or Bell nonlocality in a shared quantum system, which are captured by two inequalities where the local and nonlocal quantum resources can coexist. The faithful criterion and quantitative inequalities are all experimentally testable, which are verified through two independent, well-designed demonstrations on the Quafu quantum cloud platform.

Time-reversal-symmetry breaking (TRSB) has been central to detecting exotic phases of matter. Here, we leverage the circuit electrodynamics capabilities of superconducting devices to propose a scheme based on a multimode superconducting ring resonator for the sensitive probing of TRSB in quantum materials. A ring resonator enables nonlinear cross-interactions between the modes which act as built-in amplifiers to be harnessed for enhanced sensing. Using a driven-dissipative model, we explore the nonlinear dynamics of a two-mode superconducting circuit with self- and cross-Kerr nonlinearities under conditions near the bifurcation threshold. By mapping the optimal parameter regimes, we show that even when the photon occupation numbers are subjected to different initial conditions, they can be driven into a symmetric configuration which is broken even with weak TRSB. Through a full quantum analysis we demonstrate that the Kerr-nonlinear interactions up-convert the magnetic effects of the material-resonator hybrid system, enhancing the probing of TRSB. Our findings highlight the utility of superconducting microwave resonators outside of quantum information processing, as a tool for probing exotic states of matter.

We study the structure of multipartite entanglement in monitored quantum circuits exhibiting measurement-induced phase transitions (MIPTs). Using a one-dimensional Clifford circuit subject to local measurements with a probability $p$, we show numerically that the entanglement depth, corresponding to the size of the largest cluster of entangled qubits, scales as a power law with system size on both sides of the transition. The power law exponent is 1 in the entangling phase and continuously decreases to 0 as $p\to 1$ in the disentangling phase. In addition, we find that the spatial support of the largest cluster exhibits an approximate fractal geometry with a tunable fractal dimension controlled by the measurement rate. We argue that this structure arises from a competition between unitary-driven coagulation of entangled clusters and measurement-induced fragmentation, giving rise to a fractal steady state reminiscent of classical coagulation-fragmentation models. Away from the MIPT critical point, the fractal dimension matches the entanglement depth power law exponent. These results show that multipartite entanglement structure provides a fresh perspective on the emergent quantum correlations in monitored quantum circuits and noisy quantum dynamics.

Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The bottleneck of the experimental realization of the algorithm is the modular exponentiation operation. In this paper, based on a relation between the modular multiplication operator and generalizations of discrete Fourier transforms, we propose a quantum circuit for modular exponentiation. A distinctive feature of our proposal is that our circuit can be entirely implemented in terms of the standard quantum circuit for the discrete Fourier transform and its variants. The gate complexity of our proposal is $O\left(L^3\right)$ where $L$ is the number of bits required to store the number being factorized. It is possible that such a proposal may provide easier avenues for near-term generic implementations of Shor's algorithm, in contrast to existing realizations which have often explicitly adapted the circuit to the number being factorized.

Quantum-optical descriptions of strong-field processes have attracted significant attention in recent years. Typically, the theoretical modeling has been conducted in the Schrödinger picture, where results are only obtainable under certain approximations, while, in contrast, the Heisenberg picture has remained relatively unexplored. In this work, we develop an accurately controlled perturbative expansion of the time-evolution operator in the Heisenberg picture and derive beyond-semiclassical corrections to the emitter dynamics due to the coupling to the quantized electromagnetic field, capturing effects of the quantum fluctuations present in the latter. We focus on high-order harmonic generation (HHG), where the approach is accurate in parameter regimes of current interest and gives closed-form expressions for key observables. This formulation not only simplifies numerical calculations compared to the Schrödinger-picture approach but also provides a clear correspondence between nonclassical features of the emitted light and the underlying induced dynamics of the generating medium including quantum fluctuations. Moreover, the Heisenberg framework naturally yields scaling relations with the number of independent emitters, enabling us to assess whether nonclassical behavior should persist under typical experimental conditions involving large emitter ensembles. Interestingly, we find that the degree of squeezing increases with the number of emitters, whereas the photon statistics approaches a classical Poissonian distribution in the many-emitter limit. We also find that the beyond-semiclassical emitter dynamics significantly enhances the degree of squeezing of the emitted light. Our work advances the theoretical understanding of quantum-optical HHG and introduces an accessible and well-controlled framework to describe realistic experiments.

Integrating two chemically distinct atomic species into a miniaturized, high-flux cold-atom source is a key challenge for modern experiments with ultracold atomic mixtures and polar molecules. Here, we report a compact setup with in-series two-dimensional magneto-optical traps (2D MOTs) that provides high-flux cold lithium and rubidium atoms. Thanks to the efficient short-distance Zeeman slowing, the maximum 3D MOT loading rate of lithium atoms reaches a record value of $6.6\times {10}^9$ atoms/s at a moderate lithium-oven temperature of 372 degrees Celsius, which is 44 times higher than that without the Zeeman slowing light. The flux of rubidium is also as high as $2.3\times {10}^9$ atoms/s with the rubidium oven held at room temperature. Meanwhile, the entire vacuum-chamber system, including an ultra-high-vacuum science cell, is within a small volume of $65\times 55\times 70{\mathrm{cm}}^3$. Our work represents a substantial improvement over traditional bulky and complex dual-species cold-atom setups. It provides a good starting point for the fast production of a double-degenerate lithium-rubidium atomic mixture and large samples of ultracold lithium-rubidium ground-state molecules.

Nonlinear classical mechanics has established rich phenomena. These include limit tori defined by toroidal attractors supporting quasiperiodic motion with incommensurate frequencies. We study the fate of such structures in open quantum systems using two coupled driven-dissipative Kerr cavities modeled via the Lindblad master equation. Combining Liouvillian spectral theory with the truncated Wigner approximation, we characterize the quantum-to-classical crossover. In the classical limit, two pairs of purely imaginary Liouvillian eigenvalues signal persistent quasiperiodic modes. Quantum fluctuations induce small negative real parts to these eigenvalues, giving rise to finite lifetimes and leading to the quantum melting of the torus. The associated Liouvillian gaps vanish algebraically in the classical limit, indicating a dynamical critical crossover with spontaneous breaking of time-translational symmetry. Quantum trajectory analysis reveals that this melting is driven by fluctuation-induced dephasing. Using a circular-variance-based order parameter, we uncover universal scaling in system size and time. These results establish quantum melting of limit tori as a distinct and robust nonequilibrium critical phenomenon, with clear experimental signatures in trapped ions and superconducting circuits.

We study the decay of a dense, ultracold sample of weakly bound DyK dimers stored in an optical dipole trap. Our bosonic dimers are composed of the fermionic isotopes ${}^{161}\mathrm{Dy}$ and ${}^{40}\mathrm{K}$, which is of particular interest for experiments related to pairing and superfluidity in fermionic systems with mass imbalance. We have realized dipole traps with near-infrared laser light in four different wavelength regions between 1050 and 2002 $\mathrm{nm}$. We have identified trap-light-induced processes as the overall dominant source of losses, except for wavelengths around 2000 $\mathrm{nm}$, where light-induced losses appeared to be much weaker. In a trap near 1550 $\mathrm{nm}$, we found a plateau of minimal light-induced losses, and by carefully tuning the wavelength we reached conditions where losses from inelastic collisions between the trapped dimers became observable. For very weakly bound dimers close to the center of a magnetically tuned Feshbach resonance, we demonstrate the Pauli suppression of collisional losses by about an order of magnitude.

Quasinormal modes characterize the transient response of static optical cavities. Here we introduce the notion of a Floquet quasinormal mode to describe transient responses in photonic time crystals. Contrasting their static counterparts, exceptional points associated with symmetry transitions are an inherent feature, as modes spontaneously and nonperturbatively lock their phase to the oscillations of the material. We further investigate the limiting behavior of the Floquet quasinormal modes in large cavities. Distinct nonperturbative behavior arises in time-modulated systems as increasingly large time-crystal cavities come closer to achieving the maximum gain predicted from a bulk wave number band gap.

We present a scheme for laser cooling and magneto-optical trapping of the group-IV (a.k.a. group-14 or tetrel) atoms silicon (Si), germanium (Ge), tin (Sn), and lead (Pb). These elements each possess a strong type-II transition $(J\to J^{\prime }=J-1)$ between the metastable $s^2{p}^2{}^3{P}_1$ state and the excited $s^{2}p{s}^{\prime }{}^3{P}_0^{\circ }$ state at an accessible laser wavelength, making them amenable to laser cooling and trapping. We focus on the application of this scheme to Sn, which has several features that make it attractive for precision measurement applications. We perform numerical simulations of atomic beam slowing, capture into a magneto-optical trap (MOT), and subsequent sub-Doppler cooling and compression in a blue-detuned MOT of Sn atoms. We also discuss a realistic experimental setup for realizing a high phase-space density sample of Sn atoms.

We present a single-photon transduction scheme using four-wave-mixing and quantum scattering in planar, cooperative Rydberg arrays that is both efficient and highly directional and may allow for terahertz-to-optical transduction. In the four-wave-mixing scheme, two lasers drive the system, coherently trapping the system in a dark ground-state manifold and coupling a signal transition, which may be in the terahertz, to an idler transition that may be in the optical regime. The photon-mediated dipole–dipole interaction between different emitters generates collective super- and subradiant dipolar surface modes, both on the signal and the idler transition. As the array is cooperative with respect to the signal transition, an incident signal photon can efficiently couple into the array and is admixed into dipolar idler modes by way of the drive. Under specific criticality conditions, this admixture is coupled into a superradiant idler mode, which primarily decays into a specific, highly directional optical photon that propagates within the array plane. Outside of the array, this photon may then be coupled into existing quantum devices for further processing. Using a scattering-operator formalism, we derive resonance and criticality conditions that govern this two-step process and obtain analytic transduction efficiencies. For lattices of infinite extension, we predict transduction efficiencies into specific spatial directions of up to 50%, while the overall, undirected transduction efficiency can be higher, beyond 90%. An analysis for finite arrays of $N^2$ emitters shows that the output is collimated into lobes that narrow as $1/\sqrt{N}$. Our scheme combines the broadband acceptance of free-space four-wave mixing with the efficiency, directionality, and tunability of cooperative metasurfaces, offering a route toward quantum coherent THz detection and processing for astronomical spectroscopy, quantum-networked sparse-aperture imaging, and other quantum-sensing applications.

An Auger-electron–ion coincidence experiment on ${\mathrm{N}}_2$ was performed using a recently developed electron–ion coincidence imaging spectrometer equipped with a photoemission electron gun. Clear electron–ion energy correlations were observed and used to determine the state-selected dissociation channels and their corresponding dissociation limits. Molecular-frame Auger-electron angular distributions were also obtained and used to determine the symmetry of the contributing dicationic states. Triple-coincidence measurements further demonstrate that Auger electrons in the 350–360 eV region arise predominantly from $1s$ shake-off ionization, followed by Auger decay into low-lying ${\mathrm{N}}_2{}^{3+}$ states that dissociate into ${\mathrm{N}}^{2+}+{\mathrm{N}}^{+}$. These results establish electron-impact-induced Auger-electron–ion coincidence spectroscopy as a powerful tool for state-selective studies of molecular dication and trication fragmentation dynamics.

When the dynamics of a quantum system of interest is known, an informationally complete set of observables is not needed for state reconstruction via tomographic techniques: letting the system evolve before performing the measurement allows one to effectively extend the available ways to probe the system. This idea leads to dynamical quantum tomography, whose feasibility we characterize for general quantum dynamics using Krylov-based methods. Specializing in Markovian ones, we also provide deterministic tests and randomized ones to effectively assess parametric dynamics. The limits of the methods are explored by comparing unitary and open dynamics when a single observable is available, and the set of observables whose expectation can be reconstructed from the available ones characterized. The framework is illustrated with applications to a spin chain (with or without dissipation) and an electron-nuclear system.

We consider coherently coupled bosonic mixtures scattering at low energies in the presence of an external confinement along either one or two directions. We exactly solve the two-body scattering problem, showing that for large Rabi coupling the confinement-induced resonance can be displaced towards scattering lengths much smaller than the oscillator length. Our results make the observation of confinement-induced resonances more tunable and accessible, offering yet another handle for the efficient control of strong interactions in ultracold quantum gases.