Nonlocality is one of the key features of quantum physics, which is revealed through the violation of a Bell inequality. In large multipartite systems, nonlocality characterization quickly becomes a challenging task. A common practice is to make use of symmetries, low-order correlators, or the exploitation of local geometries, to restrict the class of inequalities. In this paper, we characterize translation-invariant (TI) Bell inequalities with finite-range correlators in one-dimensional geometries. We introduce a methodology based on tropical algebra tensor networks and highlight its connection to graph theory. Surprisingly, we find that the TI Bell polytope has a number of extremal points that can be uniformly upper-bounded with respect to the system size. We give an efficient method to list all vertices of the polytope for a particular system size, and characterize the tightness of a given TI Bell inequality. The connections highlighted in our work allow us to re-interpret concepts developed in the fields of tropical algebra and graph theory in the context of Bell nonlocality, and vice versa. This work extends a parallel article [M. Hu and J. Tura, Phys. Rev. Lett. 136, 100202 (2026)] on the same subject.

The onset of a quantum phase transition in the Jaynes-Cummings model (JCM) and beyond has been a central goal in quantum light-matter interactions, yet the role of dissipation—often considered detrimental—remains less explored. Here, we demonstrate the proactive creation and control of such phase transitions in a tunneling-driven two-photon JCM via dissipation engineering. We show that single-photon loss triggers a first-order quantum phase transition accompanied by the bistability within a mean-field theory, while two-photon loss stabilizes it into a continuous second-order transition with a power-law behavior near the critical point. By designing electronic dissipation, we can further realize dynamic switching of the transition order, and its balance with the photonic component provides a mechanism for tailoring photon statistics in the phase transitions. Our work transforms dissipation from a disruptive force into a resource for sculpting quantum criticality, establishing a new paradigm for designing nonequilibrium phase diagrams in open quantum systems.

Diatomic molecules with an energetically low-lying ${}^3\mathrm{\Delta }_1$ state are attractive platforms to detect new physics beyond the Standard Model, such as parity- and time-reversal-violating phenomena. One of the advantages of using a ${}^3\mathrm{\Delta }_1$ state is its tiny $\mathrm{\Lambda }$ splitting due to the coupling between the electronic and rotational angular momenta, which facilitates polarizing the molecules in small external electric fields. Theoretical estimation of the magnitude of the $\mathrm{\Lambda }$ splitting is helpful for planning new experiments. In this study, we present a theoretical model to calculate the $\mathrm{\Lambda }$ splitting. Our model integrates the relativistic four-component wave function and the traditional rotational Hamiltonian based on Hund's case (a). The multireference character of the wave function is taken into account. Our calculations for PtH and ${\mathrm{ThF}}^{+}$ molecules qualitatively agree with experiment. The $\mathrm{\Lambda }$ splitting of ${\mathrm{TaO}}^{+}$ for the rotational ground state is predicted to be around 9 kHz. This tiny splitting can reduce the systematic uncertainty, but in a practical experiment, it may cause depolarization during rotation ramp-up.

We experimentally demonstrate spatial confinement of optically driven atomic excitation by broadband composite pulses in a rare-earth ion-doped ${\text{Pr}}^{3+}\text{:}{\text{Y}}_2{\text{SiO}}_5$ crystal. The experimental data confirm that such sequences enable spatially localized excitation well below the diameter of the applied laser beam, with a substantial improvement compared to previous developments and applications of other classes of composite pulses. In particular, we derived and applied broadband composite sequences, which also work efficiently in inhomogeneously broadened media, while also maintaining robustness with regard to fluctuations of the driving laser intensity. We perform extensive measurements to assess and compare the performance of several classes of broadband composite sequences. The findings are confirmed by numerical simulations, which agree very well with the experimental data. As the concepts are also applicable to spatially confined excitations below the diffraction limit of the laser beam, the results serve as an important step towards high-resolution imaging, preparation and addressing in quantum technologies and classical applied optics.

We theoretically study the driven-dissipative dynamics of an array of two-level emitters coupled to a single photonic mode in the presence of disorder in the resonant frequencies. We introduce the notion of subradiant correlations in the dynamics, corresponding to the eigenstates of the Liouvillian with a low decay rate, that can also oscillate in time. While the usual collective subradiant states do not survive under emitter resonant frequency fluctuations, these subradiant correlations are immune to this type of disorder. We employ the group representation theory to find the number of nontrivial oscillating subradiant correlations in the system. These long-living correlations exist in finite-size systems, when their lifetime is parametrically longer than in the so-called Dicke time crystal phase.

In the present work, we introduce and explore a technique for the efficient removal of vortices from an atomic Bose-Einstein condensate through the application and subsequent removal of a one-dimensional optical lattice. We showcase a prototypical experimental realization of the technique that motivates a detailed theoretical study of vortex removal mechanisms. Through simulations of the condensate dynamics during application of the optical lattice, we also discover a vortex removal mechanism that arises in narrow, optical-lattice-induced atomic density channels for which the channel width is on the order of the nominal vortex core size and healing length. This mechanism involves the density profile typically associated with a vortex core spatially separating from the phase singularity associated with the vortex. By analyzing numerical experiments covering a wide range of variations of the optical lattice amplitude and fringe periodicity, we identify the existence of an optimal set of parameters that enables the efficient removal of all vortices from the condensate. This analysis paves the way for further studies aimed at understanding vortex dynamics in narrow channels and adds to an experimental toolkit for working with vortices and controlling the dynamical states of condensates.

High-accuracy calculations of electric dipole polarizabilities and quadrupole moments ($\mathrm{\Theta }$) of the clock states of the singly charged calcium (${\mathrm{Ca}}^{+}$), strontium (${\mathrm{Sr}}^{+}$), and barium (${\mathrm{Ba}}^{+}$) alkaline-earth ions are estimated by employing relativistic coupled-cluster (RCC) theory. It demonstrates the importance of the triple excitations in the RCC method for precise determination of the above quantities. We also observe a different trend of correlations in the $\mathrm{\Theta }$ values than an earlier study with respect to orbitals from higher angular momenta. Reliability of the results is verified by comparing the calculated energies, magnetic dipole hyperfine structure constants, and lifetimes of the atomic states with the experimental values of the ${}^{43}\mathrm{Ca}^{+}, {}^{87}\mathrm{Sr}^{+}$, and ${}^{137}\mathrm{Ba}^{+}$ ions. Nuclear quadrupole moments of these isotopes are also estimated by combining calculations with the measured electric quadrupole hyperfine structure constants, showing large deviations from the literature values.

In disordered systems, directly describing electron dynamics under a driving field—as is commonly done for atoms or crystals—remains a significant challenge. However, high-order harmonic generation (HHG), which inherently encodes information about electron motion, provides a powerful tool to qualitatively probe the dependence of electron quiver amplitude on laser intensity and wavelength. In this work, we investigate the quiver amplitude of electrons in one-dimensional disordered systems designed to mimic liquids ($\alpha$ phase) and the thermal effects in crystals ($\beta$ phase). Using the minimum chain length required to converge HHG spectra as a proxy for the quiver amplitude, we find that in the $\alpha$ phase, the quiver amplitude decreases with increasing disorder but is largely insensitive to wavelength. For both phases, the quiver amplitude decreases with increasing laser intensity under weak disorder, but this trend saturates at strong disorder. Furthermore, when the nearest-neighbor distributions match, the two phases exhibit similar HHG spectra under strong fields.

This work theoretically investigates possibilities of using the Stimulated Raman Adiabatic Passage (STIRAP) and its variants to control a coherent superposition of quantum states. We present a generalization of the so-called fractional STIRAP (f-STIRAP), demonstrating precise control over the mixing ratio of quantum states in the wave packet. In contrast to conventional f-STIRAP, designed to drive a system from an eigenstate into a coherent superposition, our scheme enables arbitrary control over the composition of an already existing superposition state. We demonstrate that an approximate version of this technique—where analytically designed laser pulses with composite envelopes are replaced by simple Gaussian pulses—achieves comparable performance in controlling the dynamics of the wave packet. A limiting case of this scheme, utilizing two pulses with identical Gaussian envelopes and tuned delay and relative phase, is also explored, revealing experimentally accessible pathways for manipulating quantum coherence. We apply our developed techniques to control the ultrafast charge migration in the spin-orbit split ground electronic states of xenon cations via intermediate valence- and core-excited states. Finally, we propose concrete experimental realizations of the developed control schemes in combination with attosecond transient absorption spectroscopy as a method to probe the system.

Achieving precise control of ultracold atomic gases requires a detailed understanding of atom loss mechanisms. Motivated by the anomalous three-body decay in a three-component Fermi gas reported by Schumacher et al. [arXiv:2301.02237], this work investigates mechanisms that possibly contribute to the observed loss. The three-body Schrödinger equation is solved in the hyperspherical adiabatic representation with pairwise van der Waals interactions, and the $S$ matrix is obtained via the eigenchannel $R$-matrix method to compute recombination rate coefficients $K_3$ and two-body cross sections. At the magnetic-field strength where the anomalous decay occurs, $K_3$ is unitary limited, exhibiting the threshold energy scaling $K_3\left(E\right)\propto E^{-1}$ that applies when only one scattering length is resonant. Consequently, the thermally averaged $\langle K_3\rangle$ acquires a temperature dependence. Because the experiment is performed in the degenerate regime, $\langle K_3\rangle$ also explicitly depends on the per-spin densities through the per-spin Fermi energies $E_F^{\left(i\right)}\propto n_i^{2/3}$. As the gas is diluted and degeneracy is reduced, $\langle K_3\rangle$ approaches the nondegenerate value and becomes a function of temperature only. Channel-resolved branching ratios and cross sections are folded into a Monte Carlo cascade simulation of secondary collisions and trap escape. The analysis indicates that typical three-body recombination events remove fewer than three atoms on average and that the atom losses are primarily due to the ejection of secondary collision products rather than the initial three-body recombination products. Therefore, a significant fraction of the released binding energy remains in the trapped ensemble as kinetic energy. Retained energy drives evaporative loss, offering a plausible, partial explanation for the anomalous decay.

We propose to use cavity Rydberg electromagnetically induced transparency to generate Schrödinger cat states of optical photons. We predict that this should make it possible to generate states with relatively large mean photon numbers. With existing technology, mean photon numbers around 30 seem feasible. The main limitation is photon loss during the process, which generates the state. The ability to tune the strength of the photon loss caused by atomic spontaneous emission makes it possible to have little decoherence despite significant photon loss during the generation of the state.

We investigate the Coulomb explosion dynamics of ${\mathrm{H}}_2$ molecules embedded in helium nanodroplets, induced by an intense ultraviolet femtosecond laser pulse. By employing ion-ion coincidence and momentum correlation spectroscopy, we identify the Coulomb-exploded double ionization of ${\mathrm{H}}_2$ molecules within the droplets. Our results demonstrate that the collisions between dissociating ${\mathrm{H}}^{+}$ ions and surrounding He atoms significantly alter both the kinetic energy distributions and the emission direction of the ion fragments. Notably, the $\mathrm{He}{\mathrm{H}}^{+}$ fragments originating from the Coulomb explosion channel exhibit higher kinetic energies in larger droplets, a phenomenon driven by the solvation dynamics that depend on the fragment's kinetic energy and droplet size. This study provides deep insights into the translation, dissociation, and solvation processes of light impurities in quantum liquid, underscoring the critical role of droplet size in shaping fragment kinetics during these processes.

We report the creation of an ultracold gas of bosonic ${}^{39}\mathrm{K}{}^{133}\mathrm{Cs}$ molecules. We first demonstrate a cooling strategy relying on sympathetic cooling of ${}^{133}\mathrm{Cs}$ to produce an ultracold mixture. From this mixture, weakly bound molecules are formed using a Feshbach resonance at 361.7 G. The molecular gas contains $7.6\left(10\right)\times {10}^3$ molecules with a lifetime of about 130 ms, limited by two-body decay. We perform Feshbach spectroscopy to observe several new interspecies resonances and characterize the bound state used for magnetoassociation. Finally, we fit the combined results to obtain improved K-Cs interaction potentials. This provides a good starting point for the creation of ultracold samples of ground-state ${}^{39}\mathrm{K}{}^{133}\mathrm{Cs}$ molecules.

Ultracold dipolar atoms and molecules provide a flexible quantum simulation platform for studying strongly interacting many-body systems. Determining microscopic Hamiltonian parameters of the simulator is crucial for it to be useful. We study effective interactions emerging in quasi-one-dimensional (q1D) dipolar quantum gases, revealing significant nonuniversal corrections to the commonly used 1D pseudopotential. We demonstrate that a full 3D treatment employing realistic interaction potentials is essential for describing the reduced-dimensional system. Our findings are particularly relevant to experiments probing excited states and nonequilibrium phenomena.

The formation and properties of a supersolid structure in a three-component ultracold Bose gas mixture at $T=0$ are investigated theoretically. The system consists of ${}^{23}\mathrm{Na}$, ${}^{39}\mathrm{K}$, and ${}^{41}\mathrm{K}$ atomic species, in which the binary mixtures of (${}^{23}\mathrm{Na},{}^{39}\mathrm{K}$) and (${}^{39}\mathrm{K},{}^{41}\mathrm{K}$) can form self-bound quantum droplets stabilized by quantum fluctuations. Two such droplets can bind together by the shared ${}^{39}\mathrm{K}$ component, forming a stable “dimer” structure, which displays vibrational modes analogous to a classical diatomic molecule. A simple protocol is proposed to create a stable linear chain formed by periodic repetition of this basic building block, i.e., an alternating sequence of (${}^{23}\mathrm{Na},{}^{39}\mathrm{K}$) and (${}^{39}\mathrm{K},{}^{41}\mathrm{K}$) droplets. This structure exhibits both periodic density modulations from the droplet ordering and global phase coherence due to the shared ${}^{39}\mathrm{K}$ component, satisfying the criteria for supersolidity. This expands the class of known supersolids by adding a system where mediated binding—rather than intrinsic long-range interactions or engineered band structures as in previously known supersolids—is the key organizing principle, thereby offering alternative directions for both theory and experiment. The low-energy excitation spectrum, probed by density perturbations, identifies modes corresponding to droplet vibrations close to the ones expected from a classical diatomic chain, coexisting with low-energy superfluid (Goldstone-type) modes.

We investigate a phase-controllable mechanism for generating optical torque in a five-level double-tripod (DT) atom-light coupling scheme interacting with four strong coherent control fields as well as two weak optical vortex probe beams carrying orbital angular momentum (OAM). The spatial phase gradients of the OAM-carrying probes induce a quantized torque that is transferred to the atoms, rotating them and generating a directed atomic flow within an annular geometry. Analytical solutions of the optical Bloch equations under steady-state conditions show that the induced torque and resulting rotational motion exhibit high sensitivity to phase variations. We show that the DT system coherently reconfigures into either coupled-$\mathrm{\Lambda }$ or double-$\mathrm{\Lambda }$ schemes depending on the relative phases, with each configuration exhibiting distinct quantized torque characteristics. This enables precise phase control of the atomic current flow, with potential applications in quantum control, precision measurement, and quantum information processing.

Spontaneous parametric down-converters (SPDCs) are the best available entanglement sources for distributing entanglement in a quantum internet. However, their intrinsically probabilistic nature, and their need to operate at low brightness to suppress multipair events, dictate that multiplexed SPDC arrays are required for high-rate distribution in that application. Early SPDC multiplexing proposals involved path switching, whose switching losses significantly degrade performance. The present paper proposes and analyzes a scheme for spectral multiplexing that provides entanglement-distribution rates well in excess of the state of the art. It builds on zero-added-loss multiplexing (ZALM) [Phys. Rev. Appl. 19, 054029 (2023)] for high-rate heralded entanglement generation, which does not require a switched array of SPDCs. Our ZALM's SPDCs rely on nonlinear crystals with $N_I$ phase-matched spectral islands, each generating two-mode squeezed-vacuum states. Also, our ZALM's multiplexing protocol uses both same-island and cross-island heralding, which allows the entanglement-delivery rate to approximately scale as $N_I^2$ in the realistic weak-squeezing regime. As a result, our scheme uses an order of magnitude fewer spectral channels than the original ZALM proposal, which may enable near-term implementations of satellite-to-ground or fiber-optic based ZALM architectures.

In one-dimensional bosonic quantum mixtures with a SU(2)-symmetry-breaking Hamiltonian, the dynamical evolution explores different particle-exchange-symmetry sectors. For the case of infinitely strong intraspecies repulsion, the hallmark of such symmetry oscillations is time modulations of the momentum distribution [Musolino et al., Phys. Rev. Lett. 133, 183402 (2024)], an observable routinely accessed in experiments with ultracold atoms. In this work we show that this phenomenon is robust in strongly interacting quantum mixtures with an arbitrary interspecies-to-intraspecies interaction-strength ratio. Taking as the initial state the ground state of the SU(2)-symmetric Hamiltonian and time evolving with the symmetry-breaking Hamiltonian, we analyze how the amplitude and frequency of symmetry oscillations, and thus of the momentum-distribution oscillations, depend on the strength of the symmetry-breaking perturbation. We find that the set of symmetry sectors which are coupled during the time evolution is dictated by the spin-flip symmetry of the initial state and show that the population of the initial state may vanish periodically, even in the thermodynamic limit, thus revealing the robustness and universality of the symmetry oscillations.

We demonstrate that the Fourier transform of a function leads to interference effects in phase space which allow the reconstruction of the essential properties of the original function, even when we restrict the inverse Fourier transform to the phase factor rather than the complete Fourier transform. We analyze this phase-only reconstruction, known from signal processing, in quantum mechanics for the elementary example of a superposition of two real-valued Gaussians. We employ the Wigner function as well as techniques of semiclassical quantum mechanics to show that their key features, such as their separation and their width, are indeed encoded in the phase of the Fourier transform. For this example, the amplitude-only reconstruction performing the inverse Fourier transform of the absolute value of the Fourier transform fails.

We propose an effective scheme to enhance $N$-photon bundle emission of the squeezed mode via parametric driving. By placing a ${\chi }^{\left(2\right)}$ nonlinear medium and a typical two-level qubit into a cavity, the atom-cavity coupling strength is greatly enhanced while an additional squeezed reservoir is introduced to suppress noise amplification. As a consequence, it is demonstrated that the emitted probabilities of two-photon bundles are obviously increased, whereas the purity remains nearly unchanged. Remarkably, even for the more challenging case of three-photon bundles, our scheme still achieves a significant enhancement in their generation. The light resource with squeezed photons may find potential applications in quantum sensing technology and quantum metrology.