Periodically driven systems, or Floquet systems, exhibit many novel dynamics and interesting out-of-equilibrium phases of matter. Those phases arising with the quantum systems' symmetries, such as global U(1) symmetry, can even show dynamical stability with symmetry protection. Here we experimentally demonstrate a U(1) symmetry-protected prethermal phase, via performing a digital-analog quantum simulation on a superconducting quantum processor. The dynamical stability of this phase is revealed by its robustness against external perturbations. We also find that the site-averaged square of the two-spin correlation function in this phase is stabilized by the interaction between the spins. Our work reveals a promising prospect in discovering emergent quantum dynamical phases with digital-analog quantum simulators.

The estimation of physical parameters with Heisenberg sensitivity and beyond is one of the crucial problems for current quantum metrology. Commonly, an unavoidable lossy effect is believed to be the main obstacle when applying fragile quantum states. To utilize the lossy quantum metrology, we offer an interferometric procedure for estimation of phase parameters at the Heisenberg (up to $1/N$) and super-Heisenberg (up to $1/N^3$) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is a soliton Josephson junction (SJJ) system, which provides the formation of the quantum probe, the entangled Fock (NOON-like) state, beyond the superfluid-Mott insulator quantum phase transition point. We illustrate that such states are close to the optimal ones even with moderate losses. The enhancement of phase estimation accuracy remains feasible for both the linear and nonlinear metrologies with the SJJs and allows further improvement for the current experiments performed with atomic condensate solitons with a mesoscopic number of particles.

A computational study of ${\mathrm{Be}}^{4+}+\mathrm{H}\left(2s\right)$ collisions has been carried out. Two computational models have been employed: the classical trajectory Monte Carlo (CTMC) method and the numerical solution of the time-dependent Schrödinger equation (GTDSE). The integral $n$ and $nl$ partial cross sections for H excitation and electron capture, obtained with both methods, are compared at two energies: 20 and 100 keV/u. It is shown that the CTMC, with an improved hydrogenic initial distribution, provides excitation cross sections in good agreement with the numerical calculation for excitation to $\mathrm{H}(n$) with $n>3$. The agreement between the corresponding $nl$ partial cross sections from both methods is less satisfactory at 100 keV/u, where there is a transition from the low-energy mechanism that involves an increase of the populations with $l$, and the high-energy mechanism, where the dipole-allowed transitions are dominant. The electron capture cross sections calculated with the CTMC method do not depend on the initial distribution and show a reasonable agreement with the GTDSE ones, which supports the use of the CTMC method to calculate electron capture cross sections into highly excited levels and total cross sections. The mechanism of the electron capture process is discussed and CTMC calculations of the ionization process are also presented.

The asymmetric Fano profile, which is caused by the two-channel interference between discrete states and relevant continuum states, presents a great challenge to atomic and molecular physics. This study investigates the inner-valence excitations of argon $3s$ electrons in the energy range 24.5–29.5 eV using an electron energy-loss spectrometer. The absolute generalized oscillator strength densities of the $3s$ excitations and the Fano profile parameters (i.e., $q$, $f_a$, $\rho {}^2$, $f$, $S$) in $0<K^2<2.2$ a.u. for the $3s3p^{6}ns$ ($n=4$ and 5), $3s3p^{6}np$ ($n=4$ and 5), and $3s3p^{6}3d$ autoionization states are determined. For the same Rydberg series, similar momentum-transfer-dependence behaviors are observed for the Fano profile parameters $q$, $f_a$, $\rho {}^2$, $f$, and $S$. The magnitudes of $q$ and $f_a$ are found to be nearly equal for the same Rydberg series, while the corresponding $f$ and $S$ parameters decrease as the principal quantum number increases, confirming the theoretical predictions of Fano and Cooper [U. Fano and J. W. Cooper, Phys. Rev. 137, A1364 (1965)]. Moreover, the typical dipole-allowed or dipole-forbidden $K^2$-dependence behaviors of the Fano profile parameters are used to elucidate the properties of electric transition multipolarities. The parameters of the Fano profile derived in a large $K^2$ region offer an opportunity to understand the wave functions far away from the nucleus.

The recently presented general algorithm for calculating an atomic fine structure [Kędziorski et al., Chem. Phys. Lett. 751, 137476 (2020)] is employed to study the fine splitting of the lowest eight ${}^{3}P$ states of beryllium, i.e., the $1s^{2}2snp$, $n=2,\cdots ,9$, ${}^{3}P$ states. All-electron explicitly correlated Gaussian functions and a finite-nuclear-mass variational method are used in the calculations. The energies of the states are augmented with the leading ${\alpha }^2$ relativistic and ${\alpha }^3$ (and approximate ${\alpha }^4$) QED corrections ($\alpha =\frac{1}{c}$ is the fine-structure constant, and $c$ is the speed of light in atomic units). The calculated results are compared with the available experimental data.

Quantum sensor networks such as the existing networks of atomic clocks and magnetometers offer intriguing capabilities in searches for transient signals such as dark matter or fields sourced by powerful astrophysical events. The common matched-filter technique relies on the signal-to-noise-ratio (SNR) detection statistic to probe such transients. For macroscopic dark matter objects, the network would register a sweeping signal as the object propagates through at galactic velocities. A potential event is registered when the SNR from a specific template exceeds a threshold set by a desired false positive rate. Generically, to span the continuous parameter space for the network-exotic-physics encounter, one has to deal with multiple templates. In such template-bank searches, the natural generalization of the SNR statistic is the maximum-signal-to-noise-ratio (SNR-max) statistic, defined as the maximum of the absolute values of SNRs determined from individual template matching. While individual SNR realizations are Gaussian distributed, SNR-max probability distribution is non-Gaussian. Moreover, as the individual template-bank SNRs are computed using the same network data streams, SNRs become correlated between the templates. Cross-template correlations have a sizable effect on the SNR-max probability and cumulative distributions, and on the threshold SNR-max values. Computing threshold SNR-max values for large template banks is computationally prohibitive and we develop analytic approaches to computing properties of the SNR-max statistic. This is done for cases when the template bank is nearly orthogonal (small cross-template correlations) and for banks with cross-template correlation coefficient distribution “squeezed” about the most probable cross-template correlation value. Since the cross-template correlation coefficients quantify the similarity of templates, increasing correlations tend to decrease SNR-max thresholds for specific values of false positive rates. Increasing the number of templates in the bank increases the SNR-max thresholds. Our derivations are carried out for networks that may exhibit colored noise and cross-node correlations. Specific applications are illustrated with a dark matter search with atomic clocks onboard satellites of a Global Positioning System and with a “toy” planar network with cyclic rotational symmetry.

We analyze how the presence of the bound state on top of strong intercomponent contact repulsion affects the dynamics of a two-component ultracold Fermi gas confined in a one-dimensional harmonic trap. By performing full many-body numerical calculations, we retrieve dynamics of an initially phase-separated state that has been utilized to excite the spin-dipole mode in experimental settings. We observe an appearance of pairing correlations at the domain wall, heralding the onset of a molecular fraction at the interlayer between the components.

We investigate the quantum criticality and universality in Aubry-André-Harper (AAH) model with $p$-wave superconducting pairing $\mathrm{\Delta }$ in terms of the generalized fidelity susceptibility (GFS). We show that the higher order GFS is more efficient in spotlighting the critical points than lower order ones, and thus the enhanced sensitivity is propitious for extracting the associated universal information from the finite-size scaling in quasiperiodic systems. The GFS obeys power-law scaling for localization transitions and thus scaling properties of the GFS provide compelling values of critical exponents. Specifically, we demonstrate that the fixed modulation phase $\varphi =\pi$ alleviates the odd-even effect of scaling functions across the Aubry-André transition with $\mathrm{\Delta }=0$, while the scaling functions for odd and even numbers of system sizes with a finite $\mathrm{\Delta }$ cannot coincide irrespective of the value of $\varphi$. A thorough numerical analysis with odd number of system sizes reveals the correlation-length exponent $\nu \simeq$ 1.000 and the dynamical exponent $z\simeq$ 1.388 for transitions from the critical phase to the localized phase, suggesting the unusual universality class of localization transitions in the AAH model with a finite $p$-wave superconducting pairing lies in a different universality class from the Aubry-André transition. The results may be testified in near term state-of-the-art experimental settings.

The effect of slow light on second-harmonic generation in a periodically poled ${\chi }^{\left(2\right)}$ nonlinear medium is investigated theoretically. A linear $\pi$ phase-shifted grating is used to slow the group velocity of the fundamental frequency, and the resulting field enhancement greatly increases the second-harmonic conversion efficiency. A second linear grating at the input end ensures that all output is in the forward direction. We show that almost 100% conversion efficiency can be achieved for continuous wave pumping at low intensities that generate negligible conversion in the absence of the slow-light grating.

Hot alkali metal vapors enclosed in submicron spectroscopic cells provide an ideal system for fundamental studies of the atom-wall and atom-light interactions at the nanoscale. Here, we propose an approach for calculating the eigenmodes of a thin vapor layer beyond the limitations of the first-order perturbation theory in optical density for the case of quenching of atomic polarization upon collisions of atoms with dielectric walls. We show that higher-order optical density corrections lead to a remarkable density-dependent blueshift and deformation of the spectral line shapes of reflection, transmission, and absorption. We also demonstrate that the eigenmodes of the thin vapor layer can be calculated independently of the choice of optical boundary conditions. This greatly extends the applicability of the constructed theory for the development of miniature atomic sensors.

The state of a quantum system may be steered towards a predesignated target state, employing a sequence of weak blind measurements (where the detector's readouts are traced out). Here we analyze the steering of a two-level system using the interplay of a system Hamiltonian and weak measurements and show that any pure or mixed state can be targeted. We show that the optimization of such a steering protocol is underlain by the presence of Liouvillian exceptional points. More specifically, for high-purity target states, optimal steering implies purely relaxational dynamics marked by a second-order exceptional point, whereas for low-purity target states, it implies an oscillatory approach to the target state. The dynamical phase transition between these two regimes is characterized by a third-order exceptional point.

The lifetime of the ${}^{3}P_0$ state of ${\mathrm{Bi}}^{-}$ has been measured by selective photodetachment in a cryogenic ion-beam storage ring. By measuring the lifetime as a function of applied laser powers and extrapolating to zero laser power, a lifetime of $16.0\pm 0.5$ s is deduced for electric quadrupole decay of the excited state to the ground sate. The result provides a stringent test of recent state-of-the art theoretical calculations.

Measurements of the phase of two-photon matrix elements are presented for resonant and antiresonant two-color ionization of helium. A tunable, narrow-bandwidth, near-infrared (NIR) laser source is used for extreme ultraviolet (XUV) high-harmonic generation (HHG). The 15th harmonic of the laser is used within ($1+1^{\prime }$) $\mathrm{XUV}+\mathrm{NIR}$ two-photon ionization and tuned in and out of resonance with members of the $1snp{}^{1}P_1$ ($n=3,4,5$) Rydberg series, covering a broad spectral range with high spectral resolution. The technique allows us to observe characteristic rapid changes in the phase of the two-photon matrix elements around the resonances and at the antiresonances between the resonances. Similar effects are observed for ($1+2^{\prime }$) $\mathrm{XUV}+\mathrm{NIR}$ three-photon ionization. The experimental results are compared to a perturbative model and to numerical solutions of the time-dependent Schrödinger equation in the single-active-electron approximation, elucidating the origin and dependences of the observed phenomena.

The decay of Rydberg-atom–ion molecules (RAIMs) due to nonadiabatic couplings between electronic potential-energy surfaces is investigated. We employ the Born-Huang representation and perform numerical simulations using a Crank-Nicolson algorithm. The nonadiabatic lifetimes of rubidium RAIMs for the lowest ten vibrational states, $\nu$, are computed for selected Rydberg principal quantum numbers, $n$. The nonadiabatic lifetimes are found to generally exceed the radiative Rydberg-atom lifetimes. We observe and explain a trend of the lifetimes as a function of $\nu$ and $n$, and attribute irregularities to quantum interference arising from a shallow potential well in an inner potential surface. Our results will be useful for future spectroscopic studies of RAIMs.

When an obstacle is moved in a superfluid faster than a critical velocity, quantized vortices are generated behind the obstacle. Here we propose a method to create more complicated topological excitations, three-dimensional skyrmions, behind a moving obstacle. We numerically show that, in a two-component Bose-Einstein condensate, component-dependent obstacle potentials can generate skyrmions in the wake, made up of quantized vortex rings in different components that are linked with each other. The lifetime of generated skyrmions can be prolonged by a guiding potential, which enables the formation of a skyrmion train.

We investigate magnetic solitons in an immiscible binary Bose-Einstein condensate (BEC), where the intraspecies interactions are slightly weaker than the interspecies interactions. While their density and phase profiles are analogous to dark-bright solitons, other characteristic properties such as maximum velocities, widths, total density depletions, and in-trap oscillations are different. In the low-velocity regime, a magnetic soliton reduces to a traveling pair of magnetic domain walls. Collisional behaviors of the solitons are also briefly discussed. We further demonstrate that these solitonic states can be realized in a quasi-one-dimensional spin-1 ferromagnetic BEC with a weak spin interaction, e.g., a ${}^{87}\mathrm{Rb}$ BEC.

The synchronization of spatial modes in the formation of multimode solitons can be considered as the transverse analog of mode locking. In this process, the inherent Kerr nonlinearity in the fiber core binds different spatial fiber modes together. However, compared to their temporal counterparts, the binding mechanism in multimode solitons is rather weak and susceptible to perturbation. In order to mitigate this effect, the propagation in multimode fibers with noninstantaneous Kerr media (NKM) is theoretically investigated. Our study focuses on the dynamics of intermodal energy transfer for the two cases of weak and strong walk-off. Both the moment method and numerical simulations of a multimode expansion of the nonlinear Schrödinger equation are employed. Scenarios of pure, hybrid, and varying NKM are investigated. For pure NKM, it is found that for weak walk-off, higher order spatial modes are accelerated in the time domain when their energy is transferred to lower order modes, that is, an effect that has previously been discussed as self-cleaning. In the hybrid case, when an additional instantaneous Kerr effect is present, this results in an enhancement of intermodal nonlinear coupling, leading to prominent oscillating evolutions of the derivatives of energy and pulse center. For varying NKM, the nonlinear refractive index and the proportion of noninstantaneous Kerr nonlinearity may both vary with pulse width. In this case, energy transfer and temporal shift are essentially determined by the magnitude of nonlinear response time of NKM. Significant temporal self-splitting at the trailing edge is observed for the lowest order mode provided only that the response time is large enough and irrespective of strong or weak walk-off.

We show two examples in which the dynamical Casimir effect can be achieved by modulating the Kerr or higher-order nonlinearities. In the first case the cavity field is coupled to an arbitrary number of qubits or a harmonic oscillator via the dipole interaction. In the second case, the modulation of the nonlinearities is accompanied by the off-resonance modulation of the cavity frequency. We present the analytic description of the phenomenon and supplement it with numeric simulations, demonstrating that photons can be created from vacuum and the resulting hyper-Poissonian photon statistics is very different from the squeezed vacuum state.

We propose a scheme for discrete time crystals (DTCs) based on the metastability of the driven-dissipative Bose-Hubbard model, linking the two metastable states as such using rotation operations and two-photon processes. Numerical analyses in finite size, through the Gutzwiller Monte Carlo approach, validate our scheme, where the couplings between different sites are taken into account. Requiring only local dissipations and uniform rotations, our scheme is feasible on the state-of-the-art noisy intermediate-scale quantum platforms, e.g., superconducting circuits and ultracold atoms. The robustness of the proposed DTC is guaranteed by construction due to the metastability. Our scheme provides a simple test bed for studying the less explored field of nonequilibrium phases of matter in physics and exploring more possibilities of quantum simulations.