We present numerically accurate calculations of the bound-state spectrum of the highly excited valence electron in the heavy alkali-metal atoms solving the radial Schrödinger eigenvalue problem with a modern spectral collocation method that applies also for a large principal quantum number $n\gg 1$. As an effective single-particle potential we favor the reputable potential of Marinescu et al. [Phys. Rev. A 49, 982 (1994)]. Recent quasiclassical calculations of the quantum defect of the valence electron agree for orbital angular momentum $l=0,1,2,...$ overall remarkably well with the results of the numerical calculations, but for the Rydberg states of rubidium and also cesium with $l=3$ this agreement is less fair. The reason for this anomaly is that in rubidium and cesium the potential acquires for $l=3$ deep inside the ionic core a second classical region, thus invalidating a standard Wentzel-Kramers-Brillouin (WKB) calculation with two widely spaced turning points. Comparing then our numerical solutions of the radial Schrödinger eigenvalue problem with the uniform analytic WKB approximation of Langer constructed around the remote turning point $r_{n,j,l}^{\left(+\right)}$ we observe everywhere a remarkable agreement, apart from a tiny region around the inner turning point $r_{n,j,l}^{(-)}$. For $s$ states the centrifugal barrier is absent and no inner turning point exists: $r_{n,j,0}^{(-)}=0$. With the help of an ansatz proposed by Fock we obtain for the $s$ states a second uniform analytic approximation to the radial wave function complementary to the WKB approximation of Langer, which is exact for $r\to 0^{+}$. From the patching condition, that is, for $l=0$ the Langer and Fock solutions should agree in the intermediate region $0<r\ll r_{n,j,l}^{\left(+\right)}$, not only an equation determining the quasiclassical quantum defect ${\delta }_0$ but also the value of the radial $s$-wave function at $r=0$ is analytically found, thus validating the Fermi-Segrè formula for the hyperfine splitting constant $A_{n,j,0}^{\left(\mathrm{HFS}\right)}$. As an application we consider recent spectroscopic data for the hyperfine splittings of the isotopes ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ and find a remarkable agreement with the predicted scaling relation $A_{n,j,0}^{\left(\mathrm{HFS}\right)}{\left(n-{\delta }_0\right)}^3=\mathrm{const}.$

Multistart spiral vortex patterns are predicted for the electron momentum distributions in the polarization plane following ionization of the helium atom by two time-delayed circularly polarized ultrashort laser pulses. For two ultraviolet (UV) pulses having the same frequency (such that two photons are required for ionization), single-color two-photon interferometry with corotating or counter-rotating time-delayed pulses is found to lead respectively to zero-start or four-start spiral vortex patterns in the ionized electron momentum distributions in the polarization plane. In contrast, two-color one-photon plus two-photon interferometry with time-delayed corotating or counter-rotating UV pulses is found to lead respectively to one-start or three-start spiral vortex patterns. These predicted multistart electron vortex patterns are found to be sensitive to the carrier frequencies, handedness, time delay, and relative phase of the two pulses. Our numerical predictions are obtained by solving the six-dimensional two-electron time-dependent Schrödinger equation (TDSE). They are explained analytically using perturbation theory (PT). Comparison of our TDSE and PT results for single-color two-photon processes probes the role played by the time-delay-dependent ionization cross channels in which one photon is absorbed from each pulse. Control of these cross channels by means of the parameters of the fields and the ionized electron detection geometries is discussed.

We study theoretically and numerically the dynamics of a passive optical fiber ring cavity pumped by a highly incoherent wave: an incoherently injected fiber laser. The theoretical analysis reveals that the turbulent dynamics of the cavity is dominated by the Raman effect. The forced-dissipative nature of the fiber cavity is responsible for a large diversity of turbulent behaviors: Aside from nonequilibrium statistical stationary states, we report the formation of a periodic pattern of spectral incoherent solitons, or the formation of different types of spectral singularities, e.g., dispersive shock waves and incoherent spectral collapse behaviors. We derive a mean-field kinetic equation that describes in detail the different turbulent regimes of the cavity and whose structure is formally analogous to the weak Langmuir turbulence kinetic equation in the presence of forcing and damping. A quantitative agreement is obtained between the simulations of the nonlinear Schrödinger equation with cavity boundary conditions and those of the mean-field kinetic equation and the corresponding singular integrodifferential reduction, without using adjustable parameters. We discuss the possible realization of a fiber cavity experimental setup in which the theoretical predictions can be observed and studied.

We study the fate of algebraic decay of correlations in a harmonically trapped two-dimensional degenerate Bose gas. The analysis is inspired by recent experiments on ultracold atoms where power-law correlations have been observed despite the presence of the external potential. We generalize the spin wave description of phase fluctuations to the trapped case and obtain an analytical expression for the one-body density matrix within this approximation. We show that algebraic decay of the central correlation function persists to lengths of about 20% of the Thomas-Fermi radius. We establish that the trap-averaged correlation function decays algebraically with a strictly larger exponent weakly changing with trap size and find indications that the recently observed enhanced scaling exponents receive significant contributions from the normal component of the gas. We discuss radial and angular correlations and propose a local correlation approximation which captures the correlations very well. Our analysis goes beyond the usual local density approximation and the developed summation techniques constitute a powerful tool to investigate correlations in inhomogeneous systems.

Violation of Mermin inequalities is tested on the five-qubit IBM quantum computer. For three, four, and five parties, quantum states that violate the corresponding Mermin inequalities are constructed using quantum circuits on superconducting qubits. Measurements on different bases are included as additional final gates in the circuits. The experimental results obtained using the quantum computer show violation of all Mermin inequalities, with a clear degradation of the results in the five-qubit case. Though this quantum computer is not competitive to test Mermin inequalities as compared to other techniques when applied to a few qubits, it does offer the opportunity to explore multipartite entanglement for four and five qubits beyond the reach of other alternative technologies.

Boson sampling is a mathematical problem that is strongly believed to be intractable for classical computers, whereas passive linear interferometers can produce samples efficiently. So far, the problem remains a computational curiosity, and the possible usefulness of boson-sampling devices is mainly limited to the proof of quantum supremacy. The purpose of this work is to investigate whether boson sampling can be used as a resource of decision and function problems that are computationally hard, and may thus have cryptographic applications. After the definition of a rather general theoretical framework for the design of such problems, we discuss their solution by means of a brute-force numerical approach, as well as by means of nonboson samplers. Moreover, we estimate the sample sizes required for their solution by passive linear interferometers, and it is shown that they are independent of the size of the Hilbert space.

We reveal the quantum and classical behaviors of the two-dimensional (2D) alternative quantum walk (AQW) in the presence of decoherence. For different kinds of decoherence, the analytic expressions for the moments of position distribution of the AQW are obtained. Taking the broken line noise and coin decoherence as examples of decoherence, we find that when decoherence emerges in only one direction, the anisotropic position distribution pattern appears, and not all the motions of the walker exhibit the transition from quantum to classical behaviors. Considering the effect of decoherence, we reveal the anisotropic correlations between the $x\left(y\right)$ position of the 2D walker and the state of the coin in 2D AQWs.

We present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform, and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless, and of charge $Ze$. Calculations are based on the Sturmian expansion of the generalized Dirac–Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); erratum R. Szmytkowski, J. Phys. B 30, 2747(E) (1997)], combined with the theory of hypergeometric functions. The final result is of an elementary form and agrees with corresponding formulas obtained earlier by other authors for some particular states of the atom.

We present a theoretical analysis of optical pathways for formation of cold ground-state ${\left(\mathrm{NaCa}\right)}^{+}$ molecular ions via an intermediate state. The formation schemes are based on ab initio potential energy curves and transition dipole moments calculated using effective-core-potential methods of quantum chemistry. In the proposed approach, starting from a mixture of cold trapped ${\mathrm{Ca}}^{+}$ ions immersed into an ultracold gas of Na atoms, ${\left(\mathrm{NaCa}\right)}^{+}$ molecular ions are photoassociated in the excited $E{}^1\mathrm{\Sigma }^{+}$ electronic state and allowed to spontaneously decay either to the ground electronic state or an intermediate state from which the population is transferred to the ground state via an additional optical excitation. By analyzing all possible pathways, we find that the efficiency of a two-photon scheme, via either the $B{}^1\mathrm{\Sigma }^{+}$ or $C{}^1\mathrm{\Sigma }^{+}$ potential, is sufficient to produce significant quantities of ground-state ${\left(\mathrm{NaCa}\right)}^{+}$ molecular ions. A single-step process results in lower formation rates that would require either a high-density sample or a very intense photoassociation laser to be viable.

The miscibility of two interacting quantum systems is an important testing ground for the understanding of complex quantum systems. Two-component Bose-Einstein condensates enable the investigation of this scenario in a particularly well controlled setting. In a homogeneous system, the transition between mixed and separated phases is fully characterized by a miscibility parameter based on the ratio of intra- to interspecies interaction strengths. Here we show, however, that this parameter is no longer the optimal one for trapped gases, for which the location of the phase boundary depends critically on atom numbers. We demonstrate how monitoring of damping rates and frequencies of dipole oscillations enables the experimental mapping of the phase diagram by numerical implementation of a fully self-consistent finite-temperature kinetic theory for binary condensates. The change in damping rate is explained in terms of surface oscillation in the immiscible regime, and counterflow instability in the miscible regime, with collisions becoming only important in the long time evolution.

A two-component, two-dimensional (2D) dipolar bosonic system in the bilayer geometry is considered. By performing quantum Monte Carlo simulations in a wide range of layer spacings we analyze in detail the pair correlation functions, the static response function, and the kinetic and interaction energies. By reducing the layer spacing we observe a transition from weakly to strongly bound dimer states. The transition is accompanied by the onset of short-range correlations, suppression of the superfluid response, and rotonization of the excitation spectrum. A dispersion law and a dynamic structure factor for the in-phase (symmetric) and out-of-phase (antisymmetric) collective modes during the dimerization is studied in detail with the stochastic reconstruction method and the method of moments. The antisymmetric mode spectrum is most strongly influenced by suppression of the inlayer superfluidity (specified by the superfluid fraction ${\gamma }_s={\rho }_s/\rho$). In a pure superfluid (normal fluid) phase, only an acoustic [optical (gapped)] mode is recovered. In a partially superfluid phase, both are present simultaneously, and the dispersion splits into two branches corresponding to a normal and a superfluid component. The spectral weight of the acoustic mode scales linearly with ${\gamma }_s$. This weight transfers to the optical branch when ${\gamma }_s$ is reduced due to formation of dimer states. In summary, we demonstrate how the interlayer dimerization in dipolar bilayers can be uniquely identified by static and dynamic properties.

We propose an optical grating for matter waves that separates molecules depending on whether their interaction with the light is conservative or dissipative. Potential applications include fundamental tests of quantum mechanics, measurement of molecular properties, and the ability to selectively prepare matter waves with different internal temperatures.

We study the preparation of heralded single-photon states using dual-pump spontaneous four-wave mixing. The dual-pump configuration, which in our case employs cross-polarized pumps, allows for a gradual variation of the nonlinear interaction strength enabled by a birefringence-induced walk-off between the pump pulses. The scheme enables the preparation of highly pure heralded single-photon states, and proves to be extremely robust against the effect of nonlinear phase modulation at the required photon-pair production rates.

In the present work, we present a high-speed method to control, manipulate, and retrieve an intense vector soliton stored in the ground-state coherences of a four-level atomic system. Additionally, we show the importance of the pulse area in determining the evolution of the system and present a constant in the evolution defined as the three-pulse area; a surprising extension to previously defined pulse areas.

We investigate the output generation of squeezed radiation of a cavity photon mode coupled to another off-resonant bosonic excitation. By modulating in time their linear interaction, we predict a high degree of output squeezing when the dispersive ultra-strong-coupling regime is achieved, i.e., when the interaction rate becomes comparable to the frequency of the lowest-energy mode. Our paper paves the way to squeezed light generation in frequency domains where the ultrastrong coupling is obtained, e.g., solid-state resonators in the GHz, THz, and mid-IR spectral ranges.

Many current quantum optical systems, such as microcavities, interact with thermal light through a small number of widely separated modes. Previous theories for photon number fluctuations of thermal light have been primarily limited to special cases that are appropriate for large volumes or distances, such as single modes, many modes, or modes of uniform spectral distribution. Herein, a theory for the general case of spectrally dependent photon number fluctuations is developed for thermal light. The error in variance of prior art is quantitatively derived for an example cavity in the case where photon counting noise dominates. A method to reduce the spectral impact of this variance is described.

We study the applicability of collisional models for non-Markovian dynamics of open quantum systems. By allowing interactions between the separate environmental degrees of freedom in between collisions we are able to construct a collision model that allows us to study quantum memory effects in open system dynamics. We also discuss the possibility to embed non-Markovian collision model dynamics into Markovian collision model dynamics in an extended state space. As a concrete example we show how, using the proposed class of collision models, we can discretely model non-Markovian amplitude damping of a qubit. In the time-continuous limit, we obtain the well-known results for spontaneous decay of a two-level system into a structured zero-temperature reservoir.

We employ the quantum-jump-trajectory approach to construct a systematic framework to study the thermodynamics at the trajectory level in a nonequilibrium open quantum system under discrete feedback control. Within this framework, we derive quantum versions of the generalized Jarzynski equalities, which are demonstrated in an isolated pseudospin system and a coherently driven two-level open quantum system. Due to quantum coherence and measurement backaction, a fundamental distinction from the classical generalized Jarzynski equalities emerges in the quantum versions, which is characterized by a large negative information gain reflecting genuinely quantum rare events. A possible experimental scheme to test our findings in superconducting qubits is discussed.

Coherent quantum-state manipulation of trapped ions using classical laser fields is a trademark of modern quantum technologies. In this work, we study aspects of work statistics and irreversibility in a single trapped ion due to sudden interaction with the impinging laser. This is clearly an out-of-equilibrium process where work is performed through illumination of an ion by the laser. Starting with the explicit evaluation of the first moments of the work distribution, we proceed to a careful analysis of irreversibility as quantified by the nonequilibrium lag. The treatment employed here is not restricted to the Lamb-Dicke limit, which allows us to investigate the interplay between nonlinearities and irreversibility. We show that in these multiquantum or sideband regimes, variation of the Lamb-Dicke parameter causes a nonmonotonic behavior of the irreversibility indicator. Counterintuitively, we find a working point where nonlinearity helps reversibility, making the sudden quench of the Hamiltonian closer to what would have been obtained quasistatically and isothermally.