We examine the role of thermal fluctuations in binary condensate mixtures of dilute atomic gases. In particular, we use the Hartree-Fock-Bogoliubov theory with the Popov approximation to probe the impact of noncondensate atoms to the phenomenon of phase separation in two-component Bose-Einstein condensates. We demonstrate that, in comparison to $T=0$, there is a suppression in the phase separation of the binary condensates at $T\ne 0$. This arises from the interaction of the condensate atoms with the thermal cloud. We also show that, when $T\ne 0$, it is possible to distinguish the phase-separated case from the miscible from the trends in the correlation function. However, this is not the case at $T=0$.

We investigate a number of diatomic molecular ions to search for strongly enhanced effects of variation of fundamental constants important for physics beyond the standard model. The relative enhancements due to fine structure and electron-to-proton mass ratio variation occur in transitions between nearly degenerate levels of different nature. Since the trapping techniques for molecular ions have already been developed, the proposed molecules ${\mathrm{HBr}}^{+}$, ${\mathrm{HI}}^{+}$, ${\mathrm{Br}}_2{}^{+}$, ${\mathrm{I}}_2{}^{+}$, ${\mathrm{IBr}}^{+}$, ${\mathrm{ICl}}^{+}$, and ${\mathrm{IF}}^{+}$ are very promising candidates for future high-resolution experiments.

We present a study of quantum contextuality of three-dimensional mixed states for the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) and the Kurzyński-Kaszlikowski (KK) noncontextuality inequalities. For any class of states whose eigenvalues are arranged in decreasing order, a universal set of measurements always exists for the KK inequality, whereas none exists for the KCBS inequality. This difference can be reflected from the spectral distribution of the overall measurement matrix. Our results would facilitate the error analysis for experimental setups, and our spectral method in the paper combined with graph theory could be useful in future studies on quantum contextuality.

We present a fully analytically solvable family of models with many-body cluster interaction and Ising interaction. This family exhibits two phases, dubbed cluster and Ising phases, respectively. The critical point turns out to be independent of the cluster size $n+2$ and is reached exactly when both interactions are equally weighted. For even $n$ we prove that the cluster phase corresponds to a nematic ordered phase and in the case of odd $n$ to a symmetry-protected topological ordered phase. Though complex, we are able to quantify the multiparticle entanglement content of neighboring spins. We prove that there exists no bipartite or, in more detail, no $n+1$-partite entanglement. This is possible since the nontrivial symmetries of the Hamiltonian restrict the state space. Indeed, only if the Ising interaction is strong enough (local) genuine $n+2$-partite entanglement is built up. Due to their analytical solvableness the $n$-cluster-Ising models serve as a prototype for studying nontrivial-spin orderings, and due to their peculiar entanglement properties they serve as a potential reference system for the performance of quantum information tasks.

We introduce the electron-nucleus mean-field configuration-interaction (EN-MFCI) approach. It consists in building an effective Hamiltonian for the electrons taking into account a mean field due to the nuclear motion and, conversely, in building an effective Hamiltonian for the nuclear motion taking into account a mean field due to the electrons. The eigenvalue problems of these Hamiltonians are solved in basis sets giving partial eigensolutions for the active degrees of freedom (DOF's), that is to say, either for the electrons or for nuclear motion. The process can be iterated or electron and nuclear motion DOF's can be contracted in a CI calculation. In the EN-MFCI reduction of the molecular Schrödinger equation to an electronic and a nuclear problem, the electronic wave functions do not depend parametrically upon nuclear coordinates. So, it is different from traditional adiabatic methods. Furthermore, when contracting electronic and nuclear functions, a direct product basis set is built in contrast with methods which treat electrons and nuclei on the same footing, but where electron-nucleus explicitly correlated coordinates are used. Also, the EN-MFCI approach can make use of the partition of molecular DOF's into translational, rotational, and internal DOF's. As a result, there is no need to eliminate translations and rotations from the calculation, and the convergence of vibrational levels is facilitated by the use of appropriate internal coordinates. The method is illustrated on diatomic molecules.

Postcollision interaction effects on the Auger decay of a deep core hole are studied both experimentally and theoretically. $K{L}_{2,3}{L}_{2,3}$ decay spectra of the Ar $1s$ vacancy are measured with high-energy resolution with excess photon energies ranging from 0 to 200 eV above the ionization threshold. Interaction of the Auger electron with the photoelectron and the ion field manifests itself in the Auger spectra as a distortion of the energy distribution of the Auger electron close to threshold. Moreover, recapture of the photoelectron due to energy exchange is dominating in the low-photon-energy range above threshold. The experimental results are compared with calculations based on the semiclassical approach to the postcollision interaction. The energies of the discrete levels and individual recapture cross sections are computed in the Hartree-Fock approximation. Good agreement is found between the calculated and experimental spectra, validating the model used.

We present extreme ultraviolet spectra of highly charged tungsten ions (${\mathrm{W}}^{19+}-{\mathrm{W}}^{32+}$) in the wavelength range of $15-55\AA$ obtained with a compact electron-beam ion trap (CoBIT) and a grazing-incidence spectrometer at the National Institute for Fusion Science. The electron energy dependence of the spectra was investigated for electron energies from 490 to $1320\mathrm{eV}$. Identification of the observed lines was aided by collisional-radiative (CR) modeling of CoBIT plasma. Good quantitative agreement was obtained between the CR-modeling results and the experimental observations. The ion charge dependence of the $6g\text{−}4f,5g\text{−}4f,5f\text{−}4d,5p\text{−}4d$, and $4f\text{−}4d$ transition wavelengths were measured.

The random-phase approximation with exchange (RPAE) is used with a $B$-spline basis to compute dynamic dipole polarizabilities of noble-gas atoms and several other closed-shell atoms (Be, Mg, Ca, Zn, Sr, Cd, and Ba). From these, values of the van der Waals $C_6$ constants for positronium interactions with these atoms are determined and compared with existing data. After correcting the RPAE polarizabilities to fit the most accurate static polarizability data, our best predictions of $C_6$ for Ps–noble-gas pairs are expected to be accurate to within 1%, and to within a few percent for the alkaline-earth metals. We also used accurate dynamic dipole polarizabilities from the literature to compute the $C_6$ coefficients for the alkali-metal atoms. Implications of increased $C_6$ values for Ps scattering from more polarizable atoms are discussed.

We report an extensive series of transitions (including collisional transfer lines) from pure and mixed levels of the NaK $A^1{\mathrm{\Sigma }}^{+}$ and $b{}^3\mathrm{\Pi }$ states to the $X^1{\mathrm{\Sigma }}^{+}$ state, observed at the Université Lyon 1 using Fourier-transform spectroscopy. We then combine these data with previously reported data on these states from emission from the $B^1\mathrm{\Pi }$ and $C^1{\mathrm{\Sigma }}^{+}$ states and from mutually perturbed levels of the $D{}^1\mathrm{\Pi }$ and $d{}^3\mathrm{\Pi }$ states. We obtain 2758 distinct term values: the full data set includes 11 624 term values, with many multiple determinations from transitions over a range of vibrational and rotational levels. The data are analyzed by fitting to potentials of the “Hannover” form [C. Samuelis et al., Phys. Rev. A 63, 012710 (2000)] plus spin-orbit (SO) functions in a simple Morse form, yielding an rms residual of approximately 0.029 ${\mathrm{cm}}^{-1}$. The empirical SO functions agree well with their ab initio counterparts obtained from electronic structure calculations based on nonempirical effective core potentials. From level energies of the $A-b$ complex calculated from the fitted potentials and SO functions, we identify reasonable candidates for transitions between Feshbach resonance states and mixed singlet-triplet gateway levels of the $A^1{\mathrm{\Sigma }}^{+}-b{}^3\mathrm{\Pi }$ manifold, leading either to $v=0$ levels of the $X$ state or to mixed singlet-triplet levels at higher energies that can be used for perturbation-facilitated double-resonance experiments.

The magnetic and electric dipole radiations due to double electron jump from $1s2s^2$ ${}^2{S}_{1/2}$ state of Li isoelectronic sequence are evaluated for 20 ions with $8\le Z\le 92$ using fully relativistic multiconfiguration Dirac Fock wave functions in the active space approximation with the inclusion of finite nuclear size, Breit interaction, self-energy, and vacuum polarization. The contributions from correlation and higher-order corrections to the x-ray energies and rates are discussed in detail. The effects of relaxed and frozen spin orbitals of the initial and final states on the correlation sensitive radiative rates are analyzed. The Auger electron emission rates calculated from a scaling procedure on the available relativistic radial matrix elements for a single vacancy in the $K$ shell have been used to evaluate the fluorescence yields. The numerical results for the x-ray and Auger transitions have been compared with other available theoretical and experimental values. The calculated electric dipole results are supplemented with error estimates wherever possible.

Absolute and energy-scanned electron-impact ionization cross sections of ${\mathrm{Xe}}^{24+}$ ions in their ground level have been measured by employing a crossed-beams technique in the collision energy range from below threshold to 1000 eV. Direct ionization and excitation-autoionization cross sections were calculated using a detailed level-to-level distorted-wave method. Large discrepancy between the theoretical result, only including these two processes, shows the importance of additional ionization channels via resonant-excitation double autoionization (REDA). The carefully investigated convergence trend of REDA processes with the principal and angular-momentum quantum numbers of the recombined electron, $n^{\prime }$ and $l^{\prime }$, respectively, shows that sufficiently large $n^{\prime }$ and $l^{\prime }$ have to be included in the calculation of the total REDA contribution to correctly interpret the experiment.

In this paper we study double-ionization-induced charge asymmetric dissociation (CAD) in heteronuclear diatomic molecules. In CO we find a selective charge distribution in two CAD channels, i.e., ${\mathrm{C}}^{2+}+\mathrm{O}$ is abundantly produced but $\mathrm{C}+{\mathrm{O}}^{2+}$ is nearly nonexistent. This cannot be explained by the ionization energy difference between the two channels alone. Our study shows that the ${\mathrm{C}}^{2+}+\mathrm{O}$ channel is sequentially formed through an intermediate state ${\mathrm{C}}^{+}+\mathrm{O}$ and the selective charge distribution is the result of electron distribution in CO when exposed to intense laser fields.

The frequency shift induced by the Berry phase between two coherent superposition states with $m^{\prime }=-1$ and $m=1$ was demonstrated under constant rotation of a magnetic field with frequency $f$ for angle $\theta$ from the rotation axis. It was found that the frequency shift is $\mathit{v}=2f-2fcos\theta$ for $0\le \theta \le \pi /3$, $\mathit{v}=-2fcos\theta$ for $\pi /3<\theta <2\pi /3$, and $\mathit{v}=-2f-2fcos\theta$ for $2\pi /3\le \theta \le \pi$ in the case of the right-handed rotation. For the left-handed rotation, the frequency changes in the opposite sign. The frequency shift is zero at $\theta =0,\pi /2$, and $\pi$, and it jumps by $2f$ in the vicinity of $\theta =\pi /3\mathrm{and}2\pi /3$. We confirm that the frequency shift is given by the time derivative of the Berry phase which does not depend on the sign of the $g$ factor.

A continuous-wave atom laser formed by the outcoupling of atoms from a trapped Bose-Einstein condensate (BEC) potentially has a range of metrological applications. However, in order for the device to be truly continuous, a mechanism to replenish the atoms in the BEC is required. Here we calculate the temporal coherence properties of a continuously pumped atom laser beam outcoupled from a trapped Bose-Einstein condensate that is replenished from a reservoir at finite temperature. We find that the thermal fluctuations of the condensate can significantly decrease the temporal coherence of the output beam due to atomic interactions between the trapped BEC and the beam, and this can impact the metrological usefulness of the device. We demonstrate that a Raman outcoupling scheme imparting a sufficient momentum kick to the atom laser beam can lead to a significantly reduced linewidth.

We study quantum fluctuation-driven first-order phase transitions of a two-species bosonic system in a three-dimensional optical lattice. Using effective potential method we find that the superfluid-Mott insulator phase transition of one type of bosons can be changed from second order to first order by the quantum fluctuations of the other type of bosons. The study of the scaling behaviors near the quantum critical point shows that the first-order phase transition has a different universality from the second-order one. We also discuss the observation of this phenomenon in the realistic cold-atom experiments based on the in situ density measurements.

We investigate the steady-state spin diffusion for ultracold spin-orbit-coupled ${}^{40}\mathrm{K}$ gas by the kinetic spin Bloch equation approach both analytically and numerically. Four configurations, i.e., the spin diffusions along two specific directions with the spin polarization perpendicular (transverse configuration) and parallel (longitudinal configuration) to the effective Zeeman field are studied. It is found that the behaviors of the steady-state spin diffusion for the four configurations are very different, which are determined by three characteristic lengths: the mean free path $l_{\tau }$, the Zeeman oscillation length $l_{\mathrm{\Omega }}$, and the spin-orbit coupling oscillation length $l_{\alpha }$. It is analytically revealed and numerically confirmed that by tuning the scattering strength, the system can be divided into five regimes: I, weak scattering regime ($l_{\tau }\gtrsim l_{\mathrm{\Omega }},l_{\alpha }$); II, Zeeman field-dominated moderate scattering regime ($l_{\mathrm{\Omega }}\ll l_{\tau }\ll l_{\alpha }$); III, spin-orbit coupling-dominated moderate scattering regime ($l_{\alpha }\ll l_{\tau }\ll l_{\mathrm{\Omega }}$); IV, relatively strong scattering regime ($l_{\tau }^c\ll l_{\tau }\ll l_{\mathrm{\Omega }},l_{\alpha }$); V, strong scattering regime ($l_{\tau }\ll l_{\mathrm{\Omega }},l_{\alpha },l_{\tau }^c$), with $l_{\tau }^c$ representing the crossover length between the relatively strong and strong scattering regimes. In different regimes, the behaviors of the spacial evolution of the steady-state spin polarization are very rich, showing different dependencies on the scattering strength, Zeeman field and spin-orbit coupling strength. The rich behaviors of the spin diffusions in different regimes are hard to understand in the framework of the simple drift-diffusion model or the direct inhomogeneous broadening picture in the literature. However, almost all these rich behaviors can be well understood by means of our modified drift-diffusion model and/or modified inhomogeneous broadening picture. Specifically, several anomalous features of the spin diffusion are revealed, which are in contrast to those obtained from both the simple drift-diffusion model and the direct inhomogeneous broadening picture.

The properties of two-component Fermi gases with zero-range interactions are universal. We use an explicitly correlated Gaussian basis set expansion approach to investigate small equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement. At unitarity, we determine the ground-state energy for systems with up to 10 particles interacting through finite-range two-body potentials for both even and odd numbers of particles. We extrapolate the energies to the zero-range limit using a novel scheme that removes the linear and, in some cases, also the quadratic dependence of the ground-state energies on the two-body range. Our extrapolated zero-range energies are compared with results from the literature. We also calculate the two-body Tan contact and structural properties.

The scattering of light is perhaps the most fundamental of optical processes. However, active and dynamic control of the directionality of a scattered light field has until now remained elusive. Here we show that with an easily generated, Bessel-correlated field, this goal can be achieved, at least partially. In particular, the angular distribution of a field scattered by a random spherical particle can be tuned to gradually suppress the forward scattering intensity and even create a conelike scattered field. Our method provides a tool for the dynamic control of scattering patterns, both macroscopically and microscopically.

The Foldy-Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schrödinger-Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.

Uncertainty relations (URs) such as the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from estimation theory, a Cramér-Rao-like bound. The Heisenberg-Robertson UR is then obtained by using the Born rule and the Schrödinger equation. This allows a clear separation of the probabilistic nature of quantum mechanics from the Hilbert space structure and the dynamical law. It also simplifies the interpretation of the bound. In addition, the Heisenberg-Robertson UR is tightened for mixed states by replacing one variance by the quantum Fisher information. Thermal states of Hamiltonians with evenly gapped energy levels are shown to saturate the tighter bound for natural choices of the operators. This example is further extended to Gaussian states of a harmonic oscillator. For many-qubit systems, we illustrate the interplay between entanglement and the structure of the operators that saturate the UR with spin-squeezed states and Dicke states.