Characterization of quantum dynamics is a fundamental problem in quantum physics and quantum-information science. Several methods are known which achieve this goal, namely standard quantum-process tomography (SQPT), ancilla-assisted process tomography, and the recently proposed scheme of direct characterization of quantum dynamics (DCQD). Here, we review these schemes and analyze them with respect to some of the physical resources they require. Although a reliable figure-of-merit for process characterization is not yet available, our analysis can provide a benchmark which is necessary for choosing the scheme that is the most appropriate in a given situation, with given resources. As a result, we conclude that for quantum systems where two-body interactions are not naturally available, SQPT is the most efficient scheme. However, for quantum systems with controllable two-body interactions, the DCQD scheme is more efficient than other known quantum-process tomography schemes in terms of the total number of required elementary quantum operations.

The coupling and binding effects have been studied in $L$-subshell ionization of heavy Au, Bi, Th, and U atoms by an impact of ${{}^{28}\text{S}\text{i}}^{q+}$ ions in the energy range of 8.5–36.0 MeV. The measured $\mathit{L}$ x-ray spectra were analyzed taking into account the multiple ionization effects in outer $M$ and $N$ shells. The $L$-subshell ionization cross sections have been obtained from measured x-ray production cross sections using the $L$-shell fluorescence and Coster-Kronig yields which were modified for a reduced number of electrons and closed Coster-Kronig transitions in the multiply ionized atoms. The results are compared with the available calculations, which are based on the semiclassical approximation (SCA) as well as the plane-wave Born approximation (PWBA). We demonstrate that for silicon ion impact these theoretical approaches have to be modified to include the $L$-subshell coupling effect using the “coupled subshell model” (CSM) as well as the saturation of the binding effect at the united atom limit. The calculations modified for both effects are in much better agreement with the data. In particular, an order-of-magnitude improvement of agreement between the data and the SCA-CSM calculations including the binding-saturation effect is reported for low-energy Si ions for the $L_2$-subshell. The results are also compared with the predictions of the PWBA based ECPSSR and ECUSAR theories accounting for the energy-loss (E), Coulomb-deflection (C), and relativistic (R) effects treating the binding effect within the perturbed stationary state (PSS) approximation with correction for the binding-saturation effect introduced to describe the united-atom and separated-atom (USA) limits.

We consider collisional properties of weakly bound heteronuclear molecules (dimers) formed in a two-species mixture of atoms with a large mass difference. We focus on dimers containing light fermionic atoms as they manifest collisional stability due to an effective dimer-dimer repulsion originating from the exchange of the light atoms. In order to solve the dimer-dimer scattering problem we develop a theoretical approach, which provides a physically transparent and quantitative description of this four-atom system in terms of three- and two-body observables. We calculate the elastic scattering amplitude and the rates of inelastic processes such as the trimer formation and the relaxation of dimers into deeply bound molecular states. Irrespective of whether the heavy atoms are bosons or fermions, the inelastic rate can be significantly lower than the rate of elastic collisions. Moreover, the measurement of the inelastic rate which is a four-body observable, can be an efficient and precise tool for determining three-body observables such as the three-body parameter, positions of Efimov states, and their lifetimes.

We describe a Cs atomic magnetometer operating in the spin-exchange-relaxation-free (SERF) regime. With a vapor cell temperature of $103°\text{C}$ we achieve intrinsic magnetic resonance widths $\Delta B=17\mu \text{G}$ corresponding to an electron spin-relaxation rate of $300{\text{s}}^{-1}$ when the spin-exchange rate is ${\Gamma }_{\text{SE}}=14000{\text{s}}^{-1}$. We also observe an interesting narrowing effect due to diffusion. Signal-to-noise measurements yield a sensitivity of about $400\text{pG}/\sqrt{\text{Hz}}$. Based on photon shot noise, we project a sensitivity of $40\text{pG}/\sqrt{\text{Hz}}$. A theoretical optimization of the magnetometer indicates sensitivities on the order of $2\text{pG}/\sqrt{\text{Hz}}$ should be achievable in a $1{\text{cm}}^3$ volume. Because Cs has a higher saturated vapor pressure than other alkali metals, SERF magnetometers using Cs atoms are particularly attractive in applications requiring lower temperatures.

We describe a proof-of-principle experiment on a fully permanent magnet atom chip. We study ultracold atoms and produce a Bose-Einstein condensate. The magnetic trap is loaded efficiently by adiabatic transport of a magnetic trap via the application of uniform external fields. Radio frequency spectroscopy is used for in-trap analysis and to determine the temperature of the atomic cloud. The formation of a Bose-Einstein condensate is observed in time-of-flight images and as a narrow peak appearing in the radio frequency spectrum.

We study damping of the dipole oscillation in a Bose-condensed gas in a combined cigar-shaped harmonic trap and one-dimensional (1D) optical lattice potential at finite temperatures. In order to include the effect of thermal excitations in the radial direction, we derive a quasi-1D model of the Gross-Pitaevskii equation and the Bogoliubov equations. We use the Popov approximation to calculate the temperature dependence of the condensate fraction with varying lattice depth. We then calculate the Landau damping rate of the dipole oscillation as a function of the lattice depth and temperature. The damping rate increases with increasing lattice depth, which is consistent with experimental observations. The magnitude of the damping rate is in reasonable agreement with experimental data. We also find that the damping rate has a strong temperature dependence, showing a sharp increase with increasing temperature. Finally, we emphasize the importance of the radial thermal excitations in both equilibrium properties and the Landau damping.

Interacting Fermi gases with equal populations but unequal masses are investigated at zero temperature using local density approximation and the hydrodynamic theory of superfluids in the presence of harmonic trapping. We derive the conditions of energetic stability of the superfluid configuration with respect to phase separation and the frequencies of the collective oscillations in terms of the mass ratio and the trapping frequencies of the two components. We discuss the behavior of the gas after the trapping potential of a single component is switched off and show that, near a Feshbach resonance, the released component can still remain trapped due to many-body interaction effects. Explicit predictions are presented for a mixture of ${}^6\text{L}\text{i}$ and ${}^{40}\text{K}$ with resonant interaction.

We consider vector solitons of mixed bright-dark types in quasi-one-dimensional spinor $\left(F=1\right)$ Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system of three coupled Gross-Pitaevskii equations (GPEs) to an integrable Yajima-Oikawa system. In this way, we obtain approximate solutions for small-amplitude vector solitons of dark-dark-bright and bright-bright-dark types, in terms of the $m_F=+1,-1,0$ spinor components, respectively. By means of numerical simulations of the full GPE system, we demonstrate that these states indeed feature soliton properties, i.e., they propagate undistorted and undergo quasielastic collisions. It is also shown that in the presence of a parabolic trap the bright component(s) is (are) guided by the dark one(s) and, as a result, the small-amplitude vector soliton as a whole performs quasiharmonic oscillations. The oscillation frequency is found as a function of the spin-dependent interaction strength for both small-amplitude and large-amplitude solitons.

We report a fully analytical study of figure-eight passively mode-locked fiber lasers. An adapted master equation is established for the figure-eight fiber laser. It is of cubic complex Ginzburg-Landau type, in which the coefficients explicitly depend on the characteristics of the cavity. We derive stability conditions for passively mode-locked and continuous wave operations in both net positive dispersion and net negative dispersion. In the soliton regime, the duration and the pulse energy are studied. The model points out a great sensitivity of pulse characteristics on parameters of the cavity, in particular, on the orientation of the polarizing isolator, on the coupling coefficient of the fiber coupler and on the length of the nonlinear optical loop mirror.

We predict the existence and address the stability of two-dimensional surface solitons featuring topologically complex shapes, including dipoles, vortices, and bound states of vortex solitons, at the interface of nonlocal thermal media. Unlike their counterparts in bulk media, surface dipoles are found to be stable in the entire existence domain. Surface vortices are found to exhibit strongly asymmetric intensity and phase distributions, and are shown to be stable, too. Bound states of surface vortex solitons belong to a class of surface solitons having no counterparts in bulk media. Such states are found to be stable provided that their energy flow does not exceed an upper threshold. Our findings constitute an example of topologically complex solitons located at nonlocal two-dimensional interfaces.

We study robustness of bipartite entangled states that are positive under partial transposition (PPT). It is shown that almost all PPT entangled states are unconditionally robust, in the sense, both inseparability and positivity are preserved under sufficiently small perturbations in its immediate neighborhood. Such unconditionally robust PPT entangled states lie inside an open PPT entangled ball. We construct examples of such balls whose radii are shown to be finite and can be explicitly calculated. This provides a lower bound on the volume of all PPT entangled states. Multipartite generalization of our constructions is also outlined.

We propose an optical scheme to perform a complete Bell-state measurement of four entangled displaced states. The principal feature of the scheme is the use of the phase of the displaced photon. The main ingredients of the scheme are the resources of single photons, coherent radiation, and optical linear elements (beam splitters, phase-shifting devices). The optical scheme works with on-off photodetectors that cannot discriminate different numbers of detected photons. This type of measurement is adjusted for dense coding and a communication rate per photon is calculated for one partial case.

The electronic energy loss of molecular clusters as a function of impact parameter is far less understood than atomic energy losses. For instance, there are no analytical expressions for the energy loss as a function of impact parameter for cluster ions. In this work, we describe two procedures to evaluate the combined energy loss of molecules: Ab initio calculations within the semiclassical approximation and the coupled-channels method using atomic orbitals; and simplified models for the electronic cluster energy loss as a function of the impact parameter, namely the molecular perturbative convolution approximation (MPCA, an extension of the corresponding atomic model PCA) and the molecular unitary convolution approximation (MUCA, a molecular extension of the previous unitary convolution approximation UCA). In this work, an improved ansatz for MPCA is proposed, extending its validity for very compact clusters. For the simplified models, the physical inputs are the oscillators strengths of the target atoms and the target-electron density. The results from these models applied to an atomic hydrogen target yield remarkable agreement with their corresponding ab initio counterparts for different angles between cluster axis and velocity direction at specific energies of 150 and 300 keV/u.

We extend the idea of quantum phase transitions of light in an atom-photon system with a Dicke-Bose-Hubbard model for an arbitrary number of two-level atoms. The formulations of eigenenergies, effective Rabi frequencies, and critical chemical potentials for two atoms are derived. With a self-consistent method, we obtain a complete phase diagram for two two-level atoms on resonance, which indicates the transition from Mott insulator to superfluidity and with a mean excitations diagram for confirmation. We illustrate the generality of the method by constructing the dressed-state basis for an arbitrary number of two-level atoms. In addition, we show that the Mott insulator lobes in the phase diagrams will smash out with the increase of atom numbers. The results of this work provide a step for studying the effects with combinations of Dicke-like and Hubbard-like models to simulate strongly correlated electron systems using photons.

The most up-to-date theoretical calculation on the dissociative recombination (DR) of ${\text{D}}_2{\text{H}}^{+}$ predicts a 2–5 times lower rate coefficient than that obtained experimentally at the Test Storage Ring (TSR). In order to verify the validity either of the experimental results or the theoretical calculations we have studied the DR of ${\text{D}}_2{\text{H}}^{+}$ at the storage ring CRYRING. The rate coefficient has been measured over the interaction energy range from $\approx 0\text{eV}$ to 50 eV and has been found to have a peak at about 10 eV with a value of $1.6\times {10}^{-8}{\text{cm}}^3{\text{s}}^{-1}$, which is in excellent agreement with the result reported from TSR. Taking into account the electron temperature distributions, excellent agreement between the two storage rings measurements is also obtained at smaller interaction energies. The branching fraction analysis has been performed at $\approx 0\text{eV}$ interaction energy and revealed the following results at the $1\sigma$ confidence level: $N\left(\text{D}+\text{D}+\text{H}\right)=76.5\%\pm 2.2\%$, $N\left({\text{D}}_2+\text{H}\right)=10.0\%\pm 0.7\%$, and $N\left(\text{DH}+\text{D}\right)=13.5\%\pm 1.5\%$. The value of $2N\left({\text{D}}_2+\text{H}\right)/N\left(\text{DH}+\text{D}\right)=1.48\pm 0.22$ implies that formation of ${\text{D}}_2$ is more favorable than DH.

We observe the optomechanical multistability of a macroscopic torsion balance oscillator. The torsion oscillator forms the moving mirror of a hemispherical laser light cavity. When a laser beam is coupled into this cavity, the radiation pressure force of the intracavity beam adds to the torsion wire’s restoring force, forming an optomechanical potential. In the absence of optical damping, up to 23 stable trapping regions were observed due to local light potential minima over a range of $4\mu \mathrm{m}$ oscillator displacement. Each of these trapping positions exhibits optical spring properties. Hysteresis behavior between neighboring trapping positions is also observed. We discuss the prospect of observing optomechanical stochastic resonance, aiming at enhancing the signal-to-noise ratio (SNR) in gravity experiments.

We study the coupling between collective variables of atomic spin and light polarization in an ensemble of cold ${}^{87}\text{R}\text{b}$ probed with polarized light. The effects of multiple hyperfine levels manifest themselves as a rank-2 tensor polarizability, whose irreducible components can be selected by means of probe detuning. The $D_1$ and $D_2$ lines of Rb are explored and we identify different detunings which lead to Hamiltonians with different symmetries for rotations. As possible applications of these Hamiltonians, we describe schemes for spin squeezing, quantum cloning, quantum memory, and measuring atom number.

We propose a scheme to produce continuous-variable pair-entanglement frequency comb by enhanced Raman scattering in an optical oscillator cavity in which a hexagonally poled ${\text{LiTaO}}_3$ locates as a Raman gain crystal. The Stokes and anti-Stokes Raman signals are enhanced by a coupled quasi-phase-matching optical parametric process and their entanglement characteristics are studied by applying necessary and sufficient inseparability criterion for continuous-variable entanglement. This scheme of generating continuous-variable pair-entanglement frequency comb source may be very significant for the application in quantum communication and computation networks.

In earlier work, one of us displayed an exact Thomas-Fermi (TF) method for kinetic energy and other averages of the Compton profile for atomic closed shells in a bare Coulomb field. Here, we are also interested in the semiclassical TF-like method but now in relation to the momentum density itself in the limit of a large number of closed shells. Exact off-diagonal density matrices are also given explicitly, for both configuration and momentum spaces. Finally the x-ray scattering factor is discussed in relation to the Thomas-Fermi limit.

We report calculations of all vibrational states of $\text{H}_3{}^{+}$ in the lowest triplet state with the inclusion of the geometric phase effect. When compared with calculations without inclusion of the geometric phase, the results show that only the $E^{\prime }$ vibrational states are affected, leading to considerable shifts in the vibrational levels and changes in the splittings between the $A^{\prime }$ and $E^{\prime }$ levels. The vibrational spectrum of the heavier isotopolog $\text{D}_3{}^{+}$ is also analyzed.