We calculate the dynamic single-particle and many-particle correlation functions at nonzero temperature in one-dimensional trapped repulsive Bose gases. These correlation functions decay towards zero for increasing distance, and this decay is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. Based on previous exact results for a related untrapped Bose system and the results reported here, we also suggest the proper asymptotic form for the density-density correlation function in the trapped Bose gas as considered here.

Trapped atoms cooled down to temperatures below the Bose-Einstein condensation temperature are considered. Stationary solutions to the Gross-Pitaevskii equation (GPE) define the topological coherent modes, representing nonground-state Bose-Einstein condensates. These modes can be generated by means of alternating fields whose frequencies are in resonance with the transition frequencies between two collective energy levels corresponding to two different topological modes. The theory of resonant generation of these modes is generalized in several aspects: Multiple-mode formation is described; a shape-conservation criterion is derived, imposing restrictions on the admissible spatial dependence of resonant fields; evolution equations for the case of three coherent modes are investigated; the complete stability analysis is accomplished; the effects of harmonic generation and parametric conversion for the topological coherent modes are predicted. All considerations are realized both by employing approximate analytical methods as well as by numerically solving the GPE. Numerical solutions confirm all conclusions following from analytical methods.

Motivated by recent discussions concerning the manner in which damping appears in the electric polarizability, we show that (a) there is a dependence of the nonresonant contribution on the damping and that (b) the damping enters according to the “opposite sign prescription.” We also discuss the related question of how the damping rates in the polarizability are related to energy-level decay rates.

The present work demonstrates the utility and efficacy of a technique to measure the Coster-Kronig parameter ${(f}_{23})$ of elemental targets. For this purpose a pure gold foil was irradiated in a beam of 88-keV $\gamma$ rays from a radioactive ${}^{109}\mathrm{Cd}$ source. The photoinduced K and L x rays emitted from the gold foil were then measured in coincidence, with the data collected in the list mode. On analysis, the $f_{23}$ value of gold was found to be $0.119\pm \mathrm{0.003.}$ The technique demonstrated here is different in the sense that, in contrast to the earlier coincidence methods, where the x rays emitted directly from a radioactive source are detected in coincidence, in the present method the x rays of the elements under investigation are obtained by photoionization.

The zero-temperature phase diagram of a binary mixture of bosonic and fermionic atoms in a one-dimensional optical lattice is studied in the framework of the Bose-Fermi-Hubbard model. By exact numerical solution of the associated eigenvalue problems, ground state observables and the response to an external phase twist are evaluated. The stiffnesses under phase variations provide measures for the boson superfluid fraction and the fermionic Drude weight. Several distinct quantum phases are identified as functions of the strength of the repulsive boson-boson and the boson-fermion interactions. In addition to the bosonic Mott-insulator phase, two other insulating phases are found, where both the bosonic superfluid fraction and the fermionic Drude weight vanish simultaneously. One of these double-insulator phases exhibits a crystalline diagonal long-range order, while the other is characterized by spatial separation of the two species.

We compare theory and experiment in the Casimir force measurement between gold surfaces performed with the atomic force microscope. Both random and systematic experimental errors are found leading to a total absolute error equal to 8.5 pN at 95% confidence. In terms of the relative errors, experimental precision of 1.75% is obtained at the shortest separation of 62 nm at 95% confidence level (at 60% confidence the experimental precision of 1% is confirmed at the shortest separation). An independent determination of the accuracies of the theoretical calculations of the Casimir force and its application to the experimental configuration is carefully made. Special attention is paid to the sample-dependent variations of the optical tabulated data due to the presence of grains, contribution of surface plasmons, and errors introduced by the use of the proximity force theorem. Nonmultiplicative and diffraction-type contributions to the surface roughness corrections are examined. The electric forces due to patch potentials resulting from the polycrystalline nature of the gold films are estimated. The finite size and thermal effects are found to be negligible. The theoretical accuracy of about 1.69% and 1.1% are found at a separation 62 nm and 200 nm, respectively. Within the limits of experimental and theoretical errors very good agreement between experiment and theory is confirmed characterized by the root-mean-square deviation of about 3.5 pN within all measurement range. The conclusion is made that the Casimir force is stable relative to variations of the sample-dependent optical and electric properties, which opens new opportunities to use the Casimir effect for diagnostic purposes.

In this paper, we develop methods for optimal manipulation of coupled spin dynamics in the presence of relaxation. These methods are used to compute analytical bounds for the optimal efficiency of coherence transfer between coupled nuclear spins in presence of longitudinal and transverse relaxation. We derive relaxation optimized pulse sequences which achieve these bounds and maximize the sensitivity of the experiments in spectroscopic applications. This paper is a continuation of our previous work. Here, we take into account both the longitudinal and the transverse relaxation mechanisms, thus generalizing our previous results, where the former had been neglected.

We propose a linear optical scheme to transmit an unknown qubit robustly over bit-flip-error channel. To avoid the technical difficulty of the standard quantum error-correction code, our scheme is based on the concept of error rejection. The whole scheme is based on currently existing technology.

The proposal for quantum computing with rare-earth-metal-ion qubits in inorganic crystals makes use of the inhomogeneous broadening of optical transitions in the ions to associate individual qubits with ions responding to radiation in selected frequency channels. We show that a class of Gaussian composite pulses and complex sech pulses provide accurate qubit $\pi$ rotations, which are at the same time channel selective on a 5 MHz frequency scale and tolerant to $\pm 0.5\mathrm{MHz}$ deviations of the transition frequency of ions within a single channel. Rotations in qubit space of arbitrary angles and phases are produced by sequences of $\pi$ pulses between the excited state of the ions and coherent superpositions of the qubit states.

Experimental and theoretical cross sections for the resonant ion-pair formation (RIP) in electron collisions with rovibrationally cold ${\mathrm{H}}_3^{+}$ ions are presented. Absolute cross sections for the RIP process producing ${\mathrm{H}}^{-}$ ions are measured for center-of-mass energies between 2–20 eV using the CRYRING, heavy-ion storage ring. Theoretical cross sections are obtained using wave-packet propagation on both one- and two-dimensional models of relevant diabatic-potential energy surfaces and couplings of ${\mathrm{H}}_3^{+}$ and ${\mathrm{H}}_3.$

The collisional broadening and shift of metastable helium fine-structure lines are calculated within the impact approximation. Ab initio Born-Oppenheimer potential energy curves correlating to $\mathrm{He}\left(1\mathrm{}{}^1{S}_0\right)$ and $\mathrm{He}\left(2\mathrm{}{}^3{P}_j\right)$ atomic levels are obtained using the configuration interaction valence bond method and combined with semiempirically calculated van der Waals interaction terms between these atoms to also study j-specific and j-changing collisions. A long-range van der Waals potential well exists in the ${}^3{\Pi }_u$ potential correlated to the $\mathrm{He}\left(1\mathrm{}{}^1{S}_0\right)+\mathrm{He}\left(2\mathrm{}{}^3{P}_j\right)$ limit, whose influence on the scattering phase shift is assessed. At $T=310\mathrm{}\mathrm{K},$ the broadening and shift parameters are practically j independent and have average values of 12.60 and 1.87 MHz/Torr, respectively. The j-changing collisions have cross sections roughly five times smaller than the j-specific cross sections.

Photoassociation of cold ${}^{87}\mathrm{Rb}{(5s,f}_b=2)$ atom pairs is studied within 13 GHz of the dissociation limits ${}^{87}\mathrm{Rb}{(5p}_{3/2}{,f}_a{)+}^{87}\mathrm{Rb}{(5s,f}_b=2).\mathrm{}$ Vibrational levels in the long range, hyperfine manifolds of the $0_g^{-}$ and $1_g$ states arising from the ${}^{87}\mathrm{Rb}{(5p}_{3/2})$ fine structure limit are identified to lead to the formation of stable molecules in the photoassociation process. The vibrational bands are observed to break off, at positions matching the energetic location of potential-energy barriers predicted in the hyperfine manifolds at about 1 GHz above the ${}^{87}\mathrm{Rb}{(5p}_{3/2}{,f}_a{=3)+}^{87}\mathrm{Rb}{(5s,f}_b=1)$ dissociation limit. Empiricial potential-energy curves are derived from the data. These are found to be in agreement with predictions based on the long-range hyperfine recoupling of the excited molecular states. The selectivity of the excitation process and predissociation mechanisms are discussed.

We develop a classical model of an ideally sudden character for vibrational and rotational excitations in collisions of an atom (or an ion) with a diatomic molecule at energies as high as $10–{10}^2\mathrm{eV}.$ The energy-loss spectra with vibrotational levels left unresolved are analytically expressed with a repulsive intermolecular potential in a hard potential limit (i.e., a vanishing range of force). It turns out to be an extension of the hard shell model for a rigid-rotor molecule developed by Beck et al. two decades ago. For a homonuclear molecule, the hard potential model generally derives spectra with double peaks at both edges, one nearly elastic and another deeply inelastic. They are analogous to rotational rainbows though their positions are affected by vibrational excitation. Classical trajectory calculations with a finite-range model potential are carried out for collision systems of ${\mathrm{H}}^{+}+{\mathrm{N}}_2$ and ${\mathrm{Li}}^{+}+{\mathrm{N}}_2,$ and systematically compared with the model. It is found that the effect of vibrational excitation manifests itself the way the model predicts. It is also demonstrated that the spectra are virtually reduced to the hard potential model when the vibrational period is artificially taken much longer than a collision time, while reduced to the hard shell model when much shorter.

The energy distributions of protons emitted from the Coulomb explosion of hydrogen clusters by an intense femtosecond laser have been experimentally obtained. Ten thousand hydrogen clusters were exploded, emitting 8.1 keV protons under laser irradiation of intensity $6\times {10}^{16}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ The energy distributions are interpreted well by a spherical uniform cluster analytical model. The maximum energy of the emitted protons can be characterized by cluster size and laser intensity. The laser intensity scale for the maximum proton energy, given by a spherical cluster Coulomb-explosion model, is in fairly good agreement with the experimental results obtained at a laser intensity of ${10}^{16}–{10}^{17}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ and also when extrapolated with the results of three-dimensional particle simulations at ${10}^{20}–{10}^{21}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$

Coherent population transfer and superposition of atomic states via a technique of stimulated Raman adiabatic passage in an excited-doublet four-level atomic system have been analyzed. It is shown that the behavior of adiabatic passage in this system depends crucially on the detunings between the laser frequencies and the corresponding atomic transition frequencies. Particularly, if both the fields are tuned to the center of the two upper levels, the four-level system has two degenerate dark states, although one of them contains the contribution from the excited atomic states. The nonadiabatic coupling of the two degenerate dark states is intrinsic, it originates from the energy difference of the two upper levels. An arbitrary superposition of atomic states can be prepared due to such nonadiabatic coupling effect.

Rydberg wave packets generated by a single half-cycle pulse (HCP) interacting with a stationary Rydberg state periodically localize within a narrow region in both momentum and coordinate space (i.e., phase space). This property is the key to shaping and manipulating wave packets. We investigate the dependence of this transient localization and focusing on the principal quantum number n and on the strength of the ultrashort HCP (“kick strength,” $\Delta p).\mathrm{}$ It is shown that the localization in momentum space of the wave packet, quantified by the momentum width, obeys a universal scaling rule which is controlled by an effective Planck constant ${ħ}_{\mathrm{eff}}.$ Maximum focusing is reached in the classical limit $({ħ}_{\mathrm{eff}}\to 0).$

We investigate the scissors modes in binary mixtures of degenerate dilute quantum gases for both Bose-Bose and Bose-Fermi mixtures. For the latter we consider both the superfluid and normal hydrodynamic and collisionless regimes. We analyze the dependence of the frequencies of the scissors modes and their character as a function of the Bose-Fermi coupling and the trap geometry. We show that the scissors mode can reveal a clear trace of the hydrodynamic behavior of the Fermi gas.

We study the vortex lattices in a Bose-Einstein condensate in a rotating anisotropic harmonic trap. We first investigate the single-particle wave functions obtained by the exact solution of the problem and give simple expressions for these wave functions in the small anisotropy limit. Depending on the strength of the interactions, a few or a large number of vortices can be formed. In the limit of many vortices, we calculate the density profile of the cloud and show that the vortex lattice stays triangular. We also find that the vortex lattice planes align themselves with the weak axis of the external potential. For a small number of vortices, we numerically solve the Gross-Pitaevskii equation and find vortex configurations that are very different from the vortex configurations in an axisymmetric rotating trap.

We study the dynamics of a micromaser where the pumping atoms are strongly driven by a resonant classical field during their transit through the cavity mode. We derive a master equation for this strongly driven micromaser, involving the contributions of the unitary atom-field interactions and the dissipative effects of a thermal bath. We find analytical solutions for the temporal evolution and the steady state of this system by means of phase-space techniques, providing an unusual solvable model of an open quantum system, including pumping and decoherence. We derive closed expressions for all relevant expectation values, describing the statistics of the cavity field and the detected atomic levels. The transient regime shows the buildup of mixtures of mesoscopic fields evolving towards a super-Poissonian steady-state field that, nevertheless, yields atomic correlations that exhibit stronger nonclassical features than the conventional micromaser.

Intensity interferometry has been performed for the study of x-ray coherence. A high-resolution monochromator at $E=14.41\mathrm{}\mathrm{keV}$ was developed for enhancing the interference signal. Transverse coherence profiles of undulator radiation were evaluated from measurements of mode numbers. The obtained coherence length in vertical, which is perpendicular to the scattering plane of the monochromator, was proportional to the distance from the light source, as is expected from the Van Cittert–Zernike theorem. Vertical emittances of the storage ring were determined from the measured coherence lengths. Degradation of transverse coherence with phase object was measured and analyzed based on the propagation law of mutual intensity.