We present a convenient technique describing the condensate in dynamical equilibrium with the thermal cloud, at temperatures close to the critical one. We show that the whole isolated system may be viewed as a single classical field undergoing nonlinear dynamics leading to a steady state. In our procedure it is the observation process and the finite detection time that allow for splitting the system into the condensate and the thermal cloud.

In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schrödinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ${\rho }_{\mathrm{red}}\mathrm{}\left(t\right)\mathrm{}$ approach the exact reduced state found via $\mathrm{Imamo}\mathrm{g}¯{\mathrm{lu}}^{\prime }\mathrm{s}$ enlarged system method [Phys. Rev. A 50, 3650 (1994)].

Analyzing the S matrices associated with a host of relaxation processes allows one, using extra “chaperon” states, to construct a decoherence-free subspace (DFS) that is immune to the effects of relaxation. The method does not require knowledge of the system-bath Hamiltonian, which is rarely known. Thus, a DFS can be constructed directly from experimentally determined relaxation and dephasing rates of the relevant decoherence processes. Although the method requires resetting the coefficients of the chaperon states at various times, this resetting does not require determining the coefficients of the states belonging to the DFS that one uses for control, computations, or information storage.

It was shown by Dur [Phys. Rev. Lett. $87,$ 230402 (2001)] that N $(N>~4)$ qubits described by a certain one-parameter family $\mathcal{F}$ of bound entangled states violate the Mermin-Klyshko inequality for $N>~8.$ In this paper we prove that the states from the family $\mathcal{F}$ violate Bell inequalities derived by Żukowski and Kaszlikowski [Phys. Rev. A $56,$ R1682 (1997)], in which each observer measures three noncommuting sets of orthogonal projectors, for $N>~7.$ We also derive a simple one-parameter family of entanglement witnesses that detect entanglement for all the states belonging to $\mathcal{F}.$ It is possible that these entanglement witnesses could be generated by some Bell inequalities.

A search is conducted for the determination of expectation values of $r^q$ between Dirac and quasirelativistic radial wave functions in the quantum-defect approximation. The phenomenological and supersymmetry-inspired quantum-defect models, which have proven so far to yield accurate results, are used. The recursive structure of formulas derived on the basis of the hypervirial theorem enables us to develop explicit relations for arbitrary values of $q.\mathrm{}$ Detailed numerical calculations concerning alkali-metal-like ions of the Li, Na, and Cu isoelectronic sequences confirm the superiority of supersymmetry-based quantum-defect theory over quantum-defect orbital and exact orbital quantum number approximations. It is also shown that relativistic rather than quasirelativistic treatment may be used for consistent inclusion of relativistic effects.

We have performed nonperturbative time-dependent calculations of single and double ionization of atomic calcium by short and intense laser pulses using a two-active-electron model. It is shown that the significant enhancement of the ${\mathrm{Ca}}^{2+}$ yield observed in a recent experiment [E. Papastathopulous, M. Strehle, and G. Gerber (unpublished)] using feedback control techniques originates from the time asymmetry of the pulse shape. Numerical simulations have been performed for various asymmetrical pulses. The initial part of the pulse prepares a coherent superposition of excited states which is transferred into the double-electron continuum at later times. An asymmetric shape, with a slowly decreasing tail, therefore favors the production of ${\mathrm{Ca}}^{2+}.$ Single-active-electron calculations have also been performed to demonstrate the significant role played by electron correlations and by doubly excited states.

Using the second-order Coulomb-corrected Volkov function as a continuum state, we derive quantum mechanically analytical formulas for the photoionization rate of hydrogen atoms irradiated by a linearly polarized electric field in the tunneling regime. From the analytical formula is directly drawn the important conclusion that the role of the first-order Coulomb correction is to reduce the ionization potential. As a result, the photoionization rate is enhanced compared with that in the absence of the Coulomb correction. In addition, the second-order correction modifies the Keldysh parameter, decreases the binding energy, and increases the photoionization rates relative to those of the first-order Coulomb correction. We estimate the effects of the respective Coulomb corrections on the resonance structure of the photoionization rate, Keldysh parameter, and ponderomotive energy.

We study a four-level atomic scheme interacting with four lasers in a closed-loop configuration with a $\diamond$ (diamond) geometry. We investigate the influence of the laser phases on the steady state. We show that, depending on the phases and the decay characteristic, the system can exhibit a variety of behaviors, including population inversion and complete depletion of an atomic state. We explain the phenomena in terms of multiphoton interference, and compare our results with the phase-dependent phenomena in the double-$\Lambda$ scheme. This investigation may be useful for developing nonlinear optical devices, and for the spectroscopy and laser cooling of alkali-earth atoms.

Dynamical tunneling has been observed in atom-optics experiments by two groups. We show that the experimental results are extremely well described by time-periodic Hamiltonians with momentum quantized in units of the atomic recoil. The observed tunneling has a well-defined period when only two Floquet states dominate the dynamics. Beat frequencies are observed when three Floquet states dominate. We find frequencies that match those observed in both experiments. The dynamical origin of the dominant Floquet states is identified.

We theoretically investigate the quantum dynamics of an unstable resonator laser. Compared to a stable cavity laser of equal gain and loss it exhibits a K-fold enhanced linewidth. This excess noise factor K is a measure of the nonorthogonality of the resonator eigenmodes and amounts to an enlargement of the quantum vacuum fluctuations. Using a quantum treatment starting from first principles based on the nonorthogonal eigenmodes, we put previous theoretical predictions onto a more firm ground. While we find a position-dependent enhancement of the spontaneous emission rate into an empty mode of only $\sqrt{K},$ the constructive quantum interference of the spontaneous emission with a single oscillating mode lets the Petermann excess noise factor K reappear in the phase diffusion (laser linewidth). Hence locally enhanced spontaneous emission as well as noise enhanced by interference (amplified spontaneous emission) play an equal role in the origin of excess noise.

An improved version of the so-called Oxford protocol for entanglement purification is described, in which the usual local unitary transformations are only performed when they are really helpful. For some initial states, the modified protocol is equivalent to the original one, but for all other initial states it converges faster, is more efficient, and needs fewer operations.

We analyze beyond linear-response theory the energy loss of a slow dipole moving inside a free-electron gas. The energy loss is obtained from a nonlinear treatment of the scattering of electrons at the dipole-induced potential. This potential and the total electronic density are calculated with density-functional theory. We focus on the interference effects, i.e., the difference between the energy loss of a dipole and that of the isolated charges forming it. Comparison of our results to those obtained in linear-response theory shows that a nonlinear treatment of the screening is required to accurately describe the energy loss of slow dipoles.

We have simultaneously confined rubidium and metastable argon in a dual-species magneto-optical trap (MOT). Here a binary mixture of atomic species from different groups of the periodic table have been optically confined at ultracold temperatures. We describe the apparatus and characterize the individual, single species MOTs and the dual-species MOT. Both fluorescence and ion production are monitored. With both species trapped, we observe $\sim 5\times {10}^6$ ${}^{85}\mathrm{Rb}$ atoms and $\sim 2\times {10}^6$ ${}^{40}{\mathrm{Ar}}^{*}$ atoms. Realization of the dual-species trap opens the way for detailed studies of Penning and associative ionization, photoassociative spectroscopy, and eventually for the production of bound, ultracold RbAr molecules.

For a quantum-mechanically spread-out particle we investigate a method for determining its arrival time at a specific location. The procedure is based on the emission of a first photon from a two-level system moving into a laser-illuminated region. The resulting temporal distribution is explicitly calculated for the one-dimensional case and compared with axiomatically proposed expressions. As a main result we show that by means of a deconvolution one obtains the well-known quantum-mechanical probability flux of the particle at the location as a limiting distribution.

Probabilistic quantum nondemolition (QND) measurements can be performed using linear optics and postselection. Here we show how QND devices of this kind can be used in a straightforward way to implement a quantum relay, which is capable of extending the range of a quantum cryptography system by suppressing the effects of detector noise. Unlike a quantum repeater, a quantum relay system does not require entanglement purification or the ability to store photons.

We have measured the binary spin-exchange rate coefficient for collisions between Rb and ${}^{129}\mathrm{Xe}$ atoms at a magnetic field $B=9.4\mathrm{}\mathrm{T}$ and in the temperature range $160<T<\mathrm{}200\mathrm{}°\mathrm{C}.$ The longitudinal spin-relaxation rate ${1/T}_1$ of ${}^{129}\mathrm{Xe}$ is dominated by ${}^{129}\mathrm{Xe}-\mathrm{Rb}$ binary collisions. We measured ${1/T}_1$ using the methods of conventional nuclear magnetic resonance, with no spin enhancement by optical pumping. At the high magnetic field and large gas pressures used in this work, the contribution of ${}^{129}\mathrm{Xe}-\mathrm{Rb}$ molecules to the spin-exchange rate was less than 0.1% of the binary-collision rate. The Rb atomic number density [Rb] was measured directly from the large Faraday rotation of the polarization of near-resonant light passing through the sample cells. The rate coefficient is $\kappa {=d(1/T}_1)/d[\mathrm{Rb}]=(1.75\mathrm{}\pm 0.12)\times {10}^{-16}{\mathrm{cm}}^3/\mathrm{s}.$

An approximation is developed to deal with the ionization of atoms by bare charged ions. In this method the transition amplitude describing the three-body final state is evaluated using a continuum correlated wave and that for the initial state by an analytical continuation of the ${\Phi }_2$ model to complex momenta. This procedure introduces in the atomic bound state a kinematical correlation with the projectile motion. Doubly differential cross sections (DDCS’s) are computed for collisions of ${\mathrm{H}}^{+}$ and ${\mathrm{F}}^{9+}$ ions with He atoms. Results for the DDCS’s in the forward direction are compared with experimental data and other theoretical models. We find an enhancement of the distribution for low energy electrons and that the asymmetry of the electron capture to the continuum (ECC) peak is correctly described.

We investigate the classical dynamics of a hydrogen atom in a circularly polarized laser beam with finite radius. The spatial cutoff for the laser field allows us to use scattering processes to examine the laser-atom dynamics. We find that for certain field parameters, the delay times, the angular momentum, and the distance of closest approach of the scattered electron exhibit fractal behavior. This fractal behavior is a signature of chaos in the dynamics of the atom-field system.

The diffusion quantum Monte Carlo technique is used to solve the many-body Schrödinger equation fully quantum mechanically and nonperturbatively for bosonic atomic gases in cigar-shaped confining potentials. By varying the aspect ratio of the confining potential from 1 (spherical trap) to 10 000 (highly elongated trap), we characterize the transition from the three-dimensional regime to the (quasi-)one-dimensional regime. Our results confirm that the bosonic gas undergoes “fermionization” for large aspect ratios. Importantly, many-body correlations are included explicitly in our approach.

We investigate the crossover from three to one dimension in a Bose gas confined in highly anisotropic traps. By using quantum Monte Carlo techniques, we solve the many-body Schrödinger equation for the ground state and obtain exact results for the energy per particle and the mean square radii of the cloud in the transverse and longitudinal direction. Results are compared with the predictions of mean-field theory obtained from the Gross-Pitaevskii equation and with the one-dimensional Lieb-Liniger equation of state. We explicitly prove the occurrence of important beyond mean-field effects, including the appearance of Fermi-like properties as the system enters the Tonks gas regime.