A method is proposed that allows one to reconstruct the unitary time-evolution matrix of a quantized oscillator. It combines coherent splitting and displacement of the quantum state after the interaction of interest with a subsequent measurement of the occupation of the oscillator ground state. The time-evolution matrix in number basis is then obtained by a twofold Fourier transform of the measured data. It is shown how to realize such a method for the case of the quantized center-of-mass motion of a trapped atom. Simulations for particular examples of interactions demonstrate the feasibility of the reconstruction method even in the presence of noisy data.

Based on a microscopic model of an open system consisting of a boson field coupled linearly to a system, we formulate quantum trajectories as continuous measurements of the output field from the system. We present a formulation for the case when the field quantity that is being monitored effectively commutes with itself at different times. In general, this results in a non-Markovian evolution for the reduced system conditioned on the measurements. Under the finite-memory time approximation this evolution can be numerically simulated. The generalization of the techniques of quantum trajectories to the non-Markovian regime is expected to contribute to our understanding of open system problems beyond the Born-Markov approximation.

We present optimal measuring strategies for an estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general measuring strategies are considered in both situations, to conclude in the first case that a local, although collective, measurement suffices to estimate entanglement, a nonlocal property, optimally.

Like all of quantum information theory, quantum cryptography is traditionally based on two-level quantum systems. In this paper, a protocol for quantum key distribution based on higher-dimensional systems is presented. An experimental realization using an interferometric setup is also proposed. Analyzing this protocol from the practical side, one finds an increased key creation rate while keeping the initial laser pulse rate constant. Analyzing it for the case of intercept/resend eavesdropping strategy, an increased error rate is found compared to two-dimensional systems, hence an advantage for the legitimate users to detect an eavesdropper.

We study a means of creating multiparticle entanglement of neutral atoms using pairwise controlled dipole-dipole interactions. For tightly trapped atoms the dipolar interaction energy can be much larger than the photon scattering rate and substantial coherent evolution of the two-atom state can be achieved before decoherence occurs. Excitation of the dipoles can be made conditional on the atomic states, allowing for deterministic generation of entanglement. We derive selection rules and a figure of merit for the dipole-dipole interaction matrix elements, for alkali atoms with hyperfine structure and trapped in localized center of mass states. Different protocols are presented for implementing two-qubit quantum logic gates such as the controlled-phase and swap gates. We analyze the error probability of our gate designs, finite due to decoherence from cooperative spontaneous emission and coherent couplings outside the logical basis. Outlines for extending our model to include the full molecular interactions potentials are discussed.

Probabilistic quantum cloning and identifying machines can be constructed via unitary-reduction processes [Duan and Guo, Phys. Rev. Lett. 80, 4999 (1998)]. Given the cloning (identifying) probabilities, we derive an explicit representation of the unitary evolution and corresponding Hamiltonian to realize probabilistic cloning (identification). The logic networks are obtained by decomposing the unitary representation into universal quantum logic operations. The robustness of the networks is also discussed. Our method is suitable for a k-partite system, such as quantum computer, and may be generalized to general state-dependent cloning and identification.

We present theoretical calculations of triply differential cross sections for electron emission in ion-atom collisions, including the internuclear interaction in a semiclassical approximation. We show that projectile double collision mechanisms can be taken into account in this way. We show the structures generated in the electron emission spectra by these processes, and suggest a way to experimentally verify them using recoil ion momentum spectroscopy techniques.

We have studied in detail the continuous evolution from static field ionization to ionization by a circularly polarized microwave field by combining a z-polarized static field with a circularly polarized microwave field in the x-y plane. We have measured the ionization threshold for Na states of $27<~n<~50$ in the precessing total field $F_t,$ as a function of its angle θ from the z axis. For low n, $F_t\cong {1/16n}^4,$ independent of θ. For $n>~45,$ $F_t$ decreases from ${1/16n}^4$ to ${0.8/16n}^4$ as θ is increased from 0° to 25°, and it remains at this value until $\theta =90\mathrm{}°.$ We also observe ionization at quite low values of $F_t,$ which we attribute to resonantly enhanced ionization, with the resonances driven by a stray static field in the x-y plane.

We report a direct observation of radiation pressure, exerted on cold rubidium atoms while bouncing on an evanescent-wave atom mirror. We analyze the radiation pressure by imaging the motion of the atoms after the bounce. The number of absorbed photons is measured for laser detunings ranging from 190 MHz to 1.4 GHz and for angles from 0.9 mrad to 24 mrad above the critical angle of total internal reflection. Depending on these settings, we find velocity changes parallel with the mirror surface, ranging from 1 to 18 cm/s. This corresponds to 2 to 31 photon recoils per atom. These results are independent of the evanescent-wave optical power.

The lowest bound states of the hydrogen negative ion and negative donor systems in a homogeneous magnetic field are investigated theoretically via a full configuration-interaction approach with an anisotropic Gaussian basis set. The broad magnetic field regime $\gamma =8\mathrm{}\times {10}^{-4}-4\times {10}^3$ is covered. Nonrelativistic total energies, electron detachment energies, and transition wavelengths are presented assuming an infinite nuclear mass. The binding mechanisms are discussed in detail. The accuracy for the energies is enhanced significantly compared to previously published data.

The equation of state of a trapped atomic gas, which is an important and fundamental property for a thermodynamic system, has been elusive to date. We address here this long-standing problem by introducing the concept of pseudovolume which can play an important role as the volume. The equation of state of an ideal Bose gas trapped in an n-dimensional generic power-law potential is derived. It is not only a long-sought equation of state for the trapped Bose gas but also including that of a free Bose gas. Moreover, we find that the thermal wavelength for the particles in n-dimensional space with any kinematic characteristic must be redefined.

The dynamic structure factor of a trapped Bose-Einstein condensed gas is investigated at zero temperature in the framework of Bogoliubov theory. Different values of momentum transfer are considered, ranging from the phonon to the single-particle regime. Various approximate schemes are discussed, including the local density approximation, where the system is locally described as a uniform gas, and the impulse approximation, in which the response is fixed by the momentum distribution of the condensate. A comprehensive approach, based on the eikonal expansion, is presented. The predictions of theory are successfully compared with the results of recent two-photon Bragg scattering experiments, at both low and high momentum transfer. Relevant features of the dynamic structure factor are also discussed using the formalism of sum rules and the concept of scaling. Particular emphasis is given to the regime of high momentum transfer, in which the dynamic structure factor is sensitive to the behavior of the order parameter in momentum space, and some instructive examples showing the consequence of long-range coherence are presented.

The influence of the initial-state preparation on the diffraction of atoms in the field of a standing wave is discussed. The solution of the coherent scattering problem for rather general initial conditions involving initial atomic wave-packet splitting in the momentum space is obtained. A different effect of narrowing of the interference fringes of the diffraction pattern caused by secondary interference during the standing-wave scattering is discovered. The effect takes place at a specific type of initial wave-packet splitting involving two translation states whose momenta differ by even photon momenta, corresponding to the same, ground or excited, internal state. It is shown that a higher-order narrowing can be achieved using binomial wave packets. Further, another case that causes an asymmetrically narrowed diffraction is presented. An atomic-beam-splitting technique based on the preparation of atoms by STIRAP is proposed.

It is shown theoretically that a persistent current can be continuously created in a Bose-Einstein condensate (BEC) of alkali-metal atoms confined in a multiply connected region by making use of a spin degree of freedom of the order parameter of a BEC. We demonstrate that this persistent current is easily transformed into a vortex. Relaxation processes of these BEC after the confining field is turned off are also studied, so that our analyses are compared with time-of-flight experiments. The results are shown to clearly reflect the existence of a persistent current.

Investigations of high-order harmonic generation and frequency mixing in absorbing and dispersive media are reported. Detailed analysis of propagation effects and factors limiting the frequency conversion efficiency is given. Experimental results obtained by us and other groups are discussed and compared with calculations. The development of high-order parametric amplifiers as a new possibility to solve the frequency conversion problem is analyzed.

We study how the spectral properties of resonance fluorescence propagate through a two-atom system. Within the weak-driving-field approximation we find that, as we go from one atom to the next, the power spectrum exhibits both subnatural linewidth narrowing and large asymmetries while the noise spectrum of the squeezed quadrature narrows but remains otherwise unchanged. Analytical results for the observed spectral features of the fluorescence are provided and their origin is thoroughly discussed.

The effect of losses on the visibility of mesoscopic entanglement states is analyzed on the basis of a recently proposed generation scheme which amplifies a quantum seed through stimulated down-conversion. The visibility of the entanglement is shown with the amplifier working above threshold, for short interaction times.

A general expression is derived for the Born amplitude for electron capture by bare nuclei from hydrogenic atom targets, where capture takes place into high principal, and arbitrary angular momentum, quantum numbers, n and l. Cross sections for capture into high n and $l=0,1\mathrm{}$ are given in analytic forms. The limiting values of the ratios of the Born over the Oppenheimer-Brinkman-Kramers cross sections for $n\gg 1$ and $l=0,1\mathrm{}$ are found, and shown that they confirm the empirical law of Jackson and Schiff only approximately. For high angular momenta, it is shown that the Born cross section approaches the OBK cross section. An error in a previous publication by the author has been corrected.

Using the recently developed kinetic theory we calculate the intensity dependence and the detuning dependence of the Cs temperature and the Cs cloud radius in a magneto-optical trap (MOT). We find that the tendencies and the absolute values are in reasonable agreement with the experimental data of Drewsen et al. [Appl. Phys. B: Lasers Opt. 59, 283 (1994)] and that our kinetic theory deserves a quantitative and consistent theory of MOT’s.

We study violations of n-particle Bell inequalities (as developed by Mermin and Klyshko) under the assumption that suitable partial transposes of the density operator are positive. If all transposes with respect to a partition of the system into p subsystems are positive, the best upper bound on the violation is $2^{\left(n-p\right)/2\mathrm{}}.$ In particular, if the partial transposes with respect to all subsystems are positive, the inequalities are satisfied. This is supporting evidence for a recent conjecture by Peres that positivity of partial transposes could be equivalent to the existence of local classical models.