The Lamb shift is interpreted as a fluctuation in the electron position due to the presence of an electromagnetic field of the vacuum. The result is expressed in terms of the imaginary part of the vector potential Green function via the fluctuation dissipation theorem and Kubo’s formula. The formalism allows us to evaluate the Lamb shift in the presence of a dielectric host as well as empty space, without resorting to the detailed process of field quantization. The latter formalism is applied to a calculation of the level shifts of a hydrogen atom embedded in a homogeneous lossy dispersive medium. The transverse and longitudinal contributions of the fluctuating field of the vacuum are evaluated separately.

We report the simulations of the dynamics of quantum-logic operations with large number of qubits (up to 1000). A nuclear-spin chain in which selective excitations of spins are provided by the gradient of the external magnetic field is considered. The spins interact with their nearest neighbors. We simulate the quantum controlled-NOT (CN) gate implementation for remote qubits, which provides the long-distance entanglement. Our approach can be applied to any implementation of quantum-logic gates involving a large number of qubits.

Quantum teleportation with additional a priori information about the input state achieves higher fidelity than teleportation of a completely unknown state. However, perfect teleporation of two nonorthogonal input states requires the same amount of entanglement as perfect teleportation of an unknown state, namely one ebit. We analyze how well two-state teleportation can be achieved using every degree of pure-state entanglement. We find the highest fidelity of “teleportation” that can be achieved with only classical communication but no shared entanglement. A two-state telecloning scheme is constructed.

Auger decay rates of long-lived states of the antiprotonic helium ${}^{3,4}\mathrm{He}\mathrm{p}¯\mathrm{e}$ are calculated. The initial-state wave function is determined by using a variational approach combined with the solution of coupled differential equations. Special treatment is given to a few long-lived states, whose energy is close to that of the short-lived ones with an essentially different structure of the wave function. For these particular states, an admixture of the wave function of the near-lying short-lived states is taken into account.

A model is introduced for investigating the effect of electron-ion inelastic collisions on dielectronic recombination (DR) and for predicting its electron-density dependence. A general method for obtaining effective DR rate coefficients for optically thin dense plasmas is described. Level-by-level relativistic calculations are performed for DR of Ne-like iron, selenium, and tungsten in their ground state via the Na-like ${1s}^2{\mathrm{}\left(2s2p\right)\mathrm{}}^{7}3l{n}^{\prime }{l}^{\prime }{(n}^{\prime }=3,4)$ autoionizing configurations. The results clearly show that, as the electron density increases, the first density effect to appear is an enhancement of the DR rates through collisional transitions among the autoionizing levels. At higher densities, collisional stabilization and collisional ionization play an important role. At low electron temperatures, collisional stabilization processes enhance the DR rates, whereas at high temperatures, collisional ionization reduces them. However, in a relatively wide intermediate temperature range, the opposite contributions of the various collisional mechanisms can result in a very small total collisional effect. Additionally, it is found that all of the various collisional effects strongly decrease with the ion charge. For very highly charged ions, such as Ne-like W, the collisional effect is appreciably quenched, even at very high densities, due to the dominance of the radiative processes.

The system of a two-level atom interacting with a quantized radiation field in a gravitational field is studied by making use of a dynamical algebraic method. A full quantum treatment of the internal and external dynamics of the atom is given and an exact expression for the time evolution operator of the system is obtained. The influence of the gravitational field on the collapses and revivals of the atomic population, sub-Poissonian statistics, radiation force, atomic momentum diffusion, and squeezing of the radiation field is also investigated.

The transfer of the intrinsic coherence of short pulses to molecular systems is investigated and an explicit derivation of the excitation probability of the ultrafast multiphoton process is presented. We show that for ultrafast excitation the angular cross section splits into two distinct factors: the “frozen orientation weight,” which involves the space configuration and nonlinear dependence, and the “laser-induced coherence,” which reflects the coherent superposition of the ground- and excited-state orientations. Quantum interferences give rise to a “coherent polarizability” and provide evidence for a sharp confinement of the excited electron motion. The confinement is inversely proportional to the number of coherently excited rotational states.

We develop a general theory of adiabatic output coupling from trapped, weakly interacting, atomic Bose-Einstein condensates at finite temperatures. For weak coupling, the output rate from the condensate and the excited levels in the trap settles in a time proportional to the inverse of the spectral width of the coupling to the output modes. We discuss the properties of the output atoms in the quasi-steady-state, where the population inside the trap is not appreciably depleted. We show how the composition of the output beam, containing the condensate and the thermal component, may be controlled by changing the frequency of the output coupling lasers. This composition determines the first- and second-order coherence of the output beam. We discuss the changes in the composition of the Bose gas left in the trap, and show how nonresonant output coupling can stimulate either the evaporation of the thermal excitations in the trap or the growth of the nonthermal excitations, when pairs of correlated atoms leave the condensate.

Here we consider the continuous pumping of a dissipative QED cavity and derive the time-dependent density operator of a cavity field prepared initially as a superposition of mesoscopic coherent states. The control of the coherence of this superposition is analyzed by considering the injection of a beam of two-level Rydberg atoms through the cavity. Our treatment is compared to other approaches.

We investigate the photon statistics of light transmitted from a driven optical cavity containing one or two atoms interacting with a single mode of the cavity field. We treat arbitrary driving fields with emphasis on departure from previous weak field results. In addition effects of dephasing due to atomic transit through the cavity mode are included using two different models. We find that both models show the nonclassical correlations are quite sensitive to dephasing. The effect of multiple atoms on the system dynamics is investigated by placing two atoms in the cavity mode at different positions, therefore having different coupling strengths.

In this paper we address the problem of how much can be learned about an unknown quantum state by a measurement. To this end we consider optimal measurements for the state estimation problem, that is measurements that maximize the expectation of a fidelity function. We then enlarge the class of optimal measurements to measurements that act collectively on blocks of input states, and in addition we only require that the fidelity of the measurement be arbitrarily close to the optimal fidelity. We then consider the Shannon information of the outputs of optimal measurements, which is the amount of data produced by the measurements. We show that in the enlarged class of optimal measurements described above one can always construct an optimal measurement so that the Shannon information of its outputs equals the von Neumann entropy of the unknown states. Since this result is valid for all choices of fidelity functions and all distributions of input states, it provides a model independent answer to the question of how much can be learned about a quantum state by a measurement. Namely, this result shows that a measurement can extract at most one meaningful bit from every qubit carried by the unknown state.

We find that very different quantum copying machines are optimal depending on the indicator used to assess their performance. Several quantum copying machine models acting on nonorthogonal input states are investigated, and assessed according to two types of criteria: transfer of (Shannon) information encoded in the initial states to the copies, and fidelity between the copies and the initial states. Transformations that optimize information transfer for messages encoded in qubits are found for three situations: (1) when the message is decoded one state at a time; (2) with simple schemes that allow the message to be encoded using block-coding schemes; and (3) when the copier produces independent copies. If the message is decoded one symbol at a time, information is best copied by a Wootters-Zurek copier.

The effects of the electronic correlation in the shake-up process of atomic doubly excited asymmetric states have been investigated by using a nondegenerate perturbative method. It is shown that the overlap spectrum and the recently observed abnormal spectrum can be described by the same theoretical framework. The quantitative intrinsic relation between the well known overlap formula and the electronic correlation has been revealed analytically. The scope for applying the overlap formula has been discussed. The shake-off process has also been discussed as a continuum case of the shake-up process. It is shown that the escape electron in a shake-off process of a higher-$l$ state or with a higher escape energy tends to increase its angular momentum.

The single-shot time-resolved laser-induced-fluorescence (LIF) technique has been developed further to measure short lifetimes more accurately by considering saturation quantitatively. The temporal and spatial energy distribution in the laser pulses and the separately measured response function of the detection system enter the evaluation procedure. Investigation of LIF anisotropy has shown the necessity for applying the magic angle arrangement as predicted by theory. We obtain standard deviations of 2% for lifetimes around 2 ns. The lifetime of the prominent Be I$2s2p{}^1{P}_1^0$ level has been measured as $1.85\pm 0.04\mathrm{ns}.$ This value corresponds to an oscillator strength for the resonance transition of $1.34\pm \mathrm{0.03.}$ A comparison with theoretical and experimental literature data shows excellent to good agreement.

The vibrational cooling of ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+},$ having no dipole moment, has been studied at the storage ring TARN II. A two-dimensional imaging technique was used to measure the kinetic-energy release (KER) in the dissociative recombination of ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ as a function of the storage time at a relative energy of 0 eV. The vibrational-level populations of the ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ beams were estimated from the KER data. The estimation shows that the relative population of ${\mathrm{H}}_2^{+}$ ions in their vibrational ground states reaches more than 90% at a storage time of 26 s. This result is in agreement with the recent result in TARN II [T. Tanabe et al., Phys. Rev. Lett. 83, 2163 (1999)]. The relative population of ${\mathrm{D}}_2^{+}$ ions in their vibrational ground states is estimated to be more than 90% for a storage time of 10 s.

We consider a rotating axisymmetric trap containing a small Bose-Einstein condensate with a singly quantized vortex near the axis of symmetry. A time-dependent variational Lagrangian analysis yields the small-amplitude dynamics of the vortex and the condensate, directly determining the equations of motion of the coupled normal modes. As found previously from the Bogoliubov equations, there are two rigid dipole modes and one anomalous mode with a negative frequency when seen in the nonrotating laboratory frame.

We analyze by direct numerical simulations the effects of the wave nature of an atom on lithography with a laser standing wave. Specific calculations are done for chromium atom deposition with the experimental parameters given in the literature. In the absence of source imperfections and atomic motion during and after the deposition most of the feature width comes from diffractive aberration. Spontaneous emission broadens the linewidth further, giving a full width at half maximum about 8.9 nm and a contrast about 26:1. These are what may be achieved ultimately with the said experimental parameters and show that the nonclassical properties of the atom cannot simply be ignored. We then suggest some strategies for improving atom lithography experiments.

The mean-field properties of finite-temperature Bose-Einstein gases confined in spherically symmetric harmonic traps are surveyed numerically. The solutions of the Gross-Pitaevskii (GP) and Hartree-Fock-Bogoliubov (HFB) equations for the condensate and low-lying quasiparticle excitations are calculated self-consistently using the discrete variable representation, while the most high-lying states are obtained with a local-density approximation. Consistency of the theory for temperatures through the Bose condensation point $T_c$ requires that the thermodynamic chemical potential differ from the eigenvalue of the GP equation; the appropriate modifications lead to results that are continuous as a function of the particle interactions. The HFB equations are made gapless either by invoking the Popov approximation or by renormalizing the particle interactions. The latter approach effectively reduces the strength of the effective scattering length $a_{\mathrm{sc}},$ increases the number of condensate atoms at each temperature, and raises the value of $T_c$ relative to the Popov approximation. The renormalization effect increases approximately with the log of the atom number, and is most pronounced at temperatures near $T_c.$ Comparisons with the results of quantum Monte Carlo calculations and various local-density approximations are presented, and experimental consequences are discussed.

We propose a simple scheme of atom localization based on resonance fluorescence from a standing-wave field. The Rabi frequency is position dependent and therefore the spontaneously emitted photon carries the information of the atomic center-of-mass motion. This leads to atom localization even during the flight through the standing-wave field.

A cavity-modified master equation is derived for a coherently driven, V-type three-level atom coupled to a single-mode cavity in the bad-cavity limit. We show that population inversion in both the bare- and dressed-state bases may be achieved, originating from the enhancement of the atom-cavity interaction when the cavity is resonant with an atomic dressed-state transition. The atomic populations in the dressed-state representation are analyzed in terms of the cavity-modified transition rates. The atomic fluorescence spectrum and probe absorption spectrum are also investigated, and it is found that the spectral profiles may be controlled by adjusting the cavity frequency. Peak suppression and line narrowing occur under the appropriate conditions.