We present a Monte Carlo method for the direct simulation of evaporative cooling and the formation of the Bose-Einstein condensate of magnetically trapped atoms. The motion of the atoms in the trap is treated classically, while quantum-mechanical probability is used to describe binary elastic collisions between bosons. Two implementations of Bose statistics in the frame of a classical Monte Carlo simulation have been developed. The one involves the evaluation of the number of quantum states in single-atom phase space and the other makes use of the quantum degeneracy of energy bands. Both techniques give results compatible with the analytic results for an ideal trapped Bose gas and with the theory of a weakly interacting Bose gas, as concerns the equilibrium condensate fraction. Our simulation method also makes it possible to study the dynamic formation of the condensate, giving characteristic condensation times consistent with the experiments.

We consider a quantum superposition of Bose-Einstein condensates (BEC’s) in two immiscible internal states. A decoherence rate for the resulting Schrödinger cat is calculated and shown to be a significant threat to this macroscopic quantum superposition of BEC’s. An experimental scenario is outlined where the decoherence rate due to the thermal cloud is dramatically reduced thanks to trap engineering and “symmetrization” of the environment, which allow the Schrödinger cat to be an approximate pointer state.

It is shown that the quantum jumps in the photon number $\mathrm{n̂}$ from zero to one or more photons induced by backaction evasion quantum nondemolition measurements of a quadrature component $◯$ of the vacuum light field state are strongly correlated with the quadrature component measurement results. This correlation corresponds to the operator expectation value $〈◯\mathrm{n̂}◯〉$ which is equal to one-fourth for the vacuum even though the photon number eigenvalue is zero. Quantum nondemolition measurements of a quadrature component can thus provide experimental evidence of the nonclassical operator ordering dependence of the correlations between photon number and field components in the vacuum state.

We present a semiclassical method for determining the phase distribution and the average photon number of a steady-state micromaser field pumped by a stream of resonant two-level atoms in a superposition of their upper and lower states. Assuming the field to have a photon number distribution with a single sharp peak, we find an equation for the amplitude and the phase of the steady-state field, which has two solutions. The stability analysis shows which one of the two is physically realizable. Using the very simple time evolution of particular atomic states, valid in the semiclassical limit, we find an expression for the phase distribution of the field that contains the mean photon number as a parameter. That can be determined from the stable solution.

The finite conductivity corrections to the Casimir force in two configurations are calculated in the third and fourth orders in the relative penetration depth of electromagnetic zero oscillations into the metal. The obtained analytical perturbation results are compared with recent computations. Applications to the experiments on precision Casimir force measurements are discussed.

Studies of Rydberg atom collision processes, especially those with small reaction rate constants, are frequently complicated by spurious background signals associated with photoionization by thermal blackbody radiation and with ionization resulting from collisions with background gas. Here we demonstrate that the magnitude and relative importance of the signals that result from these processes are strongly influenced by the presence of an applied electric field. Possible causes of this dependence are discussed.

In a recent paper [Phys. Rev. A 52, 2645 (1995)], Liu et al. presented an approach for obtaining physical properties at the nuclear cusps. They compared it with the Hiller-Sucher-Feinberg (HSF) identity [Phys. Rev. A 18, 2399 (1978)] and found theirs to be superior. It is shown here that this conclusion is based on the comparison on equal footing of different types of identities, namely physical in the case of HSF and mathematical in the case of Liu et al.

Fluctuations of a rubidium atom on the surface of a fullerene cage have been observed by measuring the electric susceptibility of isolated ${\mathrm{RbC}}_{60}$ molecules. The evolution of the susceptibility with the temperature is perfectly reproduced with a very simple statistical model of relaxation. The correlation time for these fluctuations and the activation energy ${(E}_a=0.02\mathrm{}$ eV) for the motion of the alkali-metal atom on the ${\mathrm{C}}_{60}$ surface have been determined.

We present experimental evidence for the synchronization of two semiconductor lasers exhibiting chaotic emission on subnanosecond time scales. The transmitter system consists of a semiconductor laser with weak to moderate coherent optical feedback and therefore exhibits chaotic oscillations. The receiver system is realized by a solitary semiconductor laser in which a fraction of the transmitter signal is coherently injected. We find that for a considerably large parameter range, synchronized receiver output can be achieved. We discuss the physical mechanism and demonstrate that the receiver acts as a chaos pass filter, which reproduces the chaotic fluctuations of the transmitter laser, but suppresses additionally encoded signals. Signal extraction at frequencies of up to 1 GHz has been achieved. Thus we provide a simple and robust optical chaos synchronization system that is promising for the realization of communication by sending signals with chaotic carriers.

We analyze approximate transformations of pure entangled quantum states by local operations and classical communication, finding explicit conversion strategies which optimize the fidelity of transformation. These results allow us to determine the most faithful teleportation strategy via an initially shared partially entangled pure state. They also show that procedures for entanglement manipulation such as entanglement catalysis [Jonathan and Plenio, Phys. Rev. Lett. 83, 3566 (1999)] are robust against perturbation of the states involved, and motivate the notion of nonlocal fidelity, which quantifies the difference in the entangled properties of two quantum states.

We show how optically driven coupled quantum dots can be used to prepare maximally entangled Bell and Greenberger-Horne-Zeilinger states. Manipulation of the strength and duration of the selective light pulses needed for producing these highly entangled states provides us with crucial elements for the processing of solid-state-based quantum information. Theoretical predictions suggest that several hundred single quantum bit rotations and controlled-NOT gates could be performed before decoherence of the excitonic states takes place.

We have demonstrated velocity-selective coherent population trapping (VSCPT) in a two-level system created by circularly polarized light driving the $2{}^3{S}_1\to 3{}^3{P}_2$ transition in metastable helium. It is quite different from the usual VSCPT because there need be no consideration of selection rules, polarization, or internal atomic states. This most primitive case elicits the simple nature of VSCPT as a special kind of quantum interference, and demonstrates the presence of VSCPT in a system that has only two internal levels. It is readily observed for this transition because the ratio of the recoil frequency to the natural linewidth is 0.22, two orders of magnitude larger than for most laser cooling experiments. Our trapped state is fed by Doppler cooling, which is unusually effective here because of the large recoil, and is totally absent in previously described VSCPT experiments.

We consider scattering atoms from a fully Bose-Einstein condensed gas. If we take these atoms to be identical to those in the Bose-Einstein condensate, this scattering process is to a large extent analogous to Andreev reflection from the interface between a superconducting and a normal metal. We determine the scattering wave function in both the absence and the presence of a vortex. Our results show a qualitative difference between these two cases that can be understood as due to an Aharonov-Bohm effect. It leads to the possibility to experimentally study vortices in a nondestructive way.

We investigate spontaneous emission from a two-level atom embedded in a photonic crystals with three-dimensional dispersion relation, where the dependence of wave vectors on direction is taken into account. Due to the difference of the density of states of electromagnetic modes between a three-dimensional and a one-dimensional photonic crystal (lack of singularity), the dynamics of the population in the excited state and the emitted field are quite different from those of a one-dimensional photonic crystal. There is no quasi-oscillation for the population evolution. The localized field and the propagating field cannot coexist. When the upper level moves from the gap to the band, the emitted field changes from a localized field to a diffusion field and then to a propagating field. The energy of the diffusion and propagating fields propagates out incoherently and coherently, respectively. An analytical expression for the Lamb shift is obtained. The Lamb shift for the current case is smaller than that in an ordinary vacuum or in one-dimensional photonic crystals.

Klauder’s recent generalization of the harmonic oscillator coherent states [J. Phys A 29, L293 (1996)], is applicable only in nondegenerate systems, requiring some additional structure if applied to systems with degeneracies. The author suggests how this structure could be added, and applies the complete method to the hydrogen atom problem. To illustrate how a certain degree of freedom in the construction may be exercised, states are constructed, which are initially localized and evolve semiclassically, and whose long time evolution exhibits “fractional revivals.”

We verify that the van der Waals interaction and hence all dispersion interactions for the hydrogen molecule are exactly soluble. The constants $A=6.499\mathrm{}0267\dots ,$ $B=124.399\mathrm{}0835\dots ,$ and $C=1135.214\mathrm{}0398\dots$ (in Hartree units), first obtained approximately by Pauling and Beach using a linear variational method, can be shown to be obtainable to any desired accuracy via our exact solution. In addition, we shall show that an implicit energy density functional can be obtained, whose variational solution rederives the exact solution for this problem. Thus we present an exact and practical static density functional for this system. We conclude with remarks about generalizing the method to other hydrogenic systems and also to helium.

Recent high-precision experimental results for photon scattering from neon $(\approx 1\%$ accuracy) have indicated that even present sophisticated S-matrix results are not sufficient to obtain agreement, even though the photon energies involved were many times the innermost threshold energy. In this case the discrepancy was traced to the use of local exchange and the neglect of electron-correlation effects. Here we present a general scheme for applying corrections to the S-matrix results to account for nonlocal-exchange effects and electron-correlation effects, so as to obtain results expected to be accurate at the 1% level in all elements for such energies. The corrections are based on results in simpler approximations: the form-factor approximation for elastic Rayleigh scattering, and the impulse and incoherent-scattering-factor approximations for inelastic Compton scattering. The case of scattering from neon is investigated in detail for all scattering angles and for photon energies in the range 1–100 keV. The scheme breaks down below $\approx 1\hspace{0.5em}\mathrm{keV}$ for elastic scattering and at low momentum transfers for inelastic scattering. We also discuss the validity of the simpler approximations, particularly the use of the impulse approximation in describing Compton scattering.

Measurements are reported for kinematically complete electron-impact ionization collisions with oriented $3P$ sodium atoms excited from the ground state by right- and left-hand circularly polarized light. The measurements reveal a strong dependence of the ionization cross section on the helicity inversion of the exciting photon. This dichroic effect and the magnetic state resolved cross sections are described using the distorted-wave Born approximation and the dynamically screened Coulomb wave method. Within the context of these methods we investigate the role of different short- and long-range interactions involved in the process. For moderate values of incident energy we conclude that the shape and magnitude of the dichroism is predominantly determined by the Coulomb interactions of the outgoing electrons with the residual ion. For slow escaping electrons the dichroism is also influenced by the interelectronic correlations.

Energy losses of fragment protons from 0.2- and 0.5-MeV/amu ${\mathrm{H}}_2^{+}$ were measured at transmission through amorphous carbon foils of thickness less than $25\mu \mathrm{g}/{\mathrm{cm}}^2.$ The energy losses of randomly oriented fragment protons and those of the fragment protons aligned in the direction of motion show how the spatial correlation of the protons affects the energy loss. We use the dielectric formalism to calculate the stopping power of amorphous carbon for two spatially correlated protons and compare with the experimental energy-loss data. We conclude that higher energies or thinner foils are necessary to understand the anomalous energy loss of aligned proton pairs.

It is proved that in three dimensions, and contrary to what is usually found in one dimension, the number of bound Kramers-Hennebrger states always reduces to zero in strong fields if the range of the potential is short and its depth finite. Numerical results showing the disappearance of the dressed ground state of an exponential potential in an intense high-frequency field are also presented.