We study collisional loss rates due to spin-exchange collisions in very-low-intensity ${}^{87}\mathrm{Rb}$ magneto-optical traps. The loss rate exhibits an unpredicted intensity dependence for low intensities, accounting for a large disparity between loss rates observed in light-force traps and magnetically confined Bose condensates. Possible collision mechanisms considered include light-altered collision phase shifts, flux enhancement, and excited-state hyperfine changing collisions.

We have measured the rate of hyperfine-changing collisions between ground-state ${}^{87}\mathrm{Rb}$ atoms in a magneto-optical trap. Using a population switching technique, we directly measure the rate of these collisions in both the presence and absence of near-resonant trap laser light. We see a dramatic enhancement of the collision rate by the light and observe that, in the absence of the light, the rate increases with increasing temperature. There is consistency between this latter measured rate at temperatures below $\sim 100$ $\mu \mathrm{K}$ and theoretical calculations constrained by other recent experiments.

A quantum-erasure experiment was performed on superposition states of two photons in either of two spatiotemporal modes. Symmetrical tapping of energy from the two-mode state creates a four-mode entangled state. A direct measurement of one photon in two of the modes reveals the path of the second one, thereby eliminating the possibility of observing interference between the two remaining modes. It is shown that a unitary rotation of one of the two-mode states erases the path information; as a consequence, the visibility of the other two-mode state can be resurrected.

We present a quantum version of the classical probabilistic algorithms as studied by Rabin. The quantum algorithm is based on the essential use of Grover’s operator for the quantum search of a database and of Shor’s Fourier transform for extracting the periodicity of a function, and their combined use in the counting algorithm originally introduced by Brassard et al. One of the main features of our quantum probabilistic algorithm is its full unitarity and reversibility, which would make its use possible as part of larger and more complicated networks in quantum computers. As an example of this we describe polynomial time algorithms for studying some important problems in number theory, such as the test of the primality of an integer, the so called prime number theorem, and Hardy and Littlewood’s conjecture about the asymptotic number of representations of an even integer as a sum of two primes.

Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for d-dimensional spaces, and the resulting set of unitary matrices $S\left(d\right)\mathrm{}$ is a basis for $d\times d$ matrices. If ${N=d}_1\times d_2\times \cdot \cdot \cdot \times d_b$ and $H^{\left[N\right]}=\otimes H^{\left[d_k\right]},$ we give a sufficient condition for separability of a density matrix $\rho$ relative to the $H^{\left[d_k\right]}$ in terms of the $L_1$ norm of the spin coefficients of $\rho .$ Since the spin representation depends on the form of the tensor product, the theory applies to both full and partial separability on a given space $H^{\left[N\right]}.$ It follows from this result that for a prescribed form of separability, there is always a neighborhood of the normalized identity in which every density matrix is separable. We also show that for every prime p and $n>\mathrm{}1,$ the generalized Werner density matrix $W^{\left[p^n\right]}\mathrm{}\left(s\right)\mathrm{}$ is fully separable if and only if $s<~{(1+p}^{n-1}{)}^{-1}.$

The oscillator strengths of the allowed and spin-forbidden ${5s}^2{}^1{S}_0–5s5p{}^{1,3}{P}_1^o$ transitions in the cadmium isoelectronic sequence are evaluated for $48<~Z<~57$ using the relativistic Hartree-Fock approach, including a core-polarization potential, and the multiconfiguration Dirac-Fock method, taking the valence and core-valence correlation effects into account. A good agreement is noted when comparing the two sets of theoretical data and when comparing theory with experiment for the spin-forbidden transition. The discrepancies observed between theory (both theories being in agreement) and experiment for the singlet-singlet transition indicate that some experimental data are in need of revision.

The treatment of the dynamics of ultracold molecules requires new theoretical tools. Previous work of the present authors [J. Chem. Phys. 110, 9865 (1999)] for calculation of vibrational levels by a Fourier grid representation with use of adaptative coordinates is generalized here to the treatment of the bound-continuum interaction in a two-channel problem. Two numerical methods are presented: a time-dependent method using a Chebyshev propagator to compute the correlation function and a time-independent method with diagonalization of a Hamiltonian that includes an absorbing optical potential. In both cases the adaptative coordinate is defined by a numerical rather than an analytical procedure. Lifetimes are reported for the predissociated levels of the ${\mathrm{Rb}}_2$ and ${\mathrm{Cs}}_2{0}_u^{+}{(ns+np}^2{P}_{3/2})$ spectra, where $n=5,6.\mathrm{}$ The two numerical methods give similar results. The lifetimes increase with the vibrational quantum number proportionally to the classical vibration period estimated from the Le Roy–Bernstein law for an asymptotic $R^{-3}$ potential, and the energy variation can be fitted to an analytical formula. The results are shown to be very sensitive to the molecular parameters, potentials, and couplings. The measured width of 8.5 GHz reported by Cline et al. [Phys. Rev. Lett. 73, 632 (1994)] for one predissociated level of ${}^{87}{\mathrm{Rb}}_2$ is reproduced. A strong isotopic effect is found for the rubidium dimer, the lifetimes of ${}^{85}{\mathrm{Rb}}_2$ and ${}^{87}{\mathrm{Rb}}_2$ levels differing by a factor of 3. Finally, we present a third approach, in the framework of a generalized two-channel quantum-defect theory, where lifetimes are determined by extrapolation of parameters fitted to Lu-Fano plots of computed bound levels below the $P_{1/2}$ dissociation limit. Excellent agreement is obtained with the numerical results, suggesting the possibility of fitting to experimental spectra.

We propose a simple method for the deterministic generation of an arbitrary continuous quantum state of the center-of-mass of an atom. The method’s spatial resolution gradually increases with the interaction time with no apparent fundamental limitations. Such de Broglie wave-front engineering of the atomic density can find applications in Atom Lithography, and we discuss possible implementations of our scheme in atomic beam experiments.

We present a model for light polarization in vertical-cavity surface-emitting lasers (VCSEL’s) based on semiconductor Bloch equations, which includes the effects of valence-band mixing and accounts for the possibility of different spin-flip rates for conduction electrons and holes. We calculate the stability boundaries of linearly polarized solutions and compare them with those of the model introduced by San Miguel, Feng, and Moloney [Phys. Rev. A 52, 1728 (1995)], to which our equations reduce under appropriate assumptions. We study the dependence of such boundaries on some physical parameter of the VCSEL, and show how our equations can be used to interpret some measurements of the spin-flip rate performed recently.

A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.

We perform a first-principles derivation of the general master equation to study the non-Markovian dynamics of a two-level atom (2LA) interacting with an electromagnetic field (EMF). We use the influence functional method, which can incorporate the full back reaction of the field on the atom, while adopting Grassmannian variables for the 2LA and the coherent-state representation for the EMF. We find exact master equations for the cases of a free quantum field and a cavity field in the vacuum. In response to the search for mechanisms to preserve maximal coherence in quantum computations in ion trap prototypes, we apply these equations to analyze the decoherence of a 2LA in an EMF, and find that decoherence time is close to relaxation time. This is at variance with the claims by authors who studied the same system but used a different coupling model. We explain the source of difference and argue that, contrary to common belief, the EMF, when resonantly coupled to an atom, does not decohere it as efficiently as a bath does on a quantum Brownian particle. The master equations for non-Markovian dynamics derived here are expected to be useful for exploring new regimes of 2LAEMF interaction, which is becoming physically important experimentally.

We present two methods for optimal entanglement concentration from pure entangled states by local actions only. However, a prior knowledge of the Schmidt coefficients is required. The first method is optimally efficient only when a finite ensemble of pure entangled states are available, whereas the second method realizes the single pair optimal concentration probability. We also propose an entanglement-assisted method that is again optimally efficient even for a single pair. We also discuss concentrating entanglement from N-partite catlike states.

A quantum system may be efficiently simulated by a quantum information processor as suggested by Feynman and developed by Lloyd, Wiesner, and Zalka. Within the limits of the experimental implementation, simulation permits the design and control of the kinematic and dynamic parameters of a quantum system. Extension to the inclusion of the effects of decoherence, if approached from a full quantum-mechanical treatment of the system and the environment, or from a semiclassical fluctuating field treatment (Langevin), requires the difficult access to dynamics on the time scale of the environment correlation time. Alternatively, a quantum-statistical approach may be taken which exploits the natural decoherence of the experimental system, and requires a more modest control of the dynamics. This is illustrated for quantum simulations of a four-level quantum system by a two-spin NMR ensemble quantum information processor.

We consider low-rank density operators $\varrho$ supported on a $M\times N$ Hilbert space for arbitrary M and N $(M<~N),$ and with a positive partial transpose (PPT) ${\varrho }^{T_A}>~0.$ For rank $r\left(\varrho \right)<~N$ we prove that having a PPT is necessary and sufficient for $\varrho$ to be separable; in this case we also provide its minimal decomposition in terms of pure product states. It follows from this result that there is no rank-3 bound entangled states having a PPT. We also present a necessary and sufficient condition for the separability of generic density matrices for which the sum of the ranks of $\varrho$ and ${\varrho }^{T_A}$ satisfies $r\left(\varrho \right)+r\left({\varrho }^{T_A}\right)<~2MN-M-N+2.\mathrm{}$ This separability condition has the form of a constructive check, thus also providing a pure product state decomposition for separable states, and it works in those cases where a system of couple polynomial equations has a finite number of solutions, as expected in most cases.

A triggering device sensitive to a single photon is discussed. It is based on a balanced quantum nondemolition (QND) measurement proposed by Chuang and Yamamoto [Phys. Rev. Lett. 76, 4281 (1996)]. The balanced measurement measures the total photon number and obtains no which-path/mode information. Hence, the timing of the photon can be determined without destroying its wave function or entangling the probe field. This could have extensive use in the realization of long-distance quantum communications systems.

We present a detailed theoretical evaluation for the $g_j$ factor of a bound electron in hydrogenlike ions up to $Z=94.\mathrm{}$ All quantum electrodynamical corrections of order $(\alpha /\pi )$ are evaluated in detail and various other contributions to the $g_j$ factor are computed and listed for 61 Z. A comparison with all existing experiments is carried out and excellent agreement is found. The present uncertainty in our calculations is discussed. It is not possible to improve this precision with only minor effort since two-photon bound-state QED terms are uncalculated up to now.

Using a laser-induced fluorescence method detailed analysis of profiles of the ${}^{114}\mathrm{Cd}$ 326.1-nm line perturbed by xenon was performed, which revealed departures from the ordinary Voigt profile. These departures are shown to be consistent with fits of experimental profiles to a speed-dependent asymmetric Voigt profile. Coefficients of the pressure broadening, shift, and collision-time asymmetry are determined and compared with those calculated in the adiabatic approximation for the Czuchaj-Stoll potentials.

Electron-impact excitation cross sections for Kr have been measured by means of the optical method over a range of incident-electron energies between onset and 250 eV. By measuring cascade transitions into the ${4p}^{5}5p$ levels from higher-lying levels and subtracting this contribution from the observed transitions out of the ${4p}^{5}5p$ levels, we are able to determine the cross sections for direct electron excitation into the ten levels of the ${4p}^{5}5p$ configuration $(2p$ in Paschen’s notation). The general trends of these cross sections for Kr are compared with previous measurements from our labs on Ne, Ar, and Xe. We note that the optical emission cross sections for transitions from levels resonant with the ground level vary with gas pressure. Fitting this observed pressure dependence to a simple model allows us to test theoretical values of the transition coefficients for these levels.

Singly and doubly K-shell-vacant states in atomic Li, produced by 95-MeV/u ${\mathrm{Ar}}^{18+}$ projectiles, have been investigated. At this high velocity, excitation and ionization are expected to be well described by perturbation theories. High-resolution spectra for Auger electron emission, occurring in the energy range ∼50–90 eV and resulting from the deexcitation of singly or doubly excited states, were measured for various electron emission angles. Both single-K-shell excitation and double-K-shell vacancy production show strong dependences on the electron emission angle. Experimental anisotropy parameters for the ${}^{2}P$ states resulting from single-K-shell excitation are in good agreement with predictions of the Born approximation. In the case of double-K-shell-vacancy (i.e., hollow atom) production, the two K vacancies are found to come about mainly by ionization plus excitation of the atomic Li target giving rise to excited states in ${\mathrm{Li}}^{+}.$ Strong line intensities from the ${2s}^2{}^{1}S$ and $2s3s{}^{3}S$ excited-state configurations are explained in terms of shake processes, providing direct spectral identification for the electron-electron (e-e) interaction in producing the doubly vacant K-shell configurations. Production of the $2s3s{}^{3}S$ state, which has an intensity greater than that of the ${2s}^2{}^{1}S$ state, is attributed to a three-electron transition involving two shake transitions. Production of the $2s2p{}^{3}P$ state has a large contribution from the dielectronic manifestation of the e-e interaction resulting from slow electron emission.

The energy loss of a heavy bare projectile with charge $Z_P$ moving in a free-electron gas is studied within the framework of the binary collisional formalism. The transition-matrix element is expanded in a perturbative series, and terms up to $Z_P^3$ (second Born approximation) are conserved. The Mermin-Lindhard dielectric response function is employed to describe the cylindric potential induced by the projectile. The formalism is applied to the calculation of energy-loss distributions for fixed charges (protons, neutral hydrogen, and antiprotons) colliding with aluminum. We also investigate how the $Z_P^3$ collisional correction affects the total stopping for antiprotons in aluminum and silicon, and for protons in aluminum. In this latest case, different charge states of the projectile are considered. Results are in good agreement with experimental data in the high-energy region.