We analyze, within the generalized multichannel quantum defect theory framework, atomic binary collision cross sections over the 1 muK to 10 mK energy range just above the entrance channel threshold, a domain where the Wigner threshold law should apply. By adjusting the strength of a constant external magnetic field a Feshbach resonance is tuned at will over this energy range. In the threshold regime, the quasibound state interacts with an opening continuum whose wave function presents a strong energy dependence which reflects the breakdown of the WKB approximation. The effective discrete-continuum interactions become very sensitive to the energy. The consequences of these variations have been investigated by including threshold effects in the analysis of the Fano configuration-interaction theory [ Phys. Rev. 124, 1866 (1961) ] in terms of quantum defect theory quantities proposed by [ Lecomte J. Phys. B 20, 3645 (1987) ]. This analysis shows that the energy variations are in general so important that it becomes meaningless to associate a width with a Feshbach resonance. However, it is still possible to define the resonance energy, as long as the energy variation of the shift of the resonance, induced by the effective discrete-continuum interaction, remains linear over an energy range corresponding to the magnitude of the shift.

A controlled interference is proposed to reduce, by two orders of magnitude, the decoherence of a quantum gate for which the gate fidelity is limited by coupling to states other than the /0> and /1> qubit states. This phenomenon is demonstrated in an ultracold neutral atom implementation of a phase gate using qubits based on motional states in individual wells of an optical lattice.

We study an implementation of a two-qubit universal quantum gate with neutral (87)Rb atoms trapped in a far-detuned two-color optical lattice. The qubit states \0> and \1> represent the ground and first excited motional states of an atom in a laser induced potential well. By varying the ratio of the laser intensities of the two colors, the barrier between two neighboring atoms is lowered, creating two-particle entanglement. We predict the duration of operation of a conditional pi-phase gate with a time-dependent configuration interaction model.

We present a theoretical analysis of the density dependent frequency shift in Cs fountain clocks using the highly constrained binary collision model described by Leo et al. [Phys. Rev. Lett. 85, 2721 (2000)]. We predict a reversal in the clock shift at temperatures near 0.08 microK. Our results show that s waves dominate the collision process. However, as a consequence of the large scattering lengths in Cs the clock shift is strongly temperature dependent and does not reach a constant Wigner-law value until temperatures are less than 0.1 nK.

We calculate the energy-level shifts of a tightly confined trapped alkali-metal atom in the presence of a second trapped atom. A complete microscopic description of the interaction energy between the two atoms is used. This allows us to study tightly confined atoms near a Feshbach resonance and to evaluate the usefulness of the regularized $\ensuremath{\delta}$-function potential approximation. We present results for sodium and cesium when confined in a spherically symmetric harmonic optical trap. Possible implications of the level shifts and collisional decoherence for quantum computing with atomic systems are given.

We have calculated the time-dependent dynamics of two ultracold Na atoms in an atom trap where a time-dependent magnetic field B(t) moves a Feshbach resonance state across the energy threshold for a binary collision. Our coupled-channel scattering calculations, which reproduce the observed properties of such resonances in sodium atom collisions, can be reduced to an effective two-channel configuration-interaction model for one bound state and one continuum. The model is adapted to describe the time-dependent dynamics induced by B(t) for two atoms trapped either in a strongly confining single well of an optical lattice or in an optical potential in the presence of a Bose-Einstein condensate. We show that a simple Landau-Zener curve crossing model gives quantitative agreement with exact calculations of field-induced transition rates. If B(t) sweeps the resonance across threshold from above, two atoms in the ground state of the trap potential can be efficiently converted to translationally cold dimer molecules. If the resonance is swept from below, the atoms can be removed from the ground state and placed in hot vibrational levels of the trap. Our calculations reproduce the rapid atom loss rates observed in a Na Bose-Einstein condensate due to sweeping a Feshbach resonance state through the binary collision threshold.

At the ultracold temperatures which occur in cold atom traps and Bose-Einstein condensates, only a few partial waves contribute to the scattering of ground-state alkali-metal atoms, and cross sections are extremely sensitive to threshold effects. We present an analysis of these threshold effects, using a generalized multichannel quantum defect theory (GMQDT) to construct a close-coupled scattering wave function which is analytic in energy across thresholds. We illustrate the theory using the hyperfine transitions in Na + Na collisions, and show that it gives results completely equivalent to the usual close-coupled cross sections. The virtue of the GMQDT is that it treats both open and closed channels on an equal footing, and all interchannel dynamics is summarized in a single real symmetric matrix Y(E) which is essentially constant across thresholds (and often over excursions of energy which exceed the hyperfine splittings). The multichannel threshold energy behavior can then be related to calculable properties of the individual channels that are being closed. Many of the smaller spin depolarization cross sections are determined by very long-range alpha(2)/R-3 spin-spin interactions which are not well treated by GMQDT, and we correct these specific elements with a perturbative distorted-wave approximation which yields the observed threshold dependences and brings the GMQDT into perfect agreement with the exact close-coupled results.

This paper presents quantitative calculations of collisional loss rates for pure Na-23 or Rb-87 atoms in a binary mixture of hyperfine states \F, M]. We find that the recent observation of a dual Bose condensate consisting of Rb-87 \1, -1] and \2, 2] atoms is unique and will not occur in Na. We attribute this to the unexpectedly small inelastic spin-exchange rate associated with Rb-87 s-wave hyperfine collisions. This fortuitous result arises from nearly equal (5.45 +/- 0.26 nm) scattering lengths for two colliding Rb-87 atoms in their \1, -1] or \2, 2] states.

Quantum interferences between symmetric and antisymmetric electronic states can induce unidirectional electron transfer during the photodissociation of symmetric species like H-2(+), yielding an asymmetric proton angular distribution. This interference effect has been used to predict a very efficient mechanism for separating spatially the H+ and D+ isotopes in the photofragmentation of the quasi-symmetric HD+ molecule.

The dynamics of the photodissociation of Na-2(+) by intense laser fields (I=5.10(11)-5.10(13) W/cm(2)) are dominated by 4 electronic states for wavelengths around 780 nm. Above threshold dissociation (ATD) with absorption of 1 and 2 excess photons before dissociation Is predicted. The pulse duration (25-250 fs) is shown to be an important control parameter for the branching ratio between the ATD channels and the total dissociation probability.

We present quantum scattering calculations for the collisional relaxation rate coefficient of spin-polarized 87Rb(f = 2,m = 2) atoms, which determines the loss rate of cold Rb atoms from a magnetic trap. Unlike the lighter alkali atoms, spin-polarized 87Rb atoms can undergo dipolar relaxation due to both the normal spin-spin dipole interaction and a second-order spin-orbit interaction with distant electronic states of the dimer. We present ab initio calculations for the second-order spin-orbit terms for both Rb2 and Cs2. The corrections lead to a reduction in the relaxation rate for 87Rb. Our primary concern is to analyze the sensitivity of the 87Rb trap loss to the uncertainties in the ground state molecular potentials. Since the scattering length for the a3Σ+u state is already known, the major uncertainties are associated with the X1Σ+g potential. After testing the effect of systematically modifying the short-range form of the molecular potentials over a reasonable range, and introducing our best estimate of the second-order spin-orbit interaction, we estimate that in the low temperature limit the rate coefficient for loss of Rb atoms from the f = 2,m = 2 state is between 0.4 × 10-15 cm3/s and 2.4 × 10-15 cm3/s (where this number counts two atoms lost per collision). In a pure condensate the rate coefficient would be reduced by 1/2.

A number of unexpected features of small molecules subjected to intense laser fields, with wavelengths ranging from infrared to ultraviolet, have been observed or predicted in the past few years: above-threshold dissociation, molecular bond softening, vibrational population trapping. We review these processes for the case of the molecular ion H2+ and discuss the experimental and theoretical tools that are used to study this system. Both electron and proton energy distributions are used to interpret the experimental results. Theoretically, the fragmentation dynamics can be described equivalently as a laser-assisted half-collision process, using solutions of the time-independent Floquet theory, or as the evolution of a wavepacket subjected to a classical radiation held with a given pulse shape, using solutions of the time-dependent Schrodinger equation. A broad range of laser intensity and pulsewidth has been explored, with the short-pulse results (analysed in terms of 'dressed' potential curves) offering the best interface between theory and experiment. We finally report on a promising new avenue for coherent control of fragmentation dynamics, through the use of two-colour phase-locked radiation.

Systematic behavior of decay rates of resonances above dissociation threshold is investigated by using the theory of resonance scattering. The condition for the Rice‐Ramsperger‐Kassel‐Marcus (RRKM) rate formula to be valid is clarified by analyzing the random model of unimolecular dissociation. The decay rate averaged over many resonances agrees with the RRKM rate when the mean spacing and the mean width of the resonance states coincide with each other. On the other hand, auto‐ and mutual‐correlation functions of the non‐stationary wave functions indicate a rather paradoxical and intriguing phenomenon: In the RRKM regime, insufficient time is left for intramolecular vibrational energy redistribution (IVR) before dissociation.

A random matrix model of unimolecular decomposition is investigated based on the Feshbach theory of resonant scattering. Energies of zero-th order quasi-bound states are randomly distributed, and coupling matrix elements between these quasi-bound states and continua are generated by Gaussian random numbers. The average decay rate of the quasi-bound states exhibits systematic behavior as a function of density of quasi-bound states, average magnitude of the coupling and number of continua. The average decay rate coincides with the one predicted by the statistical theory of unimolecular decomposition (RRKM theory) when the mean spacing of the quasi-bound states is comparable with the average resonance width. Under this condition, the spectrum of the quasi-bound states is most diffuse, and we can neither resolve each quasi-bound state nor even distinguish resonant collision from direct one clearly.