Resonance Superfluidity: Renormalization of Resonance Scattering Theory

We derive a theory of superfluidity for a dilute Fermi gas that is valid when scattering resonances are present. The treatment of a resonance in many-body atomic physics requires a novel mean-field approach starting from an unconventional microscopic Hamiltonian. The mean-field equations incorporate the microscopic scattering physics, and the solutions to these equations reproduce the energy-dependent scattering properties. This theory describes the high-$T_c$ behavior of the system, and predicts a value of $T_c$ which is a significant fraction of the Fermi temperature. It is shown that this novel mean-field approach does not break down for typical experimental circumstances, even at detunings close to resonance. As an example of the application of our theory we investigate the feasibility for achieving superfluidity in an ultracold gas of fermionic $^6$Li.Comment: 15 pages, 10 figure

Tree-body loss of of trapped ultracold 87^{87}Rb atoms due to a Feshbach resonance

The loss of ultracold trapped atoms in the vicinity of a Feshbach resonance is treated as a two-stage reaction, using the Breit-Wigner theory. The first stage is the formation of a resonant diatomic molecule, and the second one is its deactivation by inelastic collisions with other atoms. This model is applied to the analysis of recent experiments on $^{87}$Rb, leading to an estimated value of $7\times 10^{-11}$ cm$^{3}/$s for the deactivation rate coefficient.Comment: LaTeX, 4 pages with 1 figures, uses REVTeX4, uses improved experimental dat

Measurement of the Zero Crossing in a Feshbach Resonance of Fermionic 6-Li

We measure a zero crossing in the scattering length of a mixture of the two lowest hyperfine states of 6-Li. To locate the zero crossing, we monitor the decrease in temperature and atom number arising from evaporation in a CO2 laser trap as a function of magnetic field B. The temperature decrease and atom loss are minimized for B=528(4) G, consistent with no evaporation. We also present preliminary calculations using potentials that have been constrained by the measured zero crossing and locate a broad Feshbach resonance at approximately 860 G, in agreement with previous theoretical predictions. In addition, our theoretical model predicts a second and much narrower Feshbach resonance near 550 G.Comment: Five pages, four figure

Atom loss and the formation of a molecular Bose-Einstein condensate by Feshbach resonance

In experiments conducted recently at MIT on Na Bose-Einstein condensates [S. Inouye et al, Nature 392, 151 (1998); J. Stenger et al, Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of a pair of atoms in the condensate. A collisional deactivation mechanism affecting a temporarily formed molecular condensate [see V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne and C. J. Williams, Phys. Rev. A 60, R765 (1999)], studied here in more detail, accounts for the results of the slow-sweep experiments. A best fit to the MIT data yields a rate coefficient for deactivating atom-molecule collisions of 1.6e-10 cm**3/s. In the case of the fast sweep experiment, a study is carried out of the combined effect of two competing mechanisms, the three-atom (atom-molecule) or four-atom (molecule-molecule) collisional deactivation vs. a process of two-atom trap-state excitation by curve crossing [F. H. Mies, P. S. Julienne, and E. Tiesinga, Phys. Rev. A 61, 022721 (2000)]. It is shown that both mechanisms contribute to the loss comparably and nonadditively.Comment: LaTeX, 14 pages, 12 PostScript figures, uses REVTeX and psfig, submitted to Physical Review

Very high precision bound state spectroscopy near a 85^{85}Rb Feshbach resonance

We precisely measured the binding energy of a molecular state near the Feshbach resonance in a $^{85}$Rb Bose-Einstein condensate (BEC). Rapid magnetic field pulses induced coherent atom-molecule oscillations in the BEC. We measured the oscillation frequency as a function of B-field and fit the data to a coupled-channels model. Our analysis constrained the Feshbach resonance position [155.041(18) G], width [10.71(2) G], and background scattering length [-443(3) a$_0$] and yielded new values for $v_{DS}$, $v_{DT}$, and $C_6$. These results improved our estimate for the stability condition of an attractive BEC. We also found evidence for a mean-field shift to the binding energy.Comment: 5 pages, 2 figures, submitted to PR

Quantum effects on the dynamics of a two-mode atom-molecule Bose-Einstein condensate

We study the system of coupled atomic and molecular condensates within the two-mode model and beyond mean-field theory (MFT). Large amplitude atom-molecule coherent oscillations are shown to be damped by the rapid growth of fluctuations near the dynamically unstable molecular mode. This result contradicts earlier predictions about the recovery of atom-molecule oscillations in the two-mode limit. The frequency of the damped oscillation is also shown to scale as $\sqrt{N}/\log N$ with the total number of atoms $N$, rather than the expected pure $\sqrt{N}$ scaling. Using a linearized model, we obtain analytical expressions for the initial depletion of the molecular condensate in the vicinity of the instability, and show that the important effect neglected by mean field theory is an initially non-exponential `spontaneous' dissociation into the atomic vacuum. Starting with a small population in the atomic mode, the initial dissociation rate is sensitive to the exact atomic amplitudes, with the fastest (super-exponential) rate observed for the entangled state, formed by spontaneous dissociation.Comment: LaTeX, 5 pages, 3 PostScript figures, uses REVTeX and epsfig, submitted to Physical Review A, Rapid Communication

Quantum Computing with Atomic Josephson Junction Arrays

We present a quantum computing scheme with atomic Josephson junction arrays. The system consists of a small number of atoms with three internal states and trapped in a far-off resonant optical lattice. Raman lasers provide the "Josephson" tunneling, and the collision interaction between atoms represent the "capacitive" couplings between the modes. The qubit states are collective states of the atoms with opposite persistent currents. This system is closely analogous to the superconducting flux qubit. Single qubit quantum logic gates are performed by modulating the Raman couplings, while two-qubit gates result from a tunnel coupling between neighboring wells. Readout is achieved by tuning the Raman coupling adiabatically between the Josephson regime to the Rabi regime, followed by a detection of atoms in internal electronic states. Decoherence mechanisms are studied in detail promising a high ratio between the decoherence time and the gate operation time.Comment: 7 figure

Quantum correlated twin atomic beams via photo-dissociation of a molecular Bose-Einstein condensate

We study the process of photo-dissociation of a molecular Bose-Einstein condensate as a potential source of strongly correlated twin atomic beams. We show that the two beams can possess nearly perfect quantum squeezing in their relative numbers.Comment: Corrected LaTeX file layou

Pseudopotential model of ultracold atomic collisions in quasi-one- and two-dimensional traps

We describe a model for s-wave collisions between ground state atoms in optical lattices, considering especially the limits of quasi-one and two dimensional axisymmetric harmonic confinement. When the atomic interactions are modelled by an s-wave Fermi-pseudopotential, the relative motion energy eigenvalues can easily be obtained. The results show that except for a bound state, the trap eigenvalues are consistent with one- and two- dimensional scattering with renormalized scattering amplitudes. For absolute scattering lengths large compared with the tightest trap width, our model predicts a novel bound state of low energy and nearly-isotropic wavefunction extending on the order of the tightest trap width.Comment: 9 pages, 8 figures; submitted to Phys. Rev.