structure separations 25 : AE lf2 =E(/=l)-£(/=2) = 7.1SkMc/sec, A£ M =£(/=l)-£(/=0) = 5.20 kMc/sec, we can calculate all the first-order gF (1), s and the secondorder E (2) 's of the N=l rotational level from Eqs. (3.9) and (3.10). The numerical values of g^( 1) and gF(=gF (0) +g> (1) ) thus calculated are shown in Table I. The signs and the orders of magnitude of g> (1), s are in agreement with the preliminary experimental values of Lichten and Brooks. 3,9 However, the absolute values of the calculated g> (1) 's are about a factor of 2 too large in almost all cases, This indicates that the first-order g> (1) 's do account for the discrepancies between gF (0), s 25 The fine-structure separations used here are the preliminary experimental results of Lichten and Brooks. One can also obtain a set of theoretical energy separations from Ref. 6. They are AJEI, 2 = 6.54 kMc/sec, AE 0 ,i = 4.10 kMc/sec. In view of the simple wave function used in Ref. 6, we use the experimental values here to calculate the &F (1), S.
In recent experiments 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 pairs of atoms belonging to the condensate many-body wavefunction. A mechanism is offered here to account for the observed losses, based on the deactivation of the resonant molecular state by interaction with a third condensate atom.Comment: LaTeX, 4 pages, 4 PostScript figures, uses REVTeX and psfig, submitted to Physical Review A, Rapid Communication
The loss of ultracold trapped atoms in the vicinity of a Feshbach resonance is treated as a twostage 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 × 10 −11 cm 3 /s for the deactivation rate coefficient. 32.80.Pj, 03.75.Fi The phenomenon of Feshbach resonance has received recently an increased attention due to its application to Bose-Einstein condensation (BEC) (see Ref.[1] and references therein). Its most outstanding effect is a drastic change of the elastic scattering length as the collision energy of an atomic pair approaches the energy of a bound level belonging to another electronic or hyperfine state. The resonance can be tuned by applying an external magnetic field, as has been proposed in Ref. [2] in order to control the BEC properties. Applications include a controlled BEC collapse [3] and bright solitons in BEC [4,5], as well as a formation of molecular BEC [1,6,7,8,9], an atom-molecule coherent superposition [10,11], and an entangled atomic gas [9].Another effect of the resonance is the abrupt increase in atom loss due to inelastic collisions of the resonant molecules [1,6,8,12], and to the formation of noncondensed atoms [7,8,13]. The determination of the loss parameters is important for an appreciation of the outcome of applications of Feshbach resonances. We present here an estimate of the rate coefficient for the deactivation of vibrationally excited resonant 87 Rb 2 molecules by collisions with other Rb atoms, based on the results of recent experiments [14].The theory presented in Refs. [1,6,8,12], based on coupled Gross-Pitaevskii equations for atomic and molecular condensates, cannot be applied to the analysis of these experiments involving a non-condensed thermal gas. The approach used here is based on the Breit-Wigner theory of resonant multichannel collisions (see e.g. Ref.[15]), as has been proposed for the system under consideration by Ref. [7]. The reaction involving the excited resonant molecule Rb 2 (m) includes a reversible input channel of formation from (and dissociation to) a pair of colliding atoms,and irreversible output channels of exoergic collisions with a third atom,bringing the molecule down to one of the lower-lying rovibrational levels of the same spin state, or to levels belonging to other spin states. (An alternative approach, presented in Refs. [16,17], treats the whole process as a one-stage recombination by a three-body collision.) Let us consider all atoms, for the time being, as distinguishable particles. According to the standard theory (see Ref. [15]), the natural resonance width Γ e associated with channel (1) is two times smaller than the corresponding width for the case of indistinguishable atoms presented in Ref.[7] (see also Refs. [1,2]). It exhibits a Wigner threshold dependence of the formwhere a a is the non-res...
Formation of atomic pairs by the dissociation of a molecular condensate or by inelastic collisions in an atomic condensate due to a time-dependent curve crossing process is studied beyond the mean-field approximation. The number of atoms formed by the spontaneous process is described by a Landau-Zener formula multiplied by an exponential amplification factor due to quantum many-body effects. The atomic pairs are formed in an entangled (squeezed) state. The rate of stimulated processes depends on the relative phase of the two fields.Comment: LaTeX, 5 pages, uses REVTeX, submitted to Physical Review Letter
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