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Physical Review A

Quantum atom-heteronuclear molecule dark state: Role of population imbalance

Hui Jing, Shuai Cui

Published Aug 11, 2010• 2 citations
Publisher

Abstract

Recently, the finite-number effect of initial atoms in coherent atom-molecule conversion was investigated by Zhao et al. [Phys. Rev. Lett. 101, 010401 (2008)]. Here, by extending to the atom-heteronuclear molecule dark state, we find that the initial populations imbalance of the atoms plays a significant role in quantum conversion rate and adiabatic fidelity. In particular, even for the finite total number of imbalanced two-species atoms, the mean-field conversion rate, contrary to the general belief, still can be remarkably close to the exact quantum results.

DOI
10.1103/physreva.82.025601

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Recently, the finite-number effect of initial atoms in coherent atom-molecule conversion was investigated by Zhao et al. [Phys. Rev. Lett. 101, 010401 (2008)]. Here, by extending to the atom-heteronuclear molecule dark state, we find that the initial populations imbalance of the atoms plays a significant role in quantum conversion rate and adiabatic fidelity. In particular, even for the finite total number of imbalanced two-species atoms, the mean-field conversion rate, contrary to the general belief, still can be remarkably close to the exact quantum results.
We study the conversion efficiency of heteronuclear Feshbach molecules in population imbalanced atomic gases formed by ramping the magnetic field adiabatically. We extend the recent work [J. E. Williams et al., New J. Phys. 8, 150 (2006)] on the theory of Feshbach molecule formations to various combinations of quantum statistics of each atomic component. A simple calculation for a harmonically trapped ideal gas is in good agreement with the recent experiment [S. B. Papp and C. E. Wieman, Phys. Rev. Lett. 97, 180404 (2006)] without any fitting parameters. We also give the conversion efficiency as an explicit function of initial peak phase space density of the majority species for population imbalanced gases. In the low-density region where Bose-Einstein condensation does not appear, the conversion efficiency is a monotonic function of the initial peak phase space density, but independent of statistics of a minority component. The quantum statistics of majority atoms has a significant effect on the conversion efficiency. In addition, Bose-Einstein condensation of an atomic component is the key element determining the maximum conversion efficiency.
Recently, Pu et al. developed an efficient strategy to find the adiabatic condition of a nonlinear system---i.e., the atom-homonuclear dimer conversion [Phys. Rev. Lett. 98, 050406 (2007)]. Here, by applying their method, we extend it to study the adiabatic condition of coherent atom--heteronuclear-diatomic- or -triatomic-molecule conversion. The different adiabatic evolutions in creating the homo- or heteronuclear dimers are compared. The impact of the two different reaction paths on the adiabatic conditions in creating the heteronuclear triatomic molecules is also discussed.
An ultracold three-species Bose–Fermi–Fermi degenerate atomic mixture 87 Rb– 40 K– 6 Li was realized very recently (Tagliber M et al 2008 Phys. Rev. Lett. 100 010401). Here, we study the creation of heteronuclear triatomic molecules in this mixture, and show that a constructive triple-path interference can lead to an almost ideal conversion rate, in comparison with the single- or double-path cases. The important effect of the initial population imbalance on the atom–molecule dark state is also investigated.