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arXiv:cond-mat/0611054

Formation of molecules and entangled atomic pairs from atomic BEC due to Feshbach resonance

Vladimir Yurovsky

Published Nov 2, 2006• 2 citations
arXivHTMLPDF

Abstract

Bose-Einstein condensate (BEC) is considered under conditions of Feshbach resonance in two-atom collisions due to a coupling of atomic pair and resonant molecular states. The association of condensate atoms can form a molecular BEC, and the molecules can dissociate to pairs of entangled atoms in two-mode squeezed states. Both entanglement and squeezing can be applied to quantum measurements and information processing. The processes in the atom-molecule quantum gas are analyzed using two theoretical approaches. The mean-field one takes into account deactivating collisions of resonant molecules with other atoms and molecules, neglecting quantum fluctuations. This method allows analysis of inhomogeneous systems, such as expanding BEC. The non-mean-field approach -- the parametric approximation -- takes into account both deactivation and quantum fluctuations. This method allows determination of optimal conditions for formation of molecular BEC and describes Bose-enhanced dissociation of molecular BEC, as well as entanglement and squeezing of the non-condensate atoms.

DOI
10.48550/arxiv.cond-mat/0611054

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arXiv:cond-mat/0006017•Physical Review A•Sep 13, 2000•54 citations
Bose-Einstein condensate (BEC) is considered under conditions of Feshbach resonance in two-atom collisions due to a coupling of atomic pair and resonant molecular states. The association of condensate atoms can form a molecular BEC, and the molecules can dissociate to pairs of entangled atoms in two-mode squeezed states. Both entanglement and squeezing can be applied to quantum measurements and information processing. The processes in the atom-molecule quantum gas are analyzed using two theoretical approaches. The mean-field one takes into account deactivating collisions of resonant molecules with other atoms and molecules, neglecting quantum fluctuations. This method allows analysis of inhomogeneous systems, such as expanding BEC. The non-mean-field approach -- the parametric approximation -- takes into account both deactivation and quantum fluctuations. This method allows determination of optimal conditions for formation of molecular BEC and describes Bose-enhanced dissociation of molecular BEC, as well as entanglement and squeezing of the non-condensate atoms.
Association in an atomic Bose-Einstein condensate, and dissociation of the resulting molecular condensate, due to a Feshbach resonance in a time-dependent magnetic field, are analyzed incorporating non-mean-field quantum corrections and inelastic collisions. Calculations for the Na atomic condensate demonstrate that there exist optimal conditions under which about 80% of the atomic population can be converted to a relatively long-lived molecular condensate (with lifetimes of 100 ms and more). Entangled atoms in two-mode squeezed states (with noise reduction of about 30 dB) may also be formed by molecular dissociation.
A theoretical analysis of expanding hybrid atom-molecule Bose-Einstein condensates is presented with application to the recent experiments of the Rempe group on 87Rb^{87}\mathrm{Rb}87Rb, in which the formation of ultracold molecules by Feshbach resonance was demonstrated. A mean-field approach is used to describe the molecular association process. The subsequent dissociation of the molecules is treated using a non-mean-field parametric approximation. The latter method is also used to derive optimal conditions for the formation of a molecular condensate.
Association in an atomic Bose‐Einstein condensate, and the subsequent dissociation of the resulting molecular condensate, due to Feshbach resonance in a time‐dependent magnetic field, are analyzed, incorporating non‐mean‐field quantum corrections and inelastic collisions. Calculations for the Na atomic condensate demonstrate that there exist optimal conditions under which about 80% of the atomic population can be converted to a relatively long‐lived molecular condensate (with lifetimes of 10 ms and longer), if the magnetic field is temporally changed one way. Entangled atoms in two‐mode squeezed states (with noise reduction of about 30 dB) are formed by molecular dissociation when the field is changed the other way.
Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bose gas is studied at finite temperatures in a single-channel mean-field approach where the Hartree-Fock energy and pairing gap are determined self-consistently. In the molecular-BEC state, the atomic excitation is gapped and the molecular excitation is gapless. The binding energy of Feshbach molecules is shifted from the vacuum value by many-body effects. When the scattering length as{a}_{s}as​ of the atoms is negative, the system is subject to mechanical collapse due to negative compressibility. The system is stable in most regions with positive scattering lengths. However, at low temperatures near the resonance, the molecular-BEC state vanishes, and the coherent mixture of atomic and molecular BEC is subject to mechanical collapse.
We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-PPP representation method. This allows us to provide an exact treatment of the molecular field depletion and sss-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process---which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion---is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.
In experiments conducted recently at MIT on Na Bose-Einstein condensates [S. Inouye et al., Nature (London) 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 $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{s}.$ 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 versus 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.