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Physical Review A

Quantum states of Bose-Einstein condensates formed by molecular dissociation

Uffe V. Poulsen, Klaus Mølmer

Published Jan 8, 2001• 59 citations
Publisher

Abstract

We analyze the atomic state obtained by photodissociation of a molecular condensate. The process is not amenable to the usual mean-field description, and we base our analysis on approximate equations for the second moments of the atomic field operators and on Monte Carlo simulations derived from a positive-P phase-space description of the system. Our calculations show that the dissociation process produces an atomic condensate in a squeezed state in analogy with the down-conversion process leading to squeezed light in quantum optics. Atomic interactions lead to a threshold similar to the one in optical down-conversion, and to an atomic ``Kerr'' effect, which ultimately deteriorates the degree of squeezing.

DOI
10.1103/physreva.63.023604

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We analyze the atomic state obtained by photodissociation of a molecular condensate. The process is not amenable to the usual mean-field description, and we base our analysis on approximate equations for the second moments of the atomic field operators and on Monte Carlo simulations derived from a positive-P phase-space description of the system. Our calculations show that the dissociation process produces an atomic condensate in a squeezed state in analogy with the down-conversion process leading to squeezed light in quantum optics. Atomic interactions lead to a threshold similar to the one in optical down-conversion, and to an atomic ``Kerr'' effect, which ultimately deteriorates the degree of squeezing.
The dissociation of a molecular Bose-Einstein condensate into its constituent particles is a process analogous to parametric down-conversion in optics. However, there is additional interest in the fact that the particles are massive, and may obey either bosonic or fermionic statistics. We describe a pairing mean-field theory related to the Hartree-Fock-Bogoliubov approach, and apply it to analyse the correlations present in recent experiments. We also perform calculations using stochastic phase-space methods for the bosonic case and compare the results of the two methods.
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.
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.
In quantum optics, the most interesting processes occur due to nonlinear interactions between the electromagnetic field and various media. The parametric processes which produce nonclassical states of the electromagnetic field have analogs in the processes of photoassociation and dissociation of atomic and molecular Bose-Einstein condensates. Just as the optical processes need a full quantum theoretical treatment in some regimes, we show that photoassociation and dissociation require full quantum treatments to be confident of the theoretical predictions we can make. If the processes take place inside an optical cavity, we show that we may also need to consider the quantum nature of the intracavity electromagnetic field. As the process of intracavity photoassociation that we analyze has no exact mapping onto a Fokker-Planck equation, we show how quantum-field-theoretical techniques can be used to write stochastic difference equations in a generalized positive-P representation, which may be solved numerically.
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. Correlated atomic pairs are formed in squeezed states. The rate of stimulated processes depends on the relative phase of the two fields.