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Physical Review A

Stability of an atom-molecule Bose-Einstein condensate against collapse

Marijan Koštrun, Juha Javanainen

Published Feb 27, 2002• 1 citation
Publisher

Abstract

We investigate the coupled atom-molecule Bose-Einstein condensate, as would ensue in an attempt to control the scattering length by means of either the Feshbach resonance or coherent photoassociation. In a mean-field model with a photoassociative coupling between the condensates, we demonstrate that the system is structurally stable. The sign of the effective scattering length notwithstanding, neither condensate will collapse.

DOI
10.1103/physreva.65.031602

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We investigate the coupled atom-molecule Bose-Einstein condensate, as would ensue in an attempt to control the scattering length by means of either the Feshbach resonance or coherent photoassociation. In a mean-field model with a photoassociative coupling between the condensates, we demonstrate that the system is structurally stable. The sign of the effective scattering length notwithstanding, neither condensate will collapse.
A study of coherent photoassociation is presented for the case of an atomic Bose-Einstein condensate. It is shown that the phenomenon is analogous to coherent optical transient in a few-level system, with a difference that the participating levels have Bose enhanced populations. A second-quantized Hamiltonian in momentum and position representation is developed to describe photoassociation. A classical version of the field theory for atoms and molecules is used to demonstrate that in the presence of photoassociating light, a joint atom-molecule condensate is unstable against the growth of the density fluctuations. ^ A simple mean-field model of atom-molecule Bose-Einstein condensate is constructed and it is shown that in the model there is no collapse, irrespective of the sign of the effective atom-atom scattering length. The properties of the two most important eigenstates, the ground state and the twin state, are determined for different values of the system parameters δ and K, the detuning and the atom-molecule coupling, respectively. It is shown that in a coupled atom-molecule system a collapse is replaced by a dynamical instability. The lines in the parameter space where these instabilities occur are in fact fractures where the underlying eigenstates discontinuously change. The features of instability are in good qualitative agreement with the experimental observations of collapse. ^
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 discuss the response of a Bose-Einstein condensate to a change in the scattering length, which is experimentally realized by tuning the magnetic field near a Feshbach resonance. In particular, we consider the collapse of the condensate induced by a sudden change in the scattering length from a large positive to a small negative value. We also consider the condensate dynamics that results from a single pulse in the magnetic field, due to which the scattering length is rapidly increased from zero to a large value and then after some time rapidly decreased again to its initial value. We focus primarily on the consequences of the quantum evaporation process on the dynamics of the Bose-Einstein condensate, but also discuss the effects of atom-molecule coherence.
We demonstrate control of the collapse and expansion of an (88)Sr Bose-Einstein condensate using an optical Feshbach resonance near the (1)S(0)-(3)P(1) intercombination transition at 689 nm. Significant changes in dynamics are caused by modifications of scattering length by up to ± 10a(bg), where the background scattering length of (88)Sr is a(bg) = -2a(0) (1a(0) = 0.053 nm). Changes in scattering length are monitored through changes in the size of the condensate after a time-of-flight measurement. Because the background scattering length is close to zero, blue detuning of the optical Feshbach resonance laser with respect to a photoassociative resonance leads to increased interaction energy and a faster condensate expansion, whereas red detuning triggers a collapse of the condensate. The results are modeled with the time-dependent nonlinear Gross-Pitaevskii equation.