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Quantum correlation in the photoassociation of a heteronuclear molecular Bose-Einstein Condensate

Zhou Lü, Weiping Zhang, Hong Yuan Ling, Han Pu

Published Oct 31, 2006• 2 citations
OpenAlex

Abstract

We study a atomic-molecular model for interspecies photoassociation. A general Hamiltonian which takes into account the s-wave scattering interactions are considered. By approximating the quantum Hamiltonian by a classical Hamiltonian, the fixed points of the system are found. The stability analysis is performed and we found that the population imbalance between the two atomic species will play an important role in the modulational instability of the system. It is found that effecient photoassociation could be achieved in wider experimental parameter region with population imbalance. The dynamics of the system is predicted with mean-field theory as well as with quantum solution. The difference between them are found and analyzed. In addition, we give a brief discussion on the role of the quantum statistical properties of the initial atomic condensate state on the dynamics of the system. The time evolution of the correlation between atoms of different species are calculated with different initial states and we found that the two species can be kept anti-correlated under appropriate conditions. We also numerically show that quantum statistical properties of the matter wave field changes due to the nonlinear interaction.

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We study a atomic-molecular model for interspecies photoassociation. A general Hamiltonian which takes into account the s-wave scattering interactions are considered. By approximating the quantum Hamiltonian by a classical Hamiltonian, the fixed points of the system are found. The stability analysis is performed and we found that the population imbalance between the two atomic species will play an important role in the modulational instability of the system. It is found that effecient photoassociation could be achieved in wider experimental parameter region with population imbalance. The dynamics of the system is predicted with mean-field theory as well as with quantum solution. The difference between them are found and analyzed. In addition, we give a brief discussion on the role of the quantum statistical properties of the initial atomic condensate state on the dynamics of the system. The time evolution of the correlation between atoms of different species are calculated with different initial states and we found that the two species can be kept anti-correlated under appropriate conditions. We also numerically show that quantum statistical properties of the matter wave field changes due to the nonlinear interaction.
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. ^
We use numerical integration of coupled differential equations in a truncated Wigner representation to show that the initial quantum state of an atomic Bose-Einstein condensate plays an important role in the process of Raman photoassociation to form a molecular condensate. Comparing the predictions for different initial quantum states, we find that, even when the stochastic prediction for an initial coherent state is close to the Gross-Pitaevskii prediction, other possible states may result in very different dynamics. The mean-field dynamics can be appreciably different, depending on the initial conditions.
A dynamical many-body theory of single color photoassociation in a Bose-Einstein condensate is presented. The theory describes the time evolution of a condensed atomic ensemble under the influence of an arbitrarily varying near-resonant laser pulse, which strongly modifies the binary scattering properties. In particular, when considering situations with rapid variations and high light intensities the approach described in this article leads, in a consistent way, beyond standard mean-field techniques. This allows one to address the question of limits to the photoassociation rate due to many-body effects which has caused extensive discussions in the recent past. Both the possible loss rate of condensate atoms and the amount of stable ground-state molecules achievable within a certain time are found to be stronger limited than according to mean-field theory. By systematically treating the dynamics of the connected Green's function for pair correlations the resonantly driven population of the excited molecular state as well as scattering into the continuum of noncondensed atomic states are taken into account. A detailed analysis of the low-energy stationary scattering properties of two atoms modified by the near resonant photoassociation laser, in particular of the dressed state spectrum of the relative motion prepares for the analysis of the many-body dynamics. The consequences of the finite lifetime of the resonantly coupled bound state are discussed in the two-body as well as in the many-body context. Extending the two body description to scattering in a tight trap reveals the modifications to the near resonant adiabatic dressed levels caused by the decay of the excited molecular state.
We investigate an integrable Hamiltonian modeling a heterotriatomic molecular Bose-Einstein condensate. This model describes a mixture of two species of atoms in different proportions, which can combine to form a triatomic molecule. Beginning with a classical analysis, we determine the fixed points of the system. Bifurcations of these points separate the parameter space into different regions. Three distinct scenarios are found, varying with the atomic population imbalance. This result suggests the ground-state properties of the quantum model exhibit a sensitivity on the atomic population imbalance, which is confirmed by a quantum analysis using different approaches, such as the ground-state expectation values, the behavior of the quantum dynamics, the energy gap, and the ground-state fidelity.
We study the coherent association of a two-species atomic condensate into a condensate of heteronuclear diatomic molecules, using both a semiclassical treatment and a quantum mechanical approach. The differences and connections between the two approaches are examined. We show that, in this coupled nonlinear atom-molecule system, the population difference between the two atomic species plays a significant role in the ground-state stability properties as well as in coherent population oscillation dynamics.