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Chinese Physics Letters

Photoassociation of Atomic BEC within Mean-Field Approximation: Exact Solutions

Wei Cai, Jing Hui, Mingsheng Zhan, Jingjun Xu

Published Apr 1, 2007• 3 citations
Publisher

Abstract

We propose an exactly solvable method to study the coherent two-colour photoassociation of an atomic Bose–Einstein condensate, by linearizing the bilinear atom–molecule coupling, which allows us to conveniently probe the quantum dynamics and statistics of the system. By preparing different initial states of the atomic condensate, we can observe very different quantum statistical properties of the system by exactly calculating the quadrature-squeezed and mode-correlated functions.

DOI
10.1088/0256-307x/24/4/006

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We propose an exactly solvable method to study the coherent two-colour photoassociation of an atomic Bose–Einstein condensate, by linearizing the bilinear atom–molecule coupling, which allows us to conveniently probe the quantum dynamics and statistics of the system. By preparing different initial states of the atomic condensate, we can observe very different quantum statistical properties of the system by exactly calculating the quadrature-squeezed and mode-correlated functions.
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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 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.
We show that the photoassociation of an atomic Bose-Einstein condensate to form condensed molecules is a chemical process which not only does not obey the Arrhenius rules for chemical reactions, but that it can also depend on the quantum statistics of the reactants. Comparing the predictions of a truncated Wigner representation for different initial quantum states, we find that, even when the quantum prediction for an initial coherent state is close to the Gross-Pitaevskii prediction, other quantum states may result in very different dynamics.
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.
We explore the quantum dynamics of photoassociation of Bose-Einstein condensed atoms into molecules using an optical cavity field. Inside of an optical resonator, photoassociation of quantum degenerate atoms involves the interaction of three coupled quantum fields for the atoms, molecules, and the photons. The feedback created by a high-QQQ optical cavity causes the cavity field to become a dynamical quantity whose behavior is linked in a nonlinear manner to the atoms inside and where vacuum fluctuations have a more important role than in free space. We develop and compare several methods for calculating the dynamics of the atom-molecule conversion process with a coherently driven cavity field. We first present an alternate operator representation for the Hamiltonian from which we derive an improved form of mean field theory and an approximate solution of the Heisenberg-Langevin (HL) equations that properly accounts for quantum noise in the cavity field. It is shown that our improved mean field theory corrects several deficiencies in traditional mean field theory based on expectation values of annihilation and creation operators. Also, we show by direct comparison to numerical solutions of the density matrix equations that our approximate quantum solution of HL equations gives an accurate description of weakly or undriven cavities where mean field theories break down.