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arXiv:1103.0063 · Physical Review A

Atom-molecule conversion with particle losses

B. Cui, L. C. Wang, X. X. Yi

Published Jan 12, 2012• 16 citations
arXivHTMLPDF

Abstract

Based on the mean-field approximation and the phase-space analysis, we study the dynamics of atom-molecule conversion systems subject to particle losses. Starting from the many-body dynamics described by a master equation, an effective nonlinear Schr\"odinger equation is introduced. The classical phase space is then specified and classified by fixed points. The boundaries, which separate different dynamical regimes, have been established and discussed. The effect of particle loss on the conversion efficiency and the self-trapping is explored. By numerically solving the master equation, we show that the mean-field approximation is a good approach to study the dynamics of this atom-molecule conversion system.

DOI
10.1103/physreva.85.013618

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Based on the mean-field approximation and the phase-space analysis, we study the dynamics of atom-molecule conversion systems subject to particle losses. Starting from the many-body dynamics described by a master equation, an effective nonlinear Schr"odinger equation is introduced. The classical phase space is then specified and classified by fixed points. The boundaries, which separate different dynamical regimes, have been established and discussed. The effect of particle loss on the conversion efficiency and the self-trapping is explored. By numerically solving the master equation, we show that the mean-field approximation is a good approach to study the dynamics of this atom-molecule conversion system.
Abstract Based on the mean-field approximation and the two-mode Bose–Hubbard model, we investigate the dynamical properties of atom-polyatomic molecule conversion systems under dissipation and dephasing. For such a many-body system problem, we partition phase space based on the states of fixed points, study the movement of fixed points and the transition to attractors in an open system. Additionally, for all the atoms that constitute a molecule, depending on whether the species of these atoms are identical or not, we introduce the innovative concepts of unbiased and biased systems. We discover that in biased conversion systems under particle losses, the evolution trajectories are distributed on a three-dimensional Bloch sphere with an internal structure. There exists a significant difference from the two-dimensional Hilbert space of an unbiased system. Finally, we discuss the sweeping rate of the time-varying magnetic field applied externally to the conversion system, and analyze a feasible scheme for the quantum coherent synthesis of triatomic molecules.
The dynamics of an atom-molecule-conversion system subject to dephasing noises is studied in this paper. Using a dephasing master equation and mean-field theory, we derive a Bloch equation for the system, and this equation is compared with the Bloch equation derived by the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy truncation approach. Fixed points of the system are calculated by solving both the Bloch equation and the master equation. Comparison between these two calculations suggests that while at short times the mean-field theory (MFT) is a good approximation for the atom-molecule-conversion system, a high-order hierarchy truncation approach is necessary for the system on a long time scale. Although the MFT cannot predict the fixed points correctly, its predictions for the stability of the fixed points are consistent with the BBGKY theory for a wide range of parameters.
We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherence (or particle loss). Starting from the full many-body dynamics described by the master equation, an effective Gross-Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.
A set of nonlinear evolution equations describing the dynamics of atoms, molecules, and photons in the course of stimulated atomic-molecular conversion in a Bose-Einstein condensate is derived and studied in the mean-field approximation. It is shown that conversion can be periodic or aperiodic in time, the rate of the process being determined, to a considerable extent, by the initial density of particles and by the initial phase difference. Depending on initial conditions, various conversion modes can be realized. The possibility of stabilization of a special state (of rest) of the system for nonzero initial number densities of particles is predicted. It is pointed out that coherence of a Bose condensate of atoms, molecules, and photons predetermines the possibility of phase control of the conversion process.
We propose a theoretical framework based on an affine-eigenstate transformation for analyzing ultracold atom-molecule conversion dynamics with particle loss. The transformation maps the mean-field dynamics to an effective two-mode representation in which fixed points, Bloch-sphere trajectories, and linear stability can be examined in a common set of variables. We give the derivation of the transformed Hamiltonian and specify the invertibility and conjugate-condition requirements under which the mapping is used. Within this representation, we distinguish ordinary, pseudo, and strict self-trapping regimes. The strict regime is associated with the balanced condition S=0 in the transformed variables; in the corresponding linearized dissipative flow, the leading attractor/repeller bifurcation term controlled by SΓ- vanishes, explaining the observed robustness against atom- and molecule-loss imbalance. We also introduce von Neumann and linear-entropy diagnostics for future mixed-state or ensemble descriptions in the transformed two-level representation, and we provide an inverse reconstruction procedure for preparing initial states that realize strict self-trapping. Finally, we discuss the limits of the mean-field and Markovian approximations and outline how finite-particle simulations and phase-modulated control protocols could connect this mechanism to decoherence-resilient quantum simulations and information-processing architectures.
A set of nonlinear evolution equations describing the dynamics of atoms, molecules, and photons in the course of stimulated atomic-molecular conversion in a Bose-Einstein condensate is derived and studied in the mean-field approximation. It is shown that conversion can be periodic or aperiodic in time, the rate of the process being determined to a considerable extent by the initial density of particles and by the initial phase difference. Depending on the initial conditions, various conversion modes can be realized. The possibility of stabilization of a special state (of rest) of the system for nonzero initial number densities of particles is predicted. It is pointed out that coherence of a Bose condensate of atoms, molecules, and photons predetermines the possibility of phase control of the conversion process.