Based on the mean-field approximation and the phase space analysis, we study the dynamics of an atom-molecule conversion system subject to particle loss. Starting from the many-body dynamics described by a master equation, an effective nonlinear Schrödinger equation is introduced. The classical phase space is then specified and classified by fixed points. The boundary, which separate different dynamical regimes have been calculated and discussed. The effect of particle loss on the conversion efficiency and the self-trapping is explored.
We analyze the dynamics of Bose-Einstein condensates in a one-dimensional driven optical lattice in the presence of distance-selective dissipation. The interplay of on-site interactions, tunneling, external driving and dissipation dominates the feature of the dynamics. Relative atomic density on each site in the lattice and the standard deviation of the relative density are calculated. The effect of the distance-selective dissipation and an external driving on the diffusion of the atoms is analyzed. As a simple example, a BEC in a double-well potential, is analyzed in detail, and the steady state is analytically derived.
Based on the mean-field approximation and the phase space analysis, we discuss the dynamics of Bose-Einstein condensates in a double-well potential. By applying a periodic modulation to the coupling between the condensates, we find the condensates can be trapped in the time-dependent eigenstates of the effective Hamiltonian, we refer to this effect as time-dependent self-trapping of BECs. A comparison of this self-trapping with the adiabatic evolution is made, finding that the adiabatic evolution beyond the traditional(linear) adiabatic condition can be achieved in BECs by manipulating the nonlinearity and the ratio of the level bias to the coupling constant. The fixed points for the system are calculated and discussed.
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