Non-Markovian dynamics of double-well Bose-Einstein condensate-reservoir system

In this thesis, we report our study on the dynamics of a symmetric double-well Bose-Einstein condensate (BEC)-reservoir system. The mentioned system is well described by total Hamiltonian composed of a sub-Hamiltonians representing the double-well BEC, multi-mode reservoir fields and the interactions of condensate atoms with the reservoir fields. The dynamical equation obtained is in the form of generalized Quantum-Heisenberg-Langevin equation (QHLE). Dissipation kernels of the QHLE determines whether the system operates within Markovian or non- Markovian basis. We found full analytical solution for the interaction free BECreservoirs for the Markovian operating system but only partial analytical solution is given for its non-Markovian counterpart. The interacting BEC-reservoirs system (Markovian and non-Markovian) invokes mean-field and noise-correlated models. The set of ordinary differential equations (ODE) of the latter models (mMF, MF, Mark, nonMark) were solved using Matlab ODE-45 solver, an effective tool for solving non-stiff ODEs. Physical quantities such as population imbalance, tunneling current, coherence and entanglement-entropy were computed numerically and analysed. The system operate on the Markovian and non-Markovian basis show distinctive features with respect to applied control parameters. As an overall conclusion, the finding shows the dynamics is more volatile in the Markovian operation in comparison to the non-Markovian operational basis for the mean-field approach especially on its driving from macroscopic quantum self trapping to the quantum tunneling state. For the noise-correlated approach on the other hand, the non-classical behaviour described by its entanglement-entropy is more prominent in the Markovian operational basis in comparison with its non-Markovian counterpart.

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