| Recent theoretical developments have demonstrated that dissipative processes in cold atom systems, such as loss of particles, instead of acting as a source of decoherence, could actually stabilize novel quantum phases of matter such as dimer superfluids in Bose gases and atomic color superfluids in Fermions. More generally, the possibility of engineering a quantum state by an appropriate design of the couplings between a system and its environnement could lead to interesting perspectives. Here, we propose a new scheme to simulate efficiently the time evolution of an open quantum system which follows a Quantum Markov Process, which is usually well adapted for cold atom systems. We use a representation of the reduced density matrix of the system in terms of a Matrix Product State (MPS) and modelize the time evolution with Matrix Product Operators (MPO). We present some results obtained on the Bose-Hubbard model with different loss processes, and compare these with other approaches. |
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