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We propose and investigate a scheme for engineering a synthetic thermal bathfor a bosonic quantum gas in a one-dimensional optical lattice based onMarkovian feedback control. The performance of our scheme is quantified by thefidelity between the steady state of the system and the effective thermalstate. For double-well and triple-well systems with non-interacting particles,the steady state is found to be an exact thermal state, which is attributed tothe fact that the transfer rates between all pairs of coupled eigenstatessatisfy detailed balance condition. The scenario changes when there are morelattice sites, where the detailed balance condition does not hold any more, butremains an accurate approximation. Remarkably, our scheme performs very well atlow and high temperature regimes, with the fidelity close to one. Theperformance at the intermediate temperature regime (where a crossover into aBose condensed regime occurs) is slightly worse, and the fidelity shows agentle decrease with increasing system size. We also discuss the interactingcases. In contrast to the non-interacting cases, the scheme is found to performbetter at a higher temperature. Another difference is that the minimaltemperature that can be engineered is nonzero and increases with theinteraction strength.

Quantum engineering of a synthetic thermal bath for bosonic atoms in a one-dimensional optical lattice via Markovian feedback control