An open quantum system, the time evolution of which is governed by a master equation, can be driven into a given pure quantum state by an appropriate design of the coupling between the system and the reservoir. This provides a route towards preparing many-body states and non-equilibrium quantum phases by quantum-reservoir engineering. Here, we discuss the example of a driven dissipative Bose–Einstein condensate of bosons and of paired fermions, where atoms in an optical lattice are coupled to a bath of Bogoliubov excitations and the atomic current represents local dissipation. In the absence of interactions, the lattice gas is driven into a pure state with long-range order. Weak interactions lead to a weakly mixed state, which in three dimensions can be understood as a depletion of the condensate, and in one and two dimensions exhibits properties reminiscent of a Luttinger liquid or a Kosterlitz–Thouless critical phase at finite temperature, with the role of the ‘finite temperature’ taken by the interactions.
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We thank E. Altman, E. Demler and M. Lukin for discussions. Work at the University of Innsbruck is supported by the Austrian Science Foundation and EU grants SCALA and OLAQI.
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Diehl, S., Micheli, A., Kantian, A. et al. Quantum states and phases in driven open quantum systems with cold atoms. Nature Phys 4, 878–883 (2008). https://doi.org/10.1038/nphys1073
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