An open quantum system, whose time evolution is governed by a master
equation, can be driven into a given pure quantum state by an appropriate
design of the system-reservoir coupling. This points out a route towards
preparing many body states and non-equilibrium quantum phases by quantum
reservoir engineering. Here we discuss in detail the example of a \emph{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 via
the atomic current representing \emph{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 3D can be understood
as a depletion of the condensate, and in 1D and 2D exhibits properties
reminiscent of a Luttinger liquid or a Kosterlitz-Thouless critical phase at
finite temperature, with the role of the ``finite temperature'' played by the
interactions.

通过系统 - 沉积物耦合的适当设计，可以将开放的量子系统驱动到给定的纯量子状态，这为通过量子沉积物工程制备多体状态和非平衡量子相提供了一条路。我们在这里详细讨论了玻色子和成对费米子的驱动耗散 Bose Einstein 凝聚的例子，其中光学晶格中的原子通过代表局部耗散的原子电流与 Bogoliubov 激发的浴相耦合。