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 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 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 KosterlitzThouless critical phase at finite temperature, with the role of the "finite temperature" played by the interactions.
There is growing interest to investigate states of matter with topological order, which support excitations in the form of anyons, and which underly topological quantum computing. Examples of such systems include lattice spin models in two dimensions. Here we show that relevant Hamiltonians can be systematically engineered with polar molecules stored in optical lattices, where the spin is represented by a single electron outside a closed shell of a heteronuclear molecule in its rotational ground state. Combining microwave excitation with the dipole-dipole interactions and spin-rotation couplings allows us to build a complete toolbox for effective twospin interactions with designable range and spatial anisotropy, and with coupling strengths significantly larger than relevant decoherence rates. As an illustration we discuss two models: a 2D square lattice with an energy gap providing for protected quantum memory, and another on stacked triangular lattices leading to topological quantum computing.
We investigate the possibility of using a dissipative process to prepare a quantum system in a desired state. We derive for any multipartite pure state a dissipative process for which this state is the unique stationary state and solve the corresponding master equation analytically. For certain states, like the Cluster states, we use this process to show that the jump operators can be chosen quasi-locally, i.e. they act non-trivially only on a few, neighboring qubits. Furthermore, the relaxation time of this dissipative process is independent of the number of subsystems. We demonstrate the general formalism by considering arbitrary MPS-PEPS states. In particular, we show that the ground state of the AKLT-model can be prepared employing a quasi-local dissipative process.
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