Abstract
We demonstrate that stationary localized solutions (discrete solitons) exist in a one dimensional Bose-Hubbard lattices with gain and loss in the semiclassical regime. Stationary solutions, by defi- nition, are robust and do not demand for state preparation. Losses, unavoidable in experiments, are not a drawback, but a necessary ingredient for these modes to exist. The semiclassical calculations are complemented with their classical limit and dynamics based on a Gutzwiller Ansatz. We argue that circuit QED architectures are ideal platforms for realizing the physics developed here. Finally, within the input-output formalism, we explain how to experimentally access the different phases, including the solitons, of the chain.
Highlights
Realizations of quantum nonlinear media as ultracold atoms in optical lattices [1], ion traps [2] or superconducting circuits [3,4] are interesting candidates for future quantum information processors
We demonstrate that stationary localized solutions exist in one-dimensional Bose-Hubbard lattices with gain and loss in a semiclassical regime
We argue that circuit quantum electrodynamic architectures are ideal platforms for realizing the physics developed here
Summary
Realizations of quantum nonlinear media as ultracold atoms in optical lattices [1], ion traps [2] or superconducting circuits [3,4] are interesting candidates for future quantum information processors. In the so-called classical limit of the Bose-Hubbard model, the operators are replaced by their c-number average, obtaining the well-known discrete nonlinear Schrodinger equation (DNLS) [6] In this limit, discrete solitons, both theoretically and experimentally, exist in different dimensions and topologies [7,8,9,10]. We first argue that for the dissipative driven Bose-Hubbard model quantum solitons have no anticontinuous limit, i.e, the uncoupled lattice system has a unique stationary solution [26,27,28]. This is important, since the single-site DD-DNLS for the same parameter regime can have different fixed points in their irreversible dynamics. The set needs to be cut at some order
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