5 research outputs found
Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
Motivated by recent experiments on trapped ultra-cold bosonic atoms in an
optical lattice potential, we consider the non-equilibrium dynamic properties
of such bosonic systems for a number of experimentally relevant situations.
When the number of bosons per lattice site is large, there is a wide parameter
regime where the effective boson interactions are strong, but the ground state
remains a superfluid (and not a Mott insulator): we describe the conditions
under which the dynamics in this regime can be described by a discrete
Gross-Pitaevskii equation. We describe the evolution of the phase coherence
after the system is initially prepared in a Mott insulating state, and then
allowed to evolve after a sudden change in parameters places it in a regime
with a superfluid ground state. We also consider initial conditions with a "pi
phase" imprint on a superfluid ground state (i.e. the initial phases of
neighboring wells differ by pi), and discuss the subsequent appearance of
density wave order and "Schrodinger cat" states.Comment: 16 pages, 11 figures; (v2) added reference
Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation
We develop a consistent perturbation theory in quantum fluctuations around
the classical evolution of a system of interacting bosons. The zero order
approximation gives the classical Gross-Pitaevskii equations. In the next order
we recover the truncated Wigner approximation, where the evolution is still
classical but the initial conditions are distributed according to the Wigner
transform of the initial density matrix. Further corrections can be
characterized as quantum scattering events, which appear in the form of a
nonlinear response of the observable to an infinitesimal displacement of the
field along its classical evolution. At the end of the paper we give a few
numerical examples to test the formalism.Comment: published versio