Abstract:
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We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting
with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but
may be a nonlinear function of the position of the particle. Physically, this corresponds to a configuration in which
damping and diffusion are spatially inhomogeneous. We derive systematically the quantum master equation for
the Brownian particle in the Born-Markov approximation and we discuss the appearance of additional terms, for
various polynomials forms of the coupling. We discuss the cases of linear and quadratic coupling in great detail
and we derive, using Wigner function techniques, the stationary solutions of the master equation for a Brownian
particle in a harmonic trapping potential. We predict quite generally Gaussian stationary states, and we compute
the aspect ratio and the spread of the distributions. In particular, we find that these solutions may be squeezed
(superlocalized) with respect to the position of the Brownian particle. We analyze various restrictions to the
validity of our theory posed by non-Markovian effects and by the Heisenberg principle. We further study the
dynamical stability of the system, by applying a Gaussian approximation to the time-dependent Wigner function,
and we compute the decoherence rates of coherent quantum superpositions in position space. Finally, we propose
a possible experimental realization of the physics discussed here, by considering an impurity particle embedded
in a degenerate quantum gas. |