Quantum Brownian motion with inhomogeneous damping and diffusion

Pietro Massignan, Aniello Lampo, Jan Wehr, and Maciej Lewenstein
Phys. Rev. A 91, 033627 – Published 23 March 2015

Abstract

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.

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  • Received 10 November 2014

DOI:https://doi.org/10.1103/PhysRevA.91.033627

©2015 American Physical Society

Authors & Affiliations

Pietro Massignan1, Aniello Lampo1, Jan Wehr2, and Maciej Lewenstein1,3,*

  • 1ICFO–Institut de Ciències Fotòniques, Av. C.F. Gauss, 3, E-08860 Castelldefels, Spain
  • 2Department of Mathematics, University of Arizona, Tucson, Arizona 85721-0089, USA
  • 3ICREA–Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, E-08010 Barcelona, Spain

  • *maciej.lewenstein@icfo.es

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Vol. 91, Iss. 3 — March 2015

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