Abstract
We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integrodifferential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments.
Highlights
The concept of polaron has been introduced by Landau and Pekar to describe the behavior of an electron in a dielectric crystal [1]
We study the physics of the impurity as an open system in the framework of quantum Brownian motion (QBM) model
We presented a discussion concerning the physics of an impurity embedded in a homogeneous Bose-Einstein condensate (BEC), adopting an open quantum system point of view, in particular recalling the paradigmatic quantum Brownian motion model
Summary
We study the physics of the impurity as an open system in the framework of quantum Brownian motion (QBM) model. In [50] a Lindblad model for QBM has been studied, for both linear and nonlinear coupling This allows one to explore the low temperature regime, as well as to consider values of the coupling between the environment and the system stronger than those permitted by the BornMarkov treatment. The drawback to this remedy is that the resulting Lindblad equation cannot be derived directly from the microscopic Hamiltonian of the system. In the Appendices, we provide the details of the derivations, analysis of the feasibility of the approach and of the presented results in the parameter regimes
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