AffiliationUniv Arizona, Dept Math, Program Appl Math
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CitationQuantum 1, 30 (2017).
Rights© The Authors (2017). This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.
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AbstractWe 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 integro-differential 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 he observed in realistic experiments.
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VersionFinal published version
SponsorsPrograma Masters d'Excel-lencia of the Fundacio Catalunya-La Pedrera; ERC Advanced Grant OSYRIS; EU IP SIQS; EU PRO QUIC; EU STREP EQuaM ; Fundacio Cellex; Spanish MINECO [SEV-2015-0522, FIS2013-46768, FIS2016-79508-P]; Generalitat de Catalunya [SGR 874]