![]() Demler, Radio-frequency spectroscopy of polarons in ultracold Bose gases, Phys. Kuhr, Quantum dynamics of a mobile spin impurity, Nature Physics 9, 235 (2013). Schmidt, Field-theoretical study of the Bose polaron, Phys. Widera, Dynamics of Single Neutral Impurity Atoms Immersed in an Ultracold Gas, Phys. Giamarchi, Quantum dynamics of impurities in a one-dimensional Bose gas, Phys. Köhl, Quantum Transport through a Tonks-Girardeau Gas, Phys. Timmermans, Strong-Coupling Polarons in Dilute Gas Bose-Einstein Condensates, Phys. Smith, Static properties of positive ions in atomic Bose-Einstein condensates, Phys. Lukin, Mesoscopic Molecular Ions in Bose-Einstein Condensates, Phys. Demler, Fermi polarons in two dimensions, Phys. Parish, Strongly interacting two-dimensional Fermi gases, (2014), arXiv:1408.2737. Http://.in/index.php/iisc/search/advancedResults Lobo, A single impurity in an ideal atomic Fermi gas: current understanding and some open problems, J. Bruun, Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases, Reports on Progress in Physics 77, 034401 (2014). ![]() Köhl, Attractive and repulsive Fermi polarons in two dimensions, Nature 485, 619 (2012). Grimm, Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture, Nature 485, 615 (2012). Zwierlein, Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms, Phys. Devreese, Advances in Polaron Physics, Springer Series in Solid-State Sciences (Springer, 2009). Fröhlich, Electrons in lattice fields, Advances In Physics 3(11):325 (1954). We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments. One important result of this paper is that we find position squeezing for the trapped impurity at long times. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. We find that back-flow in energy between the environment and the impurity occurs during evolution. ![]() When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We study the role of the memory on the dynamics of the impurity. interaction strength between the bosons, temperature, etc. 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. ![]() The Langevin equation is an integrodifferential equation that contains a memory kernel and is driven by a colored noise. We derive a generalized Langevin equation for the position of the impurity. 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.
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