Abstract
We study entanglement and squeezing of two uncoupled impurities immersed in a Bose-Einstein condensate. We treat them as two quantum Brownian particles interacting with a bath composed of the Bogoliubov modes of the condensate. The Langevin-like quantum stochastic equations derived exhibit memory effects. We study two scenarios: (i) In the absence of an external potential, we observe sudden death of entanglement; (ii) In the presence of an external harmonic potential, entanglement survives even at the asymptotic time limit. Our study considers experimentally tunable parameters.
Highlights
The Bose polaron problem was recently studied within the quantum Brownian motion (QBM) model [43, 48], which describes the dynamics of a quantum particle interacting with a bath made up of a huge number of harmonic oscillators obeying the Bose-Einstein statistics [6,49,50,51]
From here on we treat only the one dimensional case, i.e. we assume that the Bose-Einstein condensate (BEC) and the impurities are so tightly trapped in two directions as to effectively freeze the dynamics in those directions
We studied the emergent entanglement between two distinguishable polarons due to their common coupling to a BEC bath
Summary
Entanglement represents a necessary resource for a number of protocols in quantum information and for other quantum technologies, which are expected to be implemented in the foreseeable future for various practical applications [1,2,3,4,5]. The Bose polaron problem was recently studied within the quantum Brownian motion (QBM) model [43, 48], which describes the dynamics of a quantum particle interacting with a bath made up of a huge number of harmonic oscillators obeying the Bose-Einstein statistics [6,49,50,51] In this analogy, the impurity plays the role of the Brownian particle and the Bogoliubov excitations of the BEC are the bath-oscillators. This set of two coupled equations are non-local in time, namely the dynamics of both impurities in a BEC carry certain amount of memory In this context, such a feature is often related to the super-Ohmic character of the spectral density, constituting the main quantity that embodies the properties of the bath. D we study, for the trapped case, the effective equilibrium Hamiltonian of the system reached at long-times
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