Validity of the Fröhlich model for a mobile impurity in a Bose-Einstein condensate

Abstract

We analyze the many-body Hamiltonian describing a mobile impurity immersed in a Bose-Einstein condensate (BEC). Using exact unitary transformations and rigorous error estimates, we show the validity of the Bogoliubov-Fröhlich Hamiltonian for the Bose polaron in the regime of moderately strong, repulsive interactions with a dilute BEC. Moreover, we calculate analytically the universal logarithmic correction to the ground state energy that arises from an impurity mediated phonon-phonon interaction.

References in corpus (10)

• Bragg spectroscopy of a strongly interacting 85Rb Bose-Einstein condensate
• Variational study of polarons in Bose-Einstein condensates
• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• Universal aspects of a strongly interacting impurity in a dilute Bose condensate
• The condensation of a trapped dilute Bose gas with three-body interactions
• Quantum Fluctuations of Many-Body Dynamics around the Gross-Pitaevskii Equation
• Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
• Quantum Cherenkov transition of finite momentum Bose polarons
• General memory kernels and further corrections to the variational path integral approach for the Bogoliubov-Fröhlich Hamiltonian
• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime