Feynman path-integral treatment of the BEC-impurity polaron

The description of an impurity atom in a Bose-Einstein condensate can be cast in the form of Froehlich's polaron Hamiltonian, where the Bogoliubov excitations play the role of the phonons. An expression for the corresponding polaronic coupling strength is derived, relating the coupling strength...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2009-11, Vol.80 (18), Article 184504
Main Authors: Tempere, J., Casteels, W., Oberthaler, M. K., Knoop, S., Timmermans, E., Devreese, J. T.
Format: Article
Language:English
Subjects:
ATOMIC AND MOLECULAR PHYSICS
ATOMS
BOGOLYUBOV METHOD
BOSE-EINSTEIN CONDENSATION
COUPLING
EFFECTIVE MASS
EXCITATION
FEYNMAN PATH INTEGRAL
FREE ENERGY
GASES
HAMILTONIANS
IMPURITIES
LITHIUM
PHONONS
POLARONS
SCATTERING LENGTHS
SODIUM
SOLIDS
STRONG-COUPLING MODEL
TRAPPING
TRAPS
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Summary:The description of an impurity atom in a Bose-Einstein condensate can be cast in the form of Froehlich's polaron Hamiltonian, where the Bogoliubov excitations play the role of the phonons. An expression for the corresponding polaronic coupling strength is derived, relating the coupling strength to the scattering lengths, the trap size and the number of Bose condensed atoms. This allows to identify several approaches to reach the strong-coupling limit for the quantum gas polarons, whereas this limit was hitherto experimentally inaccessible in solids. We apply Feynman's path-integral method to calculate for all coupling strengths the polaronic shift in the free energy and the increase in the effective mass. The effect of temperature on these quantities is included in the description. We find similarities to the acoustic polaron results and indications of a transition between free polarons and self-trapped polarons. The prospects, based on the current theory, of investigating the polaron physics with ultracold gases are discussed for lithium atoms in a sodium condensate.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.80.184504