Soluble Model of Interacting Bosons Trapped in Harmonic Potential: Quality of Bogoliubov Approximation
M.A. Załuska-Kotur, M. Gajda and J. Mostowski
Instytut Fizyki, Polish Academy of Sciences and College of Science, Al. Lotników 32/46, 02-668 Warszawa, Poland
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Received: July 26, 2001
We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for a detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactly soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives a quite accurate description of the system in the limit of weak interactions.
DOI: 10.12693/APhysPolA.100.485
PACS numbers: 03.75.Fi, 05.30.Fk