Proper treatment of the zero mode in quantum field theory for trapped Bose-Einstein condensation

M. Okumura*, Y. Yamanaka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


So far much theoretical consideration of experiments on the Bose-Einstein condensation (BEC) of alkali-metal atoms in harmonic traps is based on the Gross-Pitaevskii (GP) equation. In this paper, we attempt to formulate the BEC in the language of quantum field theory and to estimate the quantum and thermal fluctuation effects, which are neglected in the approximation using the GP equation. First, the formulation at zero temperature is developed, and then it is extended to the finite-temperature case by means of thermofield dynamics. We treat the zero-energy mode with care, so that the canonical commutation relations hold. As a result, an infrared divergence appears, but it can be renormalized into the observed condensate number. Numerical calculations are performed. For illustration, the corrections at one-loop level to the original GP equation are given. We also calculate numerically the effects of quantum and thermal fluctuations on the distribution of condensed atoms.

Original languageEnglish
Pages (from-to)12
Number of pages1
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number1
Publication statusPublished - 2003

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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