Phase operator and condensed systems

Yusuke Nakamura, J. Takahashi, Y. Yamanaka

The unperturbed Hamiltonian for the Bose-Einstein condensate, which includes not only the first and second powers of the zero mode operators but also the higher ones, is proposed to determine a unique and stationary vacuum at zero temperature. From the standpoint of quantum field theory, it is done in a consistent manner that the canonical commutation relation of the field operator is kept. In this formulation, the condensate phase does not diffuse and is robust against the quantum fluctuation of the zero mode. The standard deviation for the phase operator depends on the condensed atom number with the exponent of $\ensuremath{-}1/3$, which is universal for both homogeneous and inhomogeneous systems.

Yee Kin Tsui

Xubing Tang, Fan Hong‐Yi

For studying the interference between two Bose–Einstein condensates we introduce the atomic coherent state (ACS) in the Schwinger bosonic realization along with the phase operator to directly calculate the interference pattern with steady relative phase cos ϕ. Eigenstates of the density operator of condensates are classified as ACS is also demonstrated. The entangled state representation is used in some calculations.

Nandor L. Balazs, Hans–Christian Pauli

Hadrien Kurkjian, Yvan Castin, Alice Sinatra

Due to atomic interactions and dispersion in the total atom number, the order parameter of a pair-condensed Fermi gas experiences a collapse in a time that we derive microscopically. As in the bosonic case, this blurring time depends on the derivative of the gas chemical potential with respect to the atom number and on the variance of that atom number. The result is obtained first using linearized time-dependent Bogoliubov--de Gennes equations, then in the random-phase approximation, and then it is generalized to beyond the mean field. In this framework, we construct and compare two phase operators for the paired fermionic field: The first one, issuing from our study of the dynamics, is the infinitesimal generator of adiabatic translations in the total number of pairs. The second one is the phase operator of the amplitude of the field of pairs on the condensate mode. We explain that these two operators differ due to the dependence of the condensate wave function on the atom number.

E. C. Lerner