Formulation for zero mode of Bose-Einstein condensate beyond Bogoliubov approximation

Abstract

It is shown for the Bose-Einstein condensate of cold atomic system that the new unperturbed Hamiltonian, which includes not only the first and second powers of the zero mode operators but also the higher ones, determines 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 $-1/3$, which is universal for both homogeneous and inhomogeneous systems.

5 pages, 2 figures

References in corpus (2)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum Field Theoretical Description of Unstable Behavior of Trapped Bose-Einstein Condensates with Complex Eigenvalues of Bogoliubov-de Gennes Equations

Cited by in corpus (15)

• Quantum hydrodynamics of the spinor Bose-Einstein condensate at non-zero temperatures
• Bose polaron in spherical trap potentials: Spatial structure and quantum depletion
• Bose-Einstein condensation of alpha clusters and new soft mode in 12C--52Fe 4N nuclei in field theoretical superfluid cluster model
• Effective field theory of Bose-Einstein condensation of $\alpha$ clusters and Nambu-Goldstone-Higgs states in ${}^{12}$C
• Bose polaron in spherically symmetric trap potentials: Ground states with zero and lower angular momenta
• Shape of a sound wave in a weakly-perturbed Bose gas
• Interacting multiple zero mode formulation and its application to a system consisting of a dark soliton in a condensate
• Thermal and quantum fluctuations of confined Bose-Einstein condensate beyond the Bogoliubov approximation
• Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature
• Self-Energy Renormalization for Inhomogeneous Nonequilibrium Systems and Field Expansion via Complete Set of Time-Dependent Wave Functions
• Bose-Einstein condensation of five $\alpha$ clusters in ${}^{20}$Ne and supersolidity
• Nonequilibrium Thermo Field Dynamics Using 4x4-Matrix Transformation for System with Bose--Einstein Condensation
• Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature. II. The general case
• Six-$\alpha$ cluster Bose-Einstein condensation and supersolid ${}^{12}$C($0_2^{+})$+${}^{12}$C($0_2^{+})$ molecular structure in ${}^{24}$Mg
• Hydrodynamic model of skyrmions and vorticities in the spin-1 Bose-Einstein condensate in ferromagnetic phase at finite temperatures