Interacting multiple zero mode formulation and its application to a system consisting of a dark soliton in a condensate

Abstract

To formulate the zero modes in a finite-size system with spontaneous breakdown of symmetries in quantum field theory is not trivial, for in the naive Bogoliubov theory, one encounters difficulties such as phase diffusion, the absence of a definite criterion for determining the ground state, and infrared divergences. A new interacting zero mode formulation that has been proposed for systems with a single zero mode to avoid these difficulties is extended to general systems with multiple zero modes. It naturally and definitely gives the interactions among the quantized zero modes, the consequences of which can be observed experimentally. In this paper, as a typical example, we consider an atomic Bose-Einstein condensed system with a dark soliton that contains two zero modes corresponding to spontaneous breakdown of the U(1) gauge and translational symmetries. Then we evaluate the standard deviations of the zero mode operators and see how the mutual interaction between the two zero modes affects them.

Quantum Squeezing of Slow-Light Dark Solitons via Electromagnetically Induced Transparency

“…Differently, in our work the eigenmodes are acquired by solving the eigenvalue prob-lem of the perturbation, and the zero modes are determined by the requirement of the completeness and orthonormality of the all eigenmodes. The results presented in our work provides a clear way to avoid puzzles and confusions on zero mode problem in previous studies [40,56,[61][62][63][64][65] of perturbation and quantum effects of dark solitons.…”

Bose polaron in spherical trap potentials: Spatial structure and quantum depletion

“…For another direction of research, we will further develop the present method to look into zero-mode physics [101][102][103], few-body physics, self-localization, and so on.…”