Coupling of quantum fluctuations in a two-component condensate

Abstract

We model frozen light stored as a spin wave via electromagnetically induced transparency quantum-memory techniques in a Bose-Einstein condensate. The joint evolution of the condensate and the frozen light is typically modeled using coupled Gross-Pitaevskii equations for the two atomic fields, but these equations are only valid in the mean-field limit. Even when the mean-field limit holds for the host condensate, coupling between the host and the spin wave component could lead to a breakdown of the mean-field approximation if the host fluctuations are large compared the mean-field value of the spin wave. We develop a theoretical framework for modeling the corrections to the mean-field theory of a two-component condensate. Our analysis commences with a full second-quantized Hamiltonian for a two-component condensate. The field operators are broken up into a mean-field and a quantum fluctuation component. The quantum fluctuations are truncated to lowest non-vanishing order. We find the transformation diagonalizing the second-quantized approximate Hamiltonian and show that it can be described using the solutions to a system of coupled differential equations.