**Coupling of quantum fluctuations in a two-component condensate**

We model frozen light stored 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 individually for each atomic-field
component, coupling between the neglected fluctuations of the two
components could lead to a breakdown of the mean-field approximation
even if it is a good approximation for each species individually. We solve
and test the effect of coupled quantum fluctuations on coherent nonlinear
evolution of the frozen light pulse to see whether this two-species
condensate could enable nonlinear quantum optical phenomena.
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.
The transformation diagonalizing the second-quantized approximate
Hamiltonian is described by coupled differential equations that are solved
with a power series expansion. We compare the consequent dynamics
with the mean-field evolution given by the two-component GrossPitaevskii equation.