Knowns and Unknowns of the Interacting Bose Gas

Sang-Hoon Kim

The condensate fraction of a homogeneous and dilute Bose gas is expanded as a power series of $\sqrt{n a^3}$ as $N_0/N = 1 -c_1 (n a^3)^{1/2} -c_2 (n a^3) - c_3 (n a^3)^{3/2}\hdots.$ The coefficient $c_1$ is well-known as $8/3 \sqrtπ$, but the others are unknown yet. Considering two-body contact interactions and applying a canonical transformation method twice we developed the method to obtain the higher order coefficients analytically. An iteration method is applied to make up a cutoff in a fluctuation term. The coefficients ares $c_2=2(π- 8/3)$ and $c_3=(4/\sqrtπ) (π-8/3)(10/3-π)$.

Jakob Yngvason

Aranya B. Bhattacherjee, Subhadeep De

We propose to use superradiant Rayleigh scattering from degenerate Bose gas to detect unknown frequencies coupled to the pump laser beam. Theoretically we show a measurement of the time evolution of population at the initial momentum state could determine the unknown frequency with respect to a known one at which the pump laser's frequency modulates. We show a range of frequencies from kHz to MHz could be determined with this method at the currently available state-of-the-art technology.

Hui Zhai

Aranya B. Bhattacherjee, Subhadeep De

We propose a new way of detecting frequencies using superradiant Rayleigh scattering from degenerate Bose gases. A measurement of the time evolution of population at the initial momentum state could determine an unknown frequency with respect to a known one at which the pump laser's frequency modulates. A range of frequencies from kHz to MHz could be determined with a fractional uncertainty of 10^{-6}.