Collective atomic recoil motion in short-pulse multi-matter-optical wave mixing

An analytical perturbation theory of short-pulse, matter-wave superradiant scatterings is presented. We show that Bragg resonant enhancement is incapacitated and both positive and negative order scatterings contribute equally. We further show that propagation gain is small and scattering events primarily occur at the end of the condensate where the generated field has maximum strength, thereby explaining the apparent ``asymmetry" in the scattered components with respect to the condensate center. In addition, the generated field travels near the speed of light in a vacuum, resulting in significant spontaneous emission when the one-photon detuning is not sufficiently large. Finally, we show that when the excitation rate increases, the generated-field front-edge-steepening and peak forward-shifting effects are due to depletion of the ground state matter wave.Comment: This manuscript was submitted for publication in Nov., 200

Two point correlations of a trapped interacting Bose gas at finite temperature

We develop a computationally tractable method for calculating correlation functions of the finite temperature trapped Bose gas that includes the effects of s-wave interactions. Our approach uses a classical field method to model the low energy modes and treats the high energy modes using a Hartree-Fock description. We present results of first and second order correlation functions, in position and momentum space, for an experimentally realistic system in the temperature range of $0.6T_c$ to $1.0T_c$. We also characterize the spatial coherence length of the system. Our theory should be applicable in the critical region where experiments are now able to measure first and second order correlations.Comment: 9 pages, 4 figure

Interference between independent fluctuating condensates

We consider a problem of interference between two independent condensates, which lack true long range order. We show that their interference pattern contains information about correlation functions within each condensate. As an example we analyze the interference between a pair of one dimensional interacting Bose liquids. We find universal scaling of the average fringe contrast with system size and temperature that depends only on the Luttinger parameter. Moreover the full distribution of the fringe contrast, which is also equivalent to the full counting statistics of the interfering atoms, changes with interaction strength and lends information on high order correlation functions. We also demonstrate that the interference between two-dimensional condensates at finite temperature can be used as a direct probe of the Kosterlitz-Thouless transition. Finally, we discuss generalization of our results to describe the intereference of a periodic array of independent fluctuating condensates.Comment: 7 pages, 3 figures, published versio

Imaging the phase of an evolving Bose-Einstein condensate wavefunction

We demonstrate a spatially resolved autocorrelation measurement with a Bose-Einstein condensate (BEC) and measure the evolution of the spatial profile of its quantum mechanical phase. Upon release of the BEC from the magnetic trap, its phase develops a form that we measure to be quadratic in the spatial coordinate. Our experiments also reveal the effects of the repulsive interaction between two overlapping BEC wavepackets and we measure the small momentum they impart to each other