Controlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances

TL;DR

This paper proposes a method to control the group velocity of a small Bose-Einstein Condensate during collision with another BEC using Feshbach resonances, enabling potential experimental observation of slowed condensate motion.

Contribution

It introduces a theoretical framework for manipulating BEC collision dynamics via Feshbach resonances, extending analogies to light slowing in dispersive media.

Findings

Derived an expression for group velocity in BEC collisions.

Estimated the maximum shift in BEC position due to Feshbach resonance effects.

Identified experimental conditions for observing the effect.

Abstract

We report on a proposal to change the group velocity of a small Bose Einstein Condensate (BEC) upon collision with another BEC in analogy to slowing of light passing through dispersive media. We make use of ultracold collisions near a magnetic Feshbach resonance, which gives rise to a sharp variation in scattering length with collision energy and thereby changes the group velocity. A generalized Gross-Pitaveskii equation is derived for a small BEC moving through a larger stationary BEC. We denote the two condensates by laser and medium BEC, respectively, to highlight the analogy to a laser pulse travelling through a medium. We derive an expression for the group velocity in a homogeneous medium as well as for the difference in distance, $\delta$, covered by the laser BEC in the presence and absence of a finite-sized medium BEC with a Thomas-Fermi density distribution. For a medium and laser of the same isotopic species, the shift $\delta$ has an upper bound of twice the Thomas-Fermi radius of the medium. For typical narrow Feshbach resonances and a medium with number density $10^{15}$ cm$^{-3}$ up to 85% of the upper bound can be achieved, making the effect experimentally observable. We also derive constraints on the experimental realization of our proposal.