Topological Vortex Formation in BEC under Gravitational Field

TL;DR

This paper investigates how gravitational effects influence vortex formation in Bose-Einstein condensates of different atomic masses, revealing that heavier atoms like Rb cause vortex fragmentation unless field reversal timing is precisely tuned.

Contribution

It demonstrates that gravitational shifts in hyperfine states affect vortex stability in BECs, especially for heavier atoms, and shows the importance of tuning the field reversal time.

Findings

Heavier atomic mass leads to greater gravitational deviation of hyperfine states.

Vortex fragmentation occurs in Rb BECs without proper tuning of reversal time.

Numerical solutions of the Gross-Pitaevskii equation reveal complex interactions causing vortex instability.

Abstract

Topological phase imprinting is a unique technique for vortex formation in a Bose-Einstein condensate (BEC) of alkali metal gas, in that it does not involve rotation: BEC is trapped in a quadrupole field with a uniform bias field which is reversed adiabatically leading to vortex formation at the center of the magnetic trap. The scenario has been experimentally verified by MIT group employing $^{23}$Na atoms. Recently similar experiments have been conducted at Kyoto University, in which BEC of $^{87}$Rb atoms has been used. In the latter experiments they found that the fine-tuning of the field reverse time $T_{\rm rev}$ is required to achieve stable vortex formation. Otherwise, they often observed vortex fragmentations or a condensate without a vortex. It is shown in this paper that this behavior is attributed to the heavy mass of the Rb atom. The confining potential, which depends on the eigenvalue $m_B$ of the hyperfine spin $\bv{F}$ along the magnetic field, is now shifted by the gravitational field perpendicular to the vortex line. Then the positions of two weak-field-seeking states with $m_B=1$ and 2 deviate from each other. This effect is more prominent for BEC with a heavy atomic mass, for which the deviation is greater and, moreover, the Thomas-Fermi radius is smaller. We found, by solving the Gross-Pitaevskii equation numerically, that two condensates interact in a very complicated way leading to fragmentation of vortices, unless $T_{\rm rev}$ is properly tuned.