Dephasing and breakdown of adiabaticity in the splitting of Bose Einstein Condensates

TL;DR

This paper investigates the quantum dynamics of Bose-Einstein Condensates in a double-well potential, identifying the timescales for adiabaticity breakdown and dephasing during the splitting process.

Contribution

It analytically derives the characteristic timescales for adiabaticity breakdown and dephasing, revealing complex dependencies on system parameters and providing insights into condensate splitting dynamics.

Findings

Adiabatic following occurs initially during barrier rise.

Breakdown of adiabaticity at a critical time $t_{ad}$.

Dephasing time $t_D$ depends non-trivially on $t_{ad}$ and ramping time.

Abstract

We study the quantum dynamics of a BEC condensate trapped in a double-well potential with a rising interwell barrier. We analytically find the characteristic time scales of the splitting process and compare our results with numerical analyses available in the literature. In first stage of the dynamics, the condensate follows adiabatically the rising of the interwell barrier. At a critical time $t_{ad}$, small amplitude fluctuations around the average trajectory increase exponentially fast, signaling the break-down of adiabaticity. We have found a highly non-trivial dependence of the dephasing time $t_D$, defined by $\sigma_{\phi}(t_D)=1$, where $\sigma_{\phi}(t)$ is the dynamical quantum phase spreading, on $t_{ad}$ and on the ramping time of the interwell barrier.