Autoresonant excitation of Bose-Einstein condensates

TL;DR

This paper investigates how Bose-Einstein condensates can be controlled using chirped frequency perturbations, analyzing the transition between quantum ladder climbing and classical autoresonance regimes through theoretical and simulation methods.

Contribution

It introduces a framework with dimensionless parameters to analyze autoresonance and ladder climbing in BECs, highlighting the effects of interactions and different driving protocols.

Findings

Identification of key parameters governing BEC excitation regimes

Analysis of transition thresholds between quantum and classical behaviors

Demonstration of effective control protocols for condensate excitation

Abstract

Controlling the state of a Bose-Einstein condensate driven by a chirped frequency perturbation in a one-dimensional anharmonic trapping potential is discussed. By identifying four characteristic time scales in this chirped-driven problem, three dimensionless parameters $P_{1,2,3}$ are defined describing the driving strength, the anharmonicity of the trapping potential, and the strength of the particles interaction, respectively. As the driving frequency passes the linear resonance in the problem, and depending on the location in the $P_{1,2,3}$ parameter space, the system may exhibit two very different evolutions, i.e. the quantum energy ladder climbing (LC) and the classical autoresonance (AR). These regimes are analysed both in theory and simulations with the emphasis on the effect of the interaction parameter $P_{3}$. In particular, the transition thresholds on the driving parameter $P_{1}$ and their width in $P_{1}$ in both the AR and LC regimes are discussed. Different driving protocols are also illustrated, showing efficient control of excitation and de-excitation of the condensate.