Order parameter for the dynamical phase transition in Bose-Einstein condensates with topological modes

TL;DR

This paper investigates a dynamic phase transition in Bose-Einstein condensates with topological modes, characterized by an order parameter that distinguishes between mode locking and non-locking regimes, with analysis supported by numerical simulations.

Contribution

It introduces an effective order parameter for the dynamical phase transition in BECs with topological modes and analyzes its behavior under realistic experimental conditions.

Findings

Identification of two distinct dynamical regimes in BECs.

The order parameter effectively characterizes the phase transition.

Numerical results align with experimental parameters.

Abstract

In a trapped Bose-Einstein condensate, subject to the action of an alternating external field, coherent topological modes can be resonantly excited. Depending on the amplitude of the external field and detuning parameter, there are two principally different regimes of motion, with mode locking and without it. The change of the dynamic regime corresponds to a dynamic phase transition. This transition can be characterized by an effective order parameter defined as the difference between fractional mode populations averaged over the temporal period of oscillations. The behavior of this order parameter, as a function of detuning, pumping amplitude, and atomic interactions is carefully analyzed. A special attention is payed to numerical calculations for the realistic case of a quadrupole exciting field and the system parameters accessible in current experiments.