Understanding dynamical phase transitions in a spinor Bose–Einstein condensate via quantum and semiclassical analyses

Abstract

Phase transitions in nonequilibrium dynamics of many body quantum systems, 
known as dynamical phase transitions (DPTs), play an important role for understanding
various dynamical phenomena observed in different branches of physics.
In general, there are two types of DPTs, the first one is characterized by 
distinct evolutionary behaviors of a physical observable, while the second one is marked by 
the vanishing overlap between the time-evolved and initial states. 
Here, we focus on exploring such DPTs from both quantum and semiclassical perspectives 
in a spinor Bose-Einstein condensate (BEC), an ideal platform for
investigating nonequilibrium dynamics.
Utilizing the sudden quench process, we demonstrate that the system exhibits 
both types of DPTs as the control parameter is quenched through
the critical value, referring to as the critical quenching. 
We show analytically how to determine the critical quenching via
the semiclassical approach and carry out a detailed examination of both semiclassical 
and quantum signatures of DPTs. 
In particular, we reveal that the occurrence of DPTs is triggered by
the separatrix in the underlying semiclassical system.
Our findings offer deeper insights into the properties of DPTs and verify the usefulness 
of semiclassical analysis for studying DPTs in quantum systems 
with well-defined semiclassical limit.