A third-order exceptional point effect on the dynamics of a single particle in a time-dependent harmonic trap

TL;DR

This paper reveals a third-order exceptional point in the dynamics of a single particle in a time-dependent harmonic trap, marking a sharp transition in behavior at a specific adiabatic parameter value, with implications for ultracold atom experiments.

Contribution

It demonstrates the existence of a third-order exceptional point in a time-dependent Hermitian system, a novel finding in the context of harmonic traps with fixed adiabatic parameters.

Findings

Transition from oscillatory to exponential dynamics at mu=2

Existence of a third-order EP at all times during the transition

Relevance to ultracold atom and ion trap experiments

Abstract

The time evolution of a single particle in a harmonic trap with time dependent frequency omega(t) is well studied. Nevertheless here we show that, when the harmonic trap is opened (or closed) as function of time while keeping the adiabatic parameter mu = [d omega(t)/dt]/omega(t)^2 fixed, a sharp transition from an oscillatory to a monotonic exponential dynamics occurs at mu = 2. At this transition point the time evolution has a third-order exceptional point (EP) at all instants. This situation, where an EP of a time-dependent Hermitian Hamiltonian is obtained at any given time, is very different from other known cases. Our finding is relevant to the dynamics of a single ion in a magnetic, optical, or rf trap, and of diluted gases of ultracold atoms in optical traps.