Effects of an exceptional point on the dynamics of a single particle in a time-dependent harmonic trap

Raam Uzdin, Emanuele G. Dalla Torre, Ronnie Kosloff, Nimrod Moiseyev

Research output: Contribution to journalArticlepeer-review

Abstract

The time evolution of a single particle in a harmonic trap with time-dependent frequency ω(t) has been well studied. Nevertheless, here we show that when the harmonic trap is opened (or closed) as a function of time while keeping the adiabatic parameter μ=[dω(t)/dt]/ω2(t) fixed, a sharp transition from an oscillatory to a monotonic exponential dynamics occurs at μ=2. At this transition point, the time evolution has an 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. In the present case, we show that the order of the EP depends on the set of observables used to describe the dynamics. 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.

Original languageAmerican English
Article number022505
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume88
Issue number2
DOIs
StatePublished - 12 Aug 2013

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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