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

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

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.

http://arxiv.org/abs/1212.3077
Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas)

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