The correspondence between exotic quantum holonomy that occurs in families of Hermitian cycles, and exceptional points (EPs) for non-Hermitian quantum theory is examined in quantum kicked tops. Under a suitable condition, an explicit expressions of the adiabatic parameter dependencies of quasienergies and stationary states, which exhibit anholonomies, are obtained. It is also shown that the quantum kicked tops with the complexified adiabatic parameter have a higher order EP, which is broken into lower order EPs with the application of small perturbations. The stability of exotic holonomy against such bifurcation is demonstrated.

http://arxiv.org/abs/1402.1634
Quantum Physics (quant-ph)

We have investigated the topological properties associated with degeneracies of a non-Hermitian Hamiltonian, called as exceptional points (EPs), in the case that three modes are interacting with each other. Even though the parametric evolution of the modes cannot be uniquely determined when encircling more than two EPs once, we can recover the initial configuration of the modes by encircling two EPs three times or three EPs twice. The group theoretical consideration provides some hint on it. We confirm our expectation by numerically calculating the modes of an open quantum system, two dielectric microdisks.

http://arxiv.org/abs/1109.4216
Quantum Physics (quant-ph)