Quantum dynamical phase transition in a system with many-body interactions

Recent experiments, [G.A. Alvarez, E.P. Danieli, P.R. Levstein, H.M. Pastawski, J. Chem. Phys. 124 (2006) 194507], have reported the observation of a quantum dynamical phase transition in the dynamics of a spin swapping gate. In order to explain this result from a microscopic perspective, we introduce a Hamiltonian model of a two level system with many-body interactions with an environment whose excitation dynamics is fully solved within the Keldysh formalism. If a particle starts in one of the states of the isolated system, the return probability oscillates with the Rabi frequency omega(0). For weak interactions with the environment 1/tau(SE) < 2 omega(0), we find a slower oscillation whose amplitude decays with a rate 1/tau(phi)= 1/(2 tau(SE)). However, beyond a finite critical interaction with the environment, 1/tau(SE) > 2 omega(0), the decay rate becomes 1/tau(phi) proportional to omega(2)(0)tau(SE). The oscillation period diverges showing a quantum dynamical phase transition to a Quantum Zeno phase consistent with the experimental observations. (c) 2006 Published by Elsevier Ltd.