Collapse-revival of entanglement in a non-commutative harmonic oscillator revealed via coherent states and path integral

Abstract

Abstract We develop an approach using coherent states and path integral to investigate the dynamics of entanglement in a simple two-dimensional non-commutative harmonic oscillator. We start by employing a Bopp shift to convert the Hamiltonian describing the system into a commutative equivalent one. This allows us to construct coherent states and calculate the propagator in standard way. By deriving the explicit expression of the time-dependent coherent states and considering its connection with the number states, we provide exact results for evaluating the degree of entanglement between the ground state and any excited state through the purity function. The interesting emerging result is that, as long as the non-commutativity parameter is non-zero, our system exhibits the phenomenon of collapse and revival of entanglement.