Generation of coherence in an exactly solvable nonlinear nanomechanical system

Abstract

This study is focused on the quantum dynamics of a nitrogen-vacancy (NV) center coupled to a nonlinear, periodically driven mechanical oscillator. For a continuous periodic driving that depends on the position of the oscillator, the mechanical motion is described by Mathieu elliptic functions. This solution is employed to study the dynamics of the quantum spin system including environmental effects and to evaluate the purity and the von Neumann entropy of the NV spin. The unitary generation of coherence is addressed. We observe that the production of coherence through a unitary transformation depends on whether the system is prepared initially in the mixed state. Production of coherence is efficient when the system initially is prepared in the region of the separatrix (i.e., the region where classical systems exhibit dynamical chaos). From the theory of dynamical chaos, we know that phase trajectories of the system passing through the homoclinic tangle have limited memory, and therefore the information about the initial conditions is lost. We proved that quantum chaos and diminishing of information about the mixed initial state favors the generation of quantum coherence through the unitary evolution. We introduced quantum distance from the homoclinic tangle and proved that for the initial states permitting efficient generation of coherence, this distance is minimal.