Coherence crossover dynamics in the strong coupling regime

The transient dynamics of quantum coherence of Gaussian states is investigated. The state is coupled to an external environment which can be described by a Fano–Anderson type Hamiltonian. Solving the quantum Langevin equation, we obtain the Greens functions which are used to compute the time evolved first and second moments of the quadrature operators. From the quadrature operator moments, we construct the covariance matrix which is used to measure the coherence in the system. The coherence is estimated using the relative entropy of coherence measure. We consider three different environment spectral densities in our analysis viz, the Ohmic, the sub-Ohmic, and the super-Ohmic densities. In our work, we study the dynamics of the coherent state, squeezed state, and displaced squeezed state. For all these states we observe that when the coupling with the system and the environment is weak, the coherence monotonically decreases and eventually vanishes in the long time limit. Thus all the states exhibit Markovian evolution in the weak coupling limit. In the strong coupling limit, the dynamics for the initial period is Markovian and after a certain period, it becomes non-Markovian where we observe an environmental backaction on the system. To confirm the non-Markovianity of the evolution we use a detection method based on Bures distance formula. Thus in the strong coupling limit, we observe a dynamical crossover from Markovian nature to non-Markovian behavior. This crossover is very abrupt under some environmental conditions and for some parameters of the quantum state. Using a quantum master equation approach we verify the crossover from the dynamics of the dissipation and fluctuation coefficients and the results endorse those obtained from coherence dynamics.