Evolution of the Number State Filtered Coherent State in a Kerr Medium.

The evolution of the classical states, as well as a quantum state under the nonlinear Hamiltonian, detaches the state from the initial state, and the evolved state wanders through various facets in the state space. In the nonlinear Kerr evolution, the number state filtered coherent state (NSFCS) derived from the coherent state (CS) is chosen as an initial state. The departure from coherence is quantified by the Hilbert–Schmidt distance between the CS and the NSFCS in the Kerr medium; it is also calculated between the CS and the photon-added coherent states (PACS) in the Kerr medium. The similarity of states between the initial state and the time-evolved NSFCS is also analyzed through the Hilbert–Schmidt distance. We show the revivals and fractional revivals of the NSFCS, in view of the expectation values of the observables, optical tomogram, and Wigner function. The NSFCS revives at the integral multiples of π. The collapse of the wave packet does not occur at an instant of π/ 2 as like the coherent states and photon-added coherent states. These features are revealed in the moments of observables and optical tomogram. Further, the distinct features of the spread of sub-packets are captured by the Wigner function. [ABSTRACT FROM AUTHOR]