Nonclassical statistical properties of finite-coherent states in the framework of the Jaynes–Cummings model

Adopting the framework of the nonresonant Jaynes–Cummings model, we investigate the nonclassical statistical properties of coherent states defined in a finite-dimensional Hilbert space, considering the single-mode cavity field prepared in a finite and discrete harmonic oscillator-like coherent state with a small average number of photons. Explicit expressions for the time evolution of various functions characterizing the quantum state, such as the Mandel's Q parameter, the photon-number distribution and its respective entropy, the discrete Wigner function, and the number-phase uncertainty relation, are investigated in detail. We also show that the atomic inversion possesses regular structures with collapses and revivals in the Rabi oscillations since the detuning between atom and field is large as compared to the coupling constant, i.e., (κ/2g)2⪢1. The numerical and analytical results obtained in this work turn evident the quantum interference effects between the components of the finite-coherent states. Furthermore, we present a discussion about unitary depolarizers in finite-dimensional Hilbert space and their connection to quantum information theory.