Dissipative dynamics of few-photons superposition states: A dynamical invariant

By numerically calculating the time-evolved Wigner functions, we investigate the dynamics of a few-photon superposed (e.g., up to two ones) state in a dissipating cavity. It is shown that, the negativity of the Wigner function of the photonic state unquestionably vanishes with the cavity's dissipation. As a consequence, the nonclassical effects related to the negativity of the Wigner function should be weakened gradually. However, it is found that the value of the second-order correlation function $g^{(2)}(0)$ (which serves usually as the standard criterion of a typical nonclassical effect, i.e., $g^{(2)}(0)<1$ implies that the photon is anti-bunching) is a dynamical invariant during the dissipative process of the cavity. This feature is also proven analytically and suggests that $g^{(2)}(0)$ might not be a good physical parameter to describe the photonic decays. Alternatively, we find that the anti-normal-order correlation function $g^{(2A)}(0)$ changes with the cavity's dissipation and thus is more suitable to describe the dissipative-dependent cavity. Finally, we propose an experimental approach to test the above arguments with a practically-existing cavity QED system.