Abstract
The fractional derivative form of the model equations of a dissiptive quantised harmonic oscillator (HO) driven by a laser field are examined within and outside the rotating wave approximation (RWA). Interplay of the two parameters, fraction derivative order, 0 < alpha < 1 and the fast oscillatory terms outside the RWA, exp(+/- 2i omega(L)t), where omega(L) is the laser frequency, affect significantly the dynamical behaviour of the average photon number, n(t), of the HO and the second order auto-correlation function, g((2))(t). Of particular, in the fractional derivative case (0 < alpha < 1) as compared with the ordinary derivative case (alpha = 1) our results show that:
1. n(t) shows faster increasing (with initial vacuum state of the HO) and decreasing (with initial number state of the HO) evolution and much reduced oscillator behaviour outside the RWA,
2. For initial number state of the HO, and non-resonant weak laser field, anti-bunching (g((2))(t) < 1) shows over longer time period. Super-chaotic behaviour g((2))(t) > 2 with relatively reduced oscillations exhibited with non-resonant strong laser field, within and outside RWA. For initial coherent state of the HO, g((2))(t) < 1 in the weak field case over longer time period, within and outside the RWA.