Effect of field quantization on Rabi oscillation of equidistant cascade four-level system

Abstract

We have exactly solved a model of equidistant cascade four-level system interacting with a single-mode radiation field both semiclassically and quantum mechanically by exploiting its similarity with Jaynes-Cummings model. For the classical field, it is shown that the Rabi oscillation of the system initially in the first level (second level) is similar to that of the system when it is initially in the fourth level (third level). We then proceed to solve the quantized version of the model where the dressed state is constructed using a six-parameter four-dimensional matrix and show that the symmetry exhibited in the Rabi oscillation of the system for the semiclassical model is completely destroyed on the quantization of the cavity field. Finally, we have studied the collapse and revival of the system for the cavity field-mode in a coherent state to discuss the restoration of symmetry and its implication is discussed.

SU(4) based classification of four-level systems and their semiclassical solution

“…Furthermore, we note that for Model-III, the Rabi oscillation of Fig.9a is similar to Fig.9(d) and Fig.9(b) is similar to Fig.9(c), repectively. The existence of the inversion symmetry within same system has already been pointed out in the equidistant three-level cascade system 14,18 . Finally in Model-III, taking the coupling parameters κ 43 → √ 3κ 43 , κ 32 → 2κ 32 and κ 21 → √ 3κ 21 to be in Eq.…”

“…Apart from that, at resonance, the detuning are taken to be ∆ Fig.7 (Fig.8) with that of Model-VI (Model-II) shown in Fig.12 (Fig.10), an inversion symmetry is clearly evident. The existence of the inversion symmetry is a unique feature of the multilevel system which was also observed in the three-level cascade system 14,18 . Furthermore, we note that for Model-III, the Rabi oscillation of Fig.9a is similar to Fig.9(d) and Fig.9(b) is similar to Fig.9(c), repectively.…”

“…10), an inversion symmetry is clearly evident. The existence of the inversion symmetry is a unique feature of the multilevel system which was also observed in the three-level cascade system 14,18 . Furthermore, we note that for Model-III, the Rabi oscillation of Fig.…”

“…The exact solution of all six semi-classical models are obtained and the symmetry exists in the pattern of the Rabi oscillation of each model is illustrated. In a recent work, we have reported that the symmetric pattern of Rabi oscillation is spontaneously broken on quantization of the cavity field not only for the cascade, lambda and vee systems 14,15,18 , but also for the equidistant cascade four-level system 13 . It is interesting to explore how the pattern of the symmetry is broken if we treat the tri-achromatic cavity field quantum mechanically.…”

“…All these studies deal with the model Hamiltonians which are proposed phenomenologically and therefore lacks proper understanding of the selection rules of allowed transition among various levels. In a recent investigation we have shown that the threelevel system can be successfully classified using SU (3) as the basis group 14,15 . It is therefore interesting to look for the straight forward but non-trivial extension of the treatment to study the four-level system where the SU (4) group plays key role to identify the possible allowed dipole transitions.…”