Generalization of the Einstein coefficients and rate equations under the quantum Rabi oscillation

Abstract

We have generalized Einstein coefficients and rate equations from quantum field theoretic point of view by bringing the fundamental processes and the quantum Rabi oscillation in a single footing for the light–matter interactions for nonzero Rabi frequency. We have analytically obtained multimode Jaynes–Cummings model results for the quantum Rabi oscillation of a two-level system in a lossy resonant cavity containing (i) thermal photons and (ii) injected photons of a coherent field. We have renormalized the coupling constant for the light–matter interactions for these cases. Our results match well with the seminal experimental data obtained in this regard by Brune et al (1996 Phys. Rev. Lett. 76 1800). We also have studied the population dynamics in this regard by applying the generalized Einstein rate equations.

Multi-mode Jaynes–Cummings model results for the collapse and the revival of the quantum Rabi oscillations in a lossy resonant cavity

“…Losses from the cavity are shown by the wavy arrows in the same figure. The frequency broadening in Brune et al 's experiment can be attributed to the multi-mode J-C model, Ĥ = [18,19], rather than the single-mode Jaynes-Cummings model [20]. Thus the theoretical explanation of the CR of the quantum Rabi oscillations in a lossy resonant cavity needs a novel approach with the multi-mode Jaynes-Cummings model.…”

“…Multi-mode J-C model [18] is well-known [20,22,23] as an extension of the single-mode J-C model [12]. Multimode J-C model has been successfully used by us [20] to explore the quantum Rabi oscillations of a two-level system interacting with a very low average number of injected coherent photons (n = 0.4) in a lossy resonant cavity as described in Brune et al 's experiment [7]. Such a very low average number of photons was treated perturbatively (up to the second order in n2 1) in Ref.…”

“…Such a very low average number of photons was treated perturbatively (up to the second order in n2 1) in Ref. [20]. However, Brune et al [7] obtained two more sets of data for low average number of injected coherent photon numbers n = 0.85 ± 0.04 and n = 1.77 ± 0.15 in the same cavity showing the CR of the quantum Rabi oscillations of a two-level system ( 87 Rb atom).…”

“…Hence we extend our method described in Ref. [20] for this purpose. The CR of the quantum Rabi oscillations, of course, were not discussed in Ref.…”

“…(8) of Ref. [20]. This equation is an outcome of the multi-mode J-C model and it is nothing but the net transition probability (P 2→1 (t)) which describes the quantum Rabi oscillations in time (t) domain for a two-level system interacting with coherent photons in a lossy resonant cavity.…”