Abstract

A single atom coupled to a quantized mode of an electromagnetic cavity, driven by an external coherent field, is described by the Hamiltonian H_djc = ig(a^†σ₋ − aσ₊) + iε(a^† − a), where (a^†, a) and (σ₊, σ) are the raising and lowering operators for the cavity mode and atom, respectively. This is the single atom version of the Hamiltonian used in the study of optical bistability. It describes the evolution of the atom-cavity system on time scales much smaller than the inverse spontaneous emission and cavity decay rates. For 2ε/g < 1, H_DJC possesses a discrete set of interaction eigenstates¹ with eigenvalues $E_{n\pm }=\pm g\sqrt{n}{\left[1-{(2\epsilon /g)}^2\right]}^{3/4}$. These form a renormalized version of the usual Jaynes-Cummings eigenstates², which correctly take into account the effect of the driving field to all orders of magnitude. We investigate the collapse and revival nature of the dynamical evolution of the single atom in a cavity, with and without dissipation and above and below the threshold 2ε/g = 1 of the driven Jaynes-Cummings Hamiltonian.

© 1992 Optical Society of America