On the nonlinear orbital motion of the driven two-photon Jaynes-Cummings model

Chuan-hua Dong, Jun Guo Lu

K.M. Ng, Chi‐Fai Lo, K. L. Liu

Amitabh Joshi

The driven two-photon Jaynes-Cummings model (JCM) exhibits a collapse and revival phenomenon in its mean photon number on a time scale much larger than the periodic revival time for two-state inversion in the usual two-photon JCM. The time scale of revivals for these oscillations is much larger than the corresponding time scale for the driven one-photon JCM and can be explained with the Hamiltonian of type ${H}_{\ensuremath{\eta}}=\ifmmode\pm\else\textpm\fi{}\sqrt{{(J}_{\ensuremath{\eta}}^{\ifmmode\dagger\else\textdagger\fi{}}+\ensuremath{\alpha}{P}_{\ensuremath{\eta}}{)}^{2}{(J}_{\ensuremath{\eta}}+\ensuremath{\alpha}{P}_{\ensuremath{\eta}}{)}^{2}}$ constructed explicitly for this purpose. The effect of Stark shifts is also studied and it is observed that the dynamics is strongly influenced by such Stark shifts both at early stages as well as at late stages of the evolution but in different ways, and thus Stark shifts play a significant role in determining the dynamical evolution of the system.

Y.-T. Chough, H. J. Carmichael

The driven Jaynes-Cummings model shows collapses and revivals of the mean photon number on a time scale much longer than the revival time for the two-state inversion. The behavior is essentially that of a nonlinear quantum oscillator with Hamiltonian H=\ensuremath{\surd}(A${\mathrm{^}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$+\ensuremath{\alpha})(A^+\ensuremath{\alpha}). \textcopyright{} 1996 The American Physical Society.

Chuanzhou Zhu, Lin Dong, Han Pu

We consider ultracold atoms inside a ring optical cavity that supports a single plane-wave mode. The cavity field, together with an external coherent laser field, drives a two-photon Raman transition between two internal pseudospin states of the atom. This gives rise to an effective coupling between atom's pseudospin and external center-of-mass (COM) motion. For the case of a single atom inside the cavity, We show how the spin-orbit coupling modifies the static and dynamic properties of the Jaynes-Cummings (JC) model. In the case of many atoms in thermodynamic limit, we show that the spin-orbit coupling modifies the Dicke superradiance phase transition boundary and the non-superradiant normal phase may become reentrant in some regimes.

Barry C. Sanders, H. J. Carmichael