Polychromatic excitation of a two-level system

Phenomena associated with a two-level atom driven by a strong monochromatic field are frequently analyzed in terms of dressed states @1#. The dressed states are the eigenstates of the coupled atom plus driving field system. A dressed-state approach has previously been extended from one field to two driving fields, that is, a bichromatically driven two level atom. The doubly dressed states have been shown to be useful in predicting @2# and explaining observed spectral features @3,4#. The purpose of this paper is to show that the dressed state formalism can be extended to cover the case of multiple driving fields, the so called polychromatic driven two-level atom, and the multiple dressed states can provide a good account of experiments involving several driving fields. We consider a two-level atom, with ground state ua& and excited state ub& and a transition frequency vab . The ua& 2ub& transition is driven by multiple fields. The individual driving fields are numbered, with the ith field having frequency v i , detuning D i5v i2vab , and Rabi frequency x i . In the experiment presented here, up to four strong fields were simultaneously applied and the field configuration for four fields is shown in Fig. 1. The effect of the pump fields was monitored by applying a weak field of frequency vp and detuning Dp5vp2vac , which probes the transition from the ground state, ua&, to the third state, uc&, that is, the Autler-Townes configuration @5#. Observed resonances of the system correspond to the eigenstates of the Hamiltonian of the atom coupled to ~dressed by! the driving fields. In general, the eigenstates of the Hamiltonian for a polychromatically driven two-level atom are grouped in an infinite number of manifolds. Because of this complexity, the solutions are most conveniently obtained by numerical methods. It is observed experimentally that the Autler-Townes spectrum of a polychromatically driven two-level atom has a complicated multipeak structure. However, instead of tackling the general case, we present a special case where we are able to give a simple physical explanation of the observed spectra. In our specially designed experiment, field i is significantly weaker than field i21, with the ith field resonant with a transition between the dressed states associated with the other (i21) fields. The interaction between atom and field is defined by the operator