Atomic systems dressed-atom approach

Rydberg atoms and microwave fields constitute an ideal system for the study of atom-strong field effects, and they have been used to explore the entire range of one electron phenomena [5]. Here we focus on an illustrative example, which has a clear parallel in laser experiments, a series of experiments which show that apparently non-resonant microwave ionization of nonhydronic atoms proceeds via a sequence of resonant microwave multiphoton transitions and that this process can be understood quantitatively using a Floquet, or dressed state approach. 

We now tackle the problem of the calculation of W2 and P for the 3-level atom described above, for which we shall use a dressed atom approach. Immediately after the detection of a first fluorescence photon at time t, the system is in the state = g,Ng,N >, i.e. atom in the ground state in presence of Ng blue photons and Ng red photons. Neglecting antiresonant terms, we see that this state is only coupled by the laser-atom interactions to the two other states = e3,Ng-l,Ng> and l4>2> eg,Ng,Ng-l> (the atom absorbs a blue or a red photon and jumps from g> to eg> or leg>). 

Complex rotation can be usefully applied also to the case of the interaction of an atom with a time-dependent perturbation. With the Floquet formalism by Shirley [41], it was shown that, for a time-periodic field, the dressed states of the combined atom-field system can be characterized non-perturbatively by the eigenstates of a time-independent, infinite-dimensional matrix. The combination of the Floquet approach with complex rotation, proposed by Chu, Reinhardt, and coworkers [37, 42, 43], permits to account for the field-induced coupling to the continuum in an efficient way. As in the time-independent case, this results in complex eigenvalues (this time to the Floquet Hamiltonian matrix) and again the imaginary parts give the transition rate to the continuum. This combination has since then been successfully used to examine various strong field phenomena a review can be found in Ref. [44]. 

An alternative description of the observed phenomena can be obtained by the dressed atom model [80]. In this approach the eigenvalues of the global system atom + field, the dressed states, are sought. The strong pump beam dresses the atom with laser photons which leads to energy levels split by the Rabi frequency. The resonances discussed in Fig. 20 then arise naturally as transitions between the (infinite) ladder of dressed states. The dressed atom model delivers a physically comprehensible description of atomic energy levels in strong fields and the reader is referred to Ref. 80 for a detailed presentation. 

In what follows we will employ the dressed-atom squeeze-transformed mode approach to treat the present system. 

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