Jaynes-Cummings model

The branch of quantum optics studying the processes of interaction of one or a few atoms with the quantized cavity modes is usually called cavity quantum electrodynamics (cavity QED). The theoretical concepts of cavity QED are based in the first place on investigation of the Jaynes-Cummings model [67] and its generalizations (for a review, see Ref. 68). The reason for this is that the model describes fairly well the physical processes under consideration and at the same time admits an exact solution. 

In the usual formulation of the Jaynes-Cummings model, the atom is considered as though it consisted of two nondegenerated levels [67]. In contrast, the radiative transitions in real atoms occur between the states with given angular quantum numbers j,m) —> j, m ) such that j >f >0 [23,26,61]. This means that, at least the upper level, is degenerated with respect to the quantum number m (—j < m electric dipole transition between the states j = l,m = 0, l) and... 

Generalizations of the Jaynes-Cummings model (34) in the case of quad-mpole and other high-order multipole transitions can be constructed in the same way. 

Here Ja denotes the atomic SU(2) generators (37) with a = z, ,Ma is the component of the field angular momentum operator (58), and H is the Jaynes-Cummings model Hamiltonian (34). 

The dual representation of the photon operators (67) reflects the transmission of phase information from the atomic transition to the radiation field via the integral of motion (70). This statement can be illustrated with the aid of the Jaynes-Cummings model (34). Employing the atomic phase states (46), we can introduce the dual representation of the atomic operators (35) as follows ... 

To illustrate the exchange of the phase information between the atomic transition and the multipole field, consider the electric dipole Jaynes-Cummings model (34). Assume that the field consists of two circularly polarized components in a coherent state each. The atom is supposed to be initially in the ground state. Then, the time-dependent wave function of the system has the form [53]... 

The experimental setup described above is suitable to test the Jaynes-Cummings model describing the dynamics of the interaction of a single atom with a single cavity mode. An important requirement is, however, that the atoms of the beam have a homogeneous velocity so that it is possible to observe the Rabi nutation in the cavity directly. In a... 

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