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Quantum Optics Journal of the European Optical Society Part B

Exact solution for spontaneous emission of the multiphoton single-atom Dicke Hamiltonian

Avia Rosenhouse, Jacob Katriel

Published Feb 1, 1990• 2 citations
Publisher

Abstract

An exact solution for spontaneous emission of the multiphoton single-atom Dicke Hamiltonian in the dipole and the rotating-wave approximations is derived in two ways: either by a generalisation of a method of solution proposed by Swain, J. Phys., vol.A5, p.1587 (1972), for the one-photon Dicke Hamiltonian or by an exact linearisation of the multiphoton single-atom Hamiltonian to a one-photon single-atom Dicke-type Hamiltonian.

DOI
10.1088/0954-8998/2/1/004

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An exact solution for spontaneous emission of the multiphoton single-atom Dicke Hamiltonian in the dipole and the rotating-wave approximations is derived in two ways: either by a generalisation of a method of solution proposed by Swain, J. Phys., vol.A5, p.1587 (1972), for the one-photon Dicke Hamiltonian or by an exact linearisation of the multiphoton single-atom Hamiltonian to a one-photon single-atom Dicke-type Hamiltonian.
The problem of a single two level atom in its excited state, placed in a cavity in which no photons are present initially, and interacting with N modes of the electromagnetic field is solved exactly in the electric dipole, rotating wave approximation. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time dependent wavefunction of the system is given. These quantities are evaluated analytically for N=1,2 and 3, and the time dependent properties of the system for these values of N are investigated and discussed.
Photon statistics are obtained from exact closed-form solutions for both spontaneous and stimulated coherent emissions by a large number of two-level atoms in a Dicke state. Depending on the initial excitation level of the atoms, three types of photon statistics are obtained for the emitted radiation field. Moments of the photon number of the emitted field are calculated in the case of initial atomic coherent states as well as Dicke states, and in the case of n-photon stimulating pulses as well as coherent stimulating pulses. In the particular case of an initial "superradiant" Dicke state stimulated by a coherent-radiation field, the emitted radiation pulse is also fully coherent. In other cases the photon distributions undergo large fluctuations.