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Journal of Modern Optics

The evolution of a micromaser cavity field without the rotating-wave approximation

Zhengdong Liu, Liang Zeng, Shiyao Zhu

Published May 1, 1998• 3 citations
Publisher

Abstract

In a micromaser, the evolution of cavity-field entropy and the Fano factor with the injected atomic number is investigated with and without the rotating-wave approximation. The micromaser may become a decreasing-entropy system under specific system parameters. Virtual-photon processes cause an additional quantum oscillation which relates to the atom–field coupling constant and the field frequency.

DOI
10.1080/09500349808230889

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Acta Physica Sinica•Jan 1, 1994•13 citations
In a micromaser, the evolution of cavity-field entropy and the Fano factor with the injected atomic number is investigated with and without the rotating-wave approximation. The micromaser may become a decreasing-entropy system under specific system parameters. Virtual-photon processes cause an additional quantum oscillation which relates to the atom–field coupling constant and the field frequency.
In a one-atom micromaser, the expression for the density matrix of the cavity field without the rotating-wave approximation (RWA) is derived using a perturbation method. The phase evolution of the cavity field is investigated without the RWA, and the results are compared with those within the RWA. It is shown that the virtual-photon processes make the symmetric phase distribution in the RWA asymmetric and cause additional quantum oscillation, which indicate the field's phase fluctuation and frequency shift. Virtual photons also cause an extra phase distribution to the field which is initially in a vacuum state. The unique characteristic of the phase properties in the course of forming a photon-number state is investigated. Other new phenomena such as the undamped oscillation of the phase variance against the injected atomic number are found.
The equations for the micromaser are derived without assuming the validity of the rotating- wave approximation (RWA) in the Scully-Lamb model for a single-mode maser off resonance. The treatment is based on Swain's continued fractions approach, by which the eigenvalues and eigenvectors of the Hamiltonian describing the system of atoms plus cavity field can be iteratively determined to any desired order and then used to obtain the micromaser equations. These are valid to second order in the parameter g, the coupling constant of the atom-field interaction. The procedure can be extended, to any desired order in g, by successive iterations. Through numerically evaluating the micromaser spectrum we compare our results with those of the RWA. We predict a relative shift, stemming from the Bloch-Siegert shift, which in case of the spectra corresponding to two-photon correlations should be measurable through atomic selective field ionization.
The development of a single-atom maser or a micromaser allows a detailed study of the atom–field interaction. The situation realized is very close to the ideal case of a single two-level atom interacting with a single-mode quantized field as treated in Section 6.2. In a micromaser a stream of two-level atoms is injected into a superconducting cavity with a high quality factor. The injection rate can be such that only one atom is present inside the resonator at any time. Due to the high quality factor of the cavity, the radiation decay time is much larger than the characteristic time of the atom–field interaction, which is given by the inverse of the single-photon Rabi frequency. Therefore, a field is built up inside the cavity when the mean time between the atoms injected into the cavity is shorter than the cavity decay time. A micromaser, therefore, allows sustained oscillations with less than one atom on the average in the cavity. The realization of a single-atom maser or a micromaser has been made possible due to the enormous progress in the construction of superconducting cavities together with the laser preparation of highly excited atoms called Rydberg atoms. The quality factor of the superconducting cavities is high enough for periodic energy exchanges between atom and cavity field to be observed. The interesting properties of the Rydberg atoms make them ideal for micromasers. In Rydberg atoms the probability of induced transitions between adjacent states becomes very large and scales as n 4 , where n denotes the principle quantum number.