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Physical Review A

Theoretical study of a two-photon double-beam laser

Shi-Yao Zhu, Marlan O. Scully

Published Nov 1, 1988• 34 citations
Publisher

Abstract

A nondegenerate two-photon laser in a cascade three-level atomic system is studied. The difference between the laser and that derived from an effective Hamiltonian is discussed. Photon number distributions about field 1 are presented. The effects of field 2 on field 1 are studied in detail. Field 2 can play a role of gain enhancement or gain reduction for field 1. This is due to two actions of field 2: reducing the population of the intermediate level and changing the detuning really acting upon field 1, which is caused by the ac Stark shift.

DOI
10.1103/physreva.38.5433

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A nondegenerate two-photon laser in a cascade three-level atomic system is studied. The difference between the laser and that derived from an effective Hamiltonian is discussed. Photon number distributions about field 1 are presented. The effects of field 2 on field 1 are studied in detail. Field 2 can play a role of gain enhancement or gain reduction for field 1. This is due to two actions of field 2: reducing the population of the intermediate level and changing the detuning really acting upon field 1, which is caused by the ac Stark shift.
Degenerate as well as nondegenerate three-level two-photon laser (TPL) models are derived. In the limit of equal cavity losses for both fields, it is shown that the nondegenerate model reduces to the degenerate one. We also demonstrate the isomorphism existing between our degenerate TPL model and that of a dressed-state TPL. All these models contain ac-Stark and population-induced shifts at difference from effective Hamiltonian models. The influence of the parameters that control these shifts on the nonlinear dynamics of a TPL is investigated. In particular, the stability of the periodic orbits that arise at the Hopf bifurcation of the system and the extension of the self-pulsing domains of the system are studied, revealing the role played by the detuning and ac-Stark parameters.
Laser actions and photon statistics for a nondegenerate two–photon laser in an effective three–level atomic system with arbitrary detuning are investigated both semiclassically and quantum mechanically, Due to the two–photon effect, the radiation field easily displays a sub–Foissonlan statistical distribution. The laser actions for a two–photon and a single–photon loss mechanisms are compared. It Is found that the detailed balance in the single–photon loss mechanism can still be preserved in the case that a first–order phase transtion takes place.
The dynamics of a two-photon laser with injected signal (TPLIS) in the limit of high quality cavity (class-A laser) is analysed by explicitly considering the underlying multi-level structure of the amplifying medium. A three-level cascade system is considered which retains the basic physics of the microscopic lasing processes. In this way the usual two-photon laser equations are consistently modified by the appearance of different dynamic frequency shifts dependent on the two-photon population inversion and on the laser intensity (ac-Stark shift). Although the basic instability scenarios are not qualitatively modified with respect to the effective two-level TPLIS, from the quantitative point of view, population-induced shifts heavily affect the threshold of appearance of instabilities.