Pump operator for lasers with multi-level excitation

¹ Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
² Department of Physics, Texas A&M University, College Station - Texas 77843, USA
³ Max-Planck-Institut für Quantenoptik - Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
⁴ Sektion Physik, Ludwig-Maximilians-Universität - München, Germany
⁵ Laboratoire de Physique des Lasers (Unité de recherche associée au CNRS (URA 282).) , Institut Galilée, Université Paris-Nord Av. J. B. Clément, F-93430 Villetaneuse, France

Received: 9 October 1995
Accepted: 17 January 1996

Abstract

In a multi-level laser the pump process involves several intermediate levels. The details of the atomic excitation are often irrelevant so that an effective heat bath description and a two-level–laser model are applicable. The heat bath approximation may be too crude, however; it does not predict phenomena such as intensity-noise squeezing and sub-Poissonian field statistics. We show how, in the general situation, the multi-level description can still be reduced to a two-level description in terms of a non-Markovian master equation where a rate matrix, rather than a single rate, accounts for the excitation process. The resulting dependence of the excitation rates on the state of the laser field constitutes a correction to the standard laser model. We hold it responsible for the dynamic noise reduction in multi-level lasers.