INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS B: QUANTUM AND SEMICLASSICAL OPTICS J. Opt. B: Quantum Semiclass. Opt. 6 (2004) 309–314 PII: S1464-4266(04)73202-4 Sub-Poissonian three-level lasing with an m-photon coherent pump Yu Golubev 1,2 , O Kocharovskaya 2 , Yu Rostovtsev 2 and M O Scully 2,3 1 Physics Institute, St Petersburg State University, 158504 St Petersburg, Russia 2 Department of Physics and Institute for Quantum Studies, Texas A&M University, College Station, TX 77843-4242, USA 3 Department of Chemistry, Princeton University, Princeton, NJ 08544-1009, USA Received 19 July 2003, accepted for publication 23 April 2004 Published 20 May 2004 Online at stacks.iop.org/JOptB/6/309 DOI: 10.1088/1464-4266/6/7/008 Abstract We theoretically consider a three-level laser with an incoherent one-way pump from a ground state into an intermediate excited state and a coherent drive into the upper laser state. The possibilities of inversionless lasing are studied. It is demonstrated that, in the case of a strong coupling with the drive laser (when its generation depends essentially on the three-level medium), the quantum properties of laser radiation can be improved by using m-quantum coherent excitation or by applying a sub-Poissonian coherent pump. Keywords: inversionless lasing, sub-Poissonian light, photodetector, coherent state 1. Introduction Three-level lasing is of interest because, first, it contains some intrinsic mechanism that ensures sub-Poissonian lasing [1] automatically without some additional efforts to distinguish it from two-level lasers [2], for example, where we need to foresee a regular pump. Second, the system is the simplest available that is able to ensure so called inversionless gain [3]. We are going to discuss both these aspects together. A laser using a -configuration of levels and statistical properties of its radiation were considered in [1], and it was demonstrated that there is reduction of the shot noise, but the efficiency was not very high. The strongest effect shown is the reduction by halves. It is then natural to search for a simple physical system which is able to overcome this result, and one of the extremely attractive candidates is the three- level laser due to its ability to produce sub-Poissonian lasing automatically. In this paper, two possible systems will be discussed. First we will propose the coherent pump which is realized by sub-Poissonian light. Obviously we can expect here some additional reduction of the laser emission noise, because, in the system as whole, in principle, the number of noise sources decreases. The same can be expected in the case when we apply the m-photon pump, because, in this case, even the Poissonian light is perceived to be sub-Poissonian. 2. Semi-classical approach 2.1. A three-level laser model The active medium of the laser consists of three-level atoms, which are schematically shown in figure 1(a). The laser levels are the uppermost (a) and the ground (b), and the coherent pump is in resonance with the adjacent transition (c−a) (-configuration). To ensure lasing we must predict some incoherent one-way pump (b → c) with a rate γ b . And our last additional requirement is for the laser transition (a−b) spontaneous emission occurring with a rate γ a . It needs to be stressed that in this configuration there is a conversion of the small frequency of the pump into the higher one of lasing. At the same time our formulae obtained for this model will be perfectly suitable for the configuration represented in figure 1(b) and thereby describe a situation with a reduction of frequency. To implement a one-way pump (b → c) in a real situation we must take into account some additional level (d ) (see figure 2) and some additional pump incoherent mechanisms ensuring processes (b → d ), (d → b) and (d → c). Further, in our formal equations just the model is considered. 1464-4266/04/070309+06$30.00 © 2004 IOP Publishing Ltd Printed in the UK 309