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Quantum Optics Journal of the European Optical Society Part B

Gain without inversion in four level atoms using pulsed lasers

Steve R. Wilkinson, Arlie V. Smith

Published Aug 1, 1994• 3 citations
Publisher

Abstract

We present results of a numerical calculation of gain without inversion in the transient regime. We show that atomic coherence and gain without population inversion can be induced on time scales short compared to atomic radiative lifetimes. We also describe the process in terms of transient dressed states.
DOI
10.1088/0954-8998/6/4/009

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We consider a four-level atomic system with a degenerate or quasidegenerate ground-state doublet and two excited states. One of the upper levels is coupled to the ground doublet by a coherent field of variable strength, which we refer to as the Raman field, whose role is to create atomic coherence between the driven atomic states. The other higher lying state is coupled to the ground states when laser action develops. This model includes an incoherent pump mechanism to create some population in the top lasing state. In appropriate conditions, for the incoherent pump rate and the Raman field strength, the absorption profile of the laser transition develops gain features. We discuss the physical origin of this gain which we find to be the consequence of a population inversion between dressed atomic states. It is interesting to compare the results of this analysis with a similar study of a three-level lambda system which was previously recognized to yield lasing without inversion.1 In this case the appearance of gain can be attributed to the induced atomic coherence.
For a four-level atomic system with a doublet of closely spaced levels, we find that, owing to the coherence that results from the vacuum of the radiation field, population trapping at excited levels and probe gain with population inversion can be achieved with weak incoherent pumping. This gain is different from both the conventional lasing gain and gain without inversion in that there exists population inversion on probe transitions but the inversion is achieved by the vacuum-induced coherence.
This thesis is concerned with the amplification of coherent radiation from an active medium under conditions which require no population inversion between the energy levels. Gain without population inversion may be obtained by creating a sufficiently strong correlation between pairs of atomic states, usually with the help of external sources of resonant electromagnetic radiation. Our main objective is to investigate two possible selections for the active medium: a three level atom in a lambda configuration and a Raman-driven four level model. For both we identify the conditions that lead to inversionless laser action, we calculate the small signal gain and investigate the physical mechanisms which are responsible for the emergence of gain. While the ultimate cause of the gain is quantum interference, we propose attractive alternative pictures based on the dressed states of the coupled atom-driving field systems. We address the important practical issue of the effect of atomic motion and related Doppler broadening on the inversionless gain profile and we also analyze the transient response of each laser model with the help of the appropriate Maxwell-Bloch equations. Finally we develop a fully quantum mechanical description of the lambda model and find that the radiated field can display unique quantum features which manifest themselves with sub-Poissonian photon fluctuations.
The emergence of laser action from an atomic system without population inversion is beginning to attract theoretical and experimental attention as a possible way of generating useful coherent radiation at unusual wavelengths. The goal of this communication is to clarify the physical origin of this phenomenon using a four-level system whose ground state consists of two quasidegenerate levels that are coupled to a higher-lying state by a Raman-like transition. In the presence of the ground-state coherence induced by the Raman field, we calculate the absorption spectrum of a weak probe whose tunable frequency scans across the transition frequencies between the two ground-state levels and another higher-lying state that may or may not be weakly excited by an incoherent pump mechanism. Our calculation, based on a dressed atomic state approach, clarifies the conditions that must be satisfied to produce gain, identifies the frequency (or frequencies) at which the gain is maximum, and elucidates the functions of the incoherent pump, the Raman field, and the coherence between the ground-state levels in this process. An appropriate set of Maxwell- Bloch equations for a ring-cavity model of this system confirms the appearance of laser action when the small-signal gain conditions are satisfied.
We explore a three-level Lambda scheme to demonstrate that the phenomenon of lasing without inversion (LWI) can be observed in the transient regime. We demonstrate that the pure LWI contribution to the gain of a probe field is distinct from both the resonant absorption (or gain) and the coherent Raman gain (or absorption) by choosing specific initial populations in the dressed-state basis. The suppression of the non-LWI (resonant and Raman) processes is followed by the "rich get richer" (capitalistic) effect for the ground-state population dynamics: Initially, the more populated ground state becomes even more populated. The conditions for the observation of the effect are specified.