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Annual Meeting Optical Society of America

Raman gain in a Λ three-level system with closely spaced ground states

M. S. Shahriar, Philip Hemmer, J. Donoghue, Mark Cronin‐Golomb, Prem Kumar

Published Jan 1, 1992• 0 citations
Publisher

Abstract

Recently, there has been much interest in the Raman gain observed in a Λ system with closely spaced ground states such that both ground states are initially equally populated and are both coupled to the excited state by a single frequency pump. This system is of interest for applications such as frequency shifting and self phase conjugation and as an example of a system that exhibits large optical gain for very small excited state populations. We have studied the mechanism of this gain theoretically and have found qualitative agreement with previously observed experimental results. Briefly, a single frequency pump interacts with both legs of the system. The gain spectrum is interpreted in terms of the energy intervals of the dressed states of the pumped system. The gain mechanism is analogous to the process of sideband amplification in a strongly driven two level system. However, the width of the gain is not limited by the linewidth of the excited state and, for low pump power, is determined by the transit time only. This is consistent with the extremely narrow gains (less than 1 kHz) observed in sodium vapor.

DOI
10.1364/oam.1992.thn1

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Physical Review A•Dec 1, 1993•41 citations
Recently, there has been much interest in the Raman gain observed in a Λ system with closely spaced ground states such that both ground states are initially equally populated and are both coupled to the excited state by a single frequency pump. This system is of interest for applications such as frequency shifting and self phase conjugation and as an example of a system that exhibits large optical gain for very small excited state populations. We have studied the mechanism of this gain theoretically and have found qualitative agreement with previously observed experimental results. Briefly, a single frequency pump interacts with both legs of the system. The gain spectrum is interpreted in terms of the energy intervals of the dressed states of the pumped system. The gain mechanism is analogous to the process of sideband amplification in a strongly driven two level system. However, the width of the gain is not limited by the linewidth of the excited state and, for low pump power, is determined by the transit time only. This is consistent with the extremely narrow gains (less than 1 kHz) observed in sodium vapor.
Measurements of stimulated Raman gain in rubidium vapor are made and compared with a detailed model. Amplification of a weak probe laser is observed in a \ensuremath{\Lambda}-type three-level system that is driven by a strong cw coupling laser. The intensity of the coupling laser is sufficiently strong that it both optically pumps the atomic levels, causing a population inversion in the ground-state hyperfine levels, and drives the stimulated Raman process producing gain. A theory that models all aspects of the gain mechanism is presented. The model includes all interactions between the external fields and the atomic transitions, including those processes that involve multiple fields interacting with the same transition. Numerical calculations are compared with gain measurements made at several coupling laser intensities and detunings from the D1D1D1 line in 85Rb.{}^{85}\mathrm{Rb}.85Rb.
Theoretical and experimental studies of stimulated Raman spectrum with the D1 line of an 85Rb atomic vapor system are performed. In this Λ-type system, we discover that the influence of the pump on the probe field includes two parts: stimulated Raman excitation and optical pumping. Depending on the pump frequency detuning and field intensity conditions, the Raman spectrum can display either gain or loss. When the optically pumped absorption spectrum is taken as background, either a narrow transparent window or an absorption doublet with widely different linewidths appears. Our theoretical analysis agrees well with our experimental observations. Based on these studies, we present an interpretation from a new viewpoint of the physics of electromagnetically induced transparency (with on-resonance pumping) and Autler-Townes splitting (with far off-resonance pumping) in a Λ-type level atomic system, giving the relationship between these two important phenomena and the Raman spectrum.
When sodium vapor is irradiated with a single-frequency dye laser (pump) tuned in the vicinity of either of the Doppler-broadened D lines and enclosed in an optical cavity, Raman shifted oscillation builds up, which is blue shifted for a blue-detuned pump and red shifted for a red-detuned pump by 1.772 GHz (sodium ground-state hyperfine splitting).1 The gain mechanism responsible for this Raman-laser action can be understood by modeling sodium as a three-level atom. The Raman laser frequency is highly correlated with that of the pump as demonstrated earlier by observing a beat frequency bandwidth between the two lasers of as low as 17 kHz.2 (The pump had rms frequency fluctuation of the order of 10 MHz.) For spectroscopic applications, for example, frequency correlated laser beams are commonly generated using acoustooptic techniques which are difficult to implement beyond the gigahertz region. The Raman laser technique is extendable, in principle, even to the millimeter range. Here we present measurements of the sodium-density and pump-intensity dependence of the Raman-laser output and compare the results with those predicted by the three-level-atom model.
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.
We calculate the absorption spectrum of a weak probe interacting with a \ensuremath{\Lambda}-shaped three-level system driven by a single pump. We find that there are four types of terms that contribute to the probe absorption: population-difference and two-photon coherence terms which derive solely from interaction with the pump (dc terms) and population-difference and two-photon coherence terms that pulsate at the pump-probe frequency offset. We find that the main features of the probe spectrum derive from the pulsating terms whereas the dc terms either interfere destructively with each other or with the pulsating terms. This is a clear extension to the three-level system of the concept of light amplification by coherence. We calculate the spectrum for three cases: (i) a degenerate population-trapped system, (ii) a degenerate system in which both transitions are population inverted, and (iii) a nondegenerate population-trapped system. The results of case (i) are similar to those for the two-level system but the population-trapped system has the advantage of avoiding pump absorption. We show that the Rabi frequency of the nonabsorbed pump can be found by determining the probe frequencies at which probe nonabsorption occurs. In (ii), the results are compared with the case where two pumps interact resonantly with a nondegenerate system. In (iii), we find that the populations in the lower states behave dispersively as a function of the pump detuning. For Rabi frequencies that are small compared to the separation between the lower levels, the lower level nearer to resonance is less populated than the other level. However, at higher Rabi frequencies, the situation is reversed. The probe spectrum contains two absorption peaks when the pump Rabi frequency is small and two emission peaks when it is large.