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Journal of Modern Optics

Variations of dispersion and transparency in four level N-scheme atomic systems

Tony Abi-Salloum, S. Snell, Jon P. Davis, Frank A. Narducci

Published Aug 17, 2011• 4 citations
Publisher

Abstract

Systems that exhibit positive and negative dispersion are of interest for numerous applications especially when accompanied by transparency. In this work, we study the variation of the sign of the dispersion in the case of a four-level ‘N-Scheme’ system. The different dynamics of the sign and value of dispersion and transparency are first explored in light of three resonances that we have previously introduced, then studied as a function of the varying strengths of the fields. As an application we consider in this work both passive and active optical gyroscopes.

DOI
10.1080/09500340.2011.603441

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Systems that exhibit positive and negative dispersion are of interest for numerous applications especially when accompanied by transparency. In this work, we study the variation of the sign of the dispersion in the case of a four-level ‘N-Scheme’ system. The different dynamics of the sign and value of dispersion and transparency are first explored in light of three resonances that we have previously introduced, then studied as a function of the varying strengths of the fields. As an application we consider in this work both passive and active optical gyroscopes.
In this work, we consider a four-level ‘N-scheme’ (three radiation fields coupling four atomic levels) that has previously been shown to feature different group velocity regimes (sub-luminal, super-luminal, and negative) controlled by the strength of the third interacting field, which is referred to as the control field. Another interesting aspect of the N-scheme is the ‘appearance’ and ‘disappearance’ of an electromagnetically induced transparency (EIT) window at resonance. In this paper, based on a study in the bare states picture, we point out differences and similarities between two settings (different strengths of the acting fields) of this four-level N-scheme. Conclusions are drawn based on a work in a simplified quasi-dressed states picture. We find that the four-level N-scheme under study can be approached as either a one or two three-level lambda-like system(s) that display the same physics regardless of the relative strength between the two fields that form the EIT portion of the system.
In this work, we theoretically study the absorption and dispersion coefficients of a probe field in four-level N-scheme atomic systems driven by two additional fields. We separate the steady-state solution of the appropriate density matrix element into the sum of three resonances. The effect of each resonance on the overall absorption and dispersion experienced by the probe is studied as a function of the strengths of the two other fields. In the limit of low saturation, we reveal the physics of these resonances and associate them with atomic excitation pathways, which we explicitly explain in the bare-states picture.
We motivate the study of an 'N-scheme' atomic system for the case of a bi-directional probe field. We derive the equations of motion. The equations were expanded in order of the counter-propagating field strength over the co-propagating field strength. We solve the equations numerically in steady state in a perturbative manner. The zeroth order solutions describe the dispersion and absorption of the co-propagating field, while the first order solutions describe the dispersion and absorption of the counter-propagating field. We investigate the solutions in two temperature regimes for a variety of field strengths. Regimes of similar dispersion for the co- and counter-propagating fields were found, as well as regimes of opposite behavior. In most cases, absorption of the fields is still a problem.
We present a comparative theoretical analysis of five different atomic schemes with respect to their performance as negative (anomalous) dispersive transparent media. The schemes discussed are the strongly driven and the degenerate two-level system, two closely spaced gain lines, and two slightly different double-$\ensuremath{\Lambda}$ schemes with incoherent pumping. The analysis shows that the degenerate two-level scheme is best suited for applications for which only modest negative dispersion but strongly reduced absorption is required, and dissipation and loss of the optical fields have to be avoided. Two closely spaced gain lines and one of the double-$\ensuremath{\Lambda}$ schemes are the best choice for applications which rely on large negative dispersion, but are not too sensitive to residual absorption and dissipation.