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Physical Review A

Vacuum-field Rabi splitting in the presence of inhomogeneous broadening: Resolution of a homogeneous linewidth in an inhomogeneously broadened system

R. Houdré, Ross P. Stanley, Marc Ilegems

Published Apr 1, 1996• 355 citations
Publisher

Abstract

We study the effect of inhomogeneous broadening of the electronic state on vacuum-field Rabi splitting. The broadening has no effect on the size of the splitting and, in general, does not lead to an inhomogeneous broadening of the split states. From a spectroscopic point of view, these results have interesting consequences, since they allow the extraction of a homogeneous line in an inhomogeneously broadened system. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.2711

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We study the effect of inhomogeneous broadening of the electronic state on vacuum-field Rabi splitting. The broadening has no effect on the size of the splitting and, in general, does not lead to an inhomogeneous broadening of the split states. From a spectroscopic point of view, these results have interesting consequences, since they allow the extraction of a homogeneous line in an inhomogeneously broadened system. \textcopyright{} 1996 The American Physical Society.
We study, theoretically and experimentally, electromagnetically induced transparency (EIT) in two different solid-state systems. Unlike many implementations in homogeneously broadened media, these systems exhibit inhomogeneous broadening of their optical and spin transitions typical of solid-state materials. We observe EIT lineshapes typical of atomic gases, including a crossover into the regime of Autler-Townes splitting, but with the substitution of the inhomogeneous widths for the homogeneous values. We obtain quantitative agreement between experiment and theory for the width of the transparency feature over a range of optical powers and inhomogeneous linewidths. We discuss regimes over which analytical and numerical treatments capture the behavior. As solid-state systems become increasingly important for scalable and integratable quantum optical and photonic devices, it is vital to understand the effects of the inhomogeneous broadening that is ubiquitous in these systems. The treatment presented here can be applied to a variety of systems, as exemplified by the common scaling of experimental results from two different systems.
The enhanced collective coupling to weak quantum fields may turn atomic or spin ensembles into an important component in quantum information processing architectures. Inhomogeneous broadening can, however, significantly reduce the coupling and the lifetime of the collective excitation that represent the quantum information. In this paper we show that the width and shape of the inhomogeneous broadening have a striking influence on the dynamics of the cavity-ensemble system and may lead to narrowing of the linewidth of the collective states. We underpin our findings with the examples of a Gaussian and a Lorentzian profile of the inhomogeneity.
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The simultaneous influence of homogeneous and inhomogeneous line-broadening mechanisms are investigated for a reference system embedded in a medium. An analytically solvable model is constructed which includes the interaction of the reference mode with N strongly coupled environmental states (causing an inhomogeneity) and weakly coupled bath states. The modulation of the reference mode is caused by transitions between the strongly coupled perturber states. These may be switched on with a different rate than they are switched off. Consequently, effects of energy of activation and the change in entropy for environmental transitions on the line shape can be analyzed. The spectral function as well as the relaxation function are discussed as a function of the relevant parameters such as the number of perturbers, the lifetime T1, the temperature, and transition rates.