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arXiv:1808.01227 · Physical Review A

Electromagnetically induced transparency in inhomogeneously broadened solid media

Haoquan Fan, Kumel H. Kagalwala, Sergey V. Polyakov, Alan L. Migdall, Elizabeth A. Goldschmidt

Published May 15, 2019• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.99.053821

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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.
We generalize the theory of electromagnetically induced transparency (EIT) and slow group velocity for the case of the homogeneous and inhomogeneous line broadening in both one- and two-photon transitions which unavoidably takes place in solid materials with a long-lived spin coherence. We identify regimes of EIT where the linewidth can be essentially reduced due to inhomogeneous broadening and, moreover, can be proportional to the amplitude of the driving field rather than the intensity. We suggest also a class of solid materials, namely, rare-earth ion doped semiconductors or dielectrics with electricdipole allowed transitions, that is very promising for realization and applications of EIT.
Electromagnetically induced transparency (EIT) is a phenomenon that can provide strong and robust interfacing between optical signals and quantum coherence of electronic spins. In its archetypical form, mainly explored with atomic media, it uses a (near-)homogeneous ensemble of three-level systems, in which two low-energy spin-1/2 levels are coupled to a common optically excited state. We investigate the implementation of EIT with c-axis divacancy color centers in silicon carbide. While this material has attractive properties for quantum device technologies with near-IR optics, implementing EIT is complicated by the inhomogeneous broadening of the optical transitions throughout the ensemble and the presence of multiple ground-state levels. These may lead to darkening of the ensemble upon resonant optical excitation. Here, we show that EIT can be established with high visibility also in this material platform upon careful design of the measurement geometry. Comparison of our experimental results with a model based on the Lindblad equations indicates that we can create coherences between different sets of two levels all-optically in these systems, with potential impact for RF-free quantum sensing applications. Our work provides an understanding of EIT in multi-level systems with significant inhomogeneities, and our considerations are valid for a wide array of defects in semiconductors.
Electromagnetically induced transparency (EIT) is a phenomenon that can provide strong and robust interfacing between optical signals and quantum coherence of electronic spins. In its archetypical form, mainly explored with atomic media, it uses a (near-)homogeneous ensemble of three-level systems, in which two low-energy spin-1/2 levels are coupled to a common optically excited state. We investigate the implementation of EIT with c-axis divacancy color centers in silicon carbide. While this material has attractive properties for quantum device technologies with near-IR optics, implementing EIT is complicated by the inhomogeneous broadening of the optical transitions throughout the ensemble and the presence of multiple ground-state levels. These may lead to darkening of the ensemble upon resonant optical excitation. Here, we show that EIT can be established with high visibility also in this material platform upon careful design of the measurement geometry. Comparison of our experimental results with a model based on the Lindblad equations indicates that we can create coherences between different sets of two levels all-optically in these systems, with potential impact for RF-free quantum sensing applications. Our work provides an understanding of EIT in multi-level systems with significant inhomogeneities, and our considerations are valid for a wide array of defects in semiconductors.
We study Lambda-type electromagnetically induced transparency (EIT) in cryogenically-cooled, europium and praseodymium doped yttrium orthosilicate (Eu:YSO and Pr:YSO). We use spectral hole burning techniques to vary the optical inhomogeneous width of the sub-ensemble of atoms participating in the EIT. The effect of inhomogeneous broadening has been studied in the context of Doppler broadened gases, but less so in solids where motional effects are absent and the coherence is not limited by the transit of atoms through the optical field. Rare earth doped crystals, like many solid-state systems, exhibit spectral hole burning in which a narrowband laser field optically pumps atoms to states in the ground manifold that are dark with respect to the applied field, opening up a transparency window that persists after the pumping laser is shuttered. More complex sequences of fields at multiple frequencies can create arbitrary spectral profiles, within bounds set by the particular energy level structure of the atoms. For both Eu:YSO and Pr:YSO, there are three hyperfine ground states and three hyperfine excited states (at zero magnetic field) and all nine transitions are dipole-allowed with varying transition strengths. We use spectral hole-burning techniques to prepare a sub-ensemble of atoms in a particular frequency class and a particular ground spin state, while also pumping atoms out of another ground state to create a Lambda system. We observe the same functional dependence of the EIT width on the optical inhomogeneous width and independently calibrated control field Rabi frequency in both systems.
Strong evidence indicating the occurrence of electromagnetically induced transparency (EIT) in a solid medium was found. Fluorescence reduction due to EIT was observed in solids. The excitation intensity dependence of the fluorescence reduction was found to be consistent with theoretical predictions for EIT. It was experimentally demonstrated that the essential condition for the observation of EIT in solids is that the Rabi frequency of excitation must be larger than the inhomogeneous width of the transition between the two states coupled to the third state by the pair of optical fields.