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Physical Review A

Atomic interference phenomena in solids with a long-lived spin coherence

Elena Kuznetsova, Olga A. Kocharovskaya, Philip Hemmer, Marlan O. Scully

Published Dec 6, 2002• 84 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.66.063802

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Conference on Lasers and Electro-Optics•Jan 1, 2018•1 citation
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.
We show for the first time an explicit expression of the linewidth of an EIT resonance in an inhomogeneously broadened three-level (Lambda) system, and the conditions for the dependence of the linewidth on a driving field strength. Both gaseous systems with the Doppler effect and solid media in which inhomogeneity of the crystalline field results in a broad distribution of atomic center frequencies are considered. We find two extreme cases: in one extreme the linewidth of EIT resonance is proportional to the intensity of a drive laser. And in the other it is proportional to the Rabi frequency of a drive laser, which recovers the result obtained by Feld and Javan. The dispersive properties of EIT, leading to slow group velocity of light, in an inhomogeneously broadened system are also considered.
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 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.
Summary form only given. Electromagnetically induced transparency (EIT) has been the subject of many experimental and theoretical studies over recent years. Most recently, substantial experimental and theoretical work in this area has been focused on the use of EIT to give ultraslow group velocities for light in both ultracold atomic gas and hot atomic vapors. Much of this interest is based on the fact that slowing the group velocity of a laser pulse down to the speed of sound in the same material can produce strong coupling between acoustic waves and the electromagnetic field. It has been suggested that a giant nonlinearity obtained by this method might be utilized for efficient multi-wave mixing and quantum nondemolition measurements. Slow light might also allow a very efficient nonlinear interaction between laser pulses of extremely low (down to a single photon) energies. Here, we report the first direct observation of an ultraslow group velocity of light down to 45 m/s in a solid, well below the speed of sound in the medium. This group velocity is fundamentally limited only by the inhomogeneous broadening of the ground state transition. At low coupling beam intensities, the fraction of centers that are pumped into the "dark state" increases with coupling laser power, so that the observed group delay is increasing with coupling beam intensity. At higher intensities, power broadening reduces the sharpness of the dispersive feature and the observed group delay decreases.
Summary form only given. Experiments in nonlinear optics and spectroscopy are often performed in atomic vapors, where the linewidths of the transitions of interest are dominated by Doppler broadening. In fact, several experiments on quantum coherent phenomena, such as lasing without inversion (LWI), and electromagnetically induced transparency (EIT), have been done in atomic vapors. Using the ideas of quantum coherence and interference, we propose a new scheme for obtaining subDoppler resolution at one transition of an inhomogeneously broadened, three-level atomic system, by use of an intense control field at the other transition.