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Journal of the Optical Society of America B

Analysis of quantum interference properties in Λ- and V-type schemes in rare-earth-ion-doped crystal with inhomogeneous broadening

Yong Zhou, Lingrui Chu, Qi Liu, Chuan‐Kui Wang, Chaohua Tan

Published Aug 20, 2019• 3 citations
Publisher

Abstract

We make a systematic analytical study on the quantum interference properties of two typical energy configuration systems (i.e., Λ- and V-type) in rare-earth-ion-doped crystal with inhomogeneous broadening. We show that the destructive quantum interference exists in the Λ-type system for the weak control field, and can lead to a transparency window in the absorption spectrum, i.e., the phenomenon of electromagnetically induced transparency. When the intensity of the control field is strong, the contribution of the quantum interference is negligibly small, the absorption doublet is mainly caused by the Autler–Townes splitting effect. For the V-type system, the transparency window opened in the absorption spectrum is due to the saturated absorption, and meanwhile, the quantum interference is constructive. The results obtained may have practical applications in solid-state all-optical quantum information processing and transformation.

DOI
10.1364/josab.36.002534

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We make a systematic analytical study on the quantum interference properties of two typical energy configuration systems (i.e., Λ- and V-type) in rare-earth-ion-doped crystal with inhomogeneous broadening. We show that the destructive quantum interference exists in the Λ-type system for the weak control field, and can lead to a transparency window in the absorption spectrum, i.e., the phenomenon of electromagnetically induced transparency. When the intensity of the control field is strong, the contribution of the quantum interference is negligibly small, the absorption doublet is mainly caused by the Autler–Townes splitting effect. For the V-type system, the transparency window opened in the absorption spectrum is due to the saturated absorption, and meanwhile, the quantum interference is constructive. The results obtained may have practical applications in solid-state all-optical quantum information processing and transformation.
Abstract In this paper, we present a theoretical analysis of the burning of a narrow transparency window on the enhanced absorption spectrum of a probe laser in a triple resonance configuration visualized as a V-type plus a two-level system. The transparency window is due to coherence effects causing electromagnetically induced transparency (EIT) in a V-type system (i.e. Autler–Townes splitting plus quantum interference), for atomic vapor at a finite temperature. Additionally, the EIT window is enhanced by velocity induced population oscillation effect, velocity selective saturation effect, optical pumping effect (a source of ground state level population dynamics) and wavelength mismatch of the resonant laser fields forming a V-type configuration.
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.
We first calculated the negative refractive index on the solid Er3+：YAlO3 crystal with a Λ-type four-level scheme proposed for atomic vapour by Thommen and Mandel and Kastel using quantum interference and electromagnetically induced transparency （EIT）. It is shown that the frequency band with the negative index is wider （～1 MHz） than that reported previously. Usually，Im［n］ is always positive，corresponding to absorption，and the ratio of refraction to absorption，|Re［n］/Im［n］|，is only of the order of unity. In our case the ratio |Re［n］/Im［n］|=4.6，which indicates that the absorption has been well suppressed by EIT approach. The negative Im［n］ may be related to the stimulated emission of 4I13/2→4I15/2 of rare earth ion Er3+. It indicates that the rare earth ion doped material with abundant energy levels and various electric and magnetic transitions is an outstanding and practical candidate for electromagnetically induced negative refractive index material.
Abstract Electromagnetically induced transparency (EIT) in five-level atomic systems is theoretically investigated for three representative configurations: M-, inverted-Y, and K-type systems driven by a weak probe field and three control laser fields. The different coupling schemes produce different quantum interference pathways and two-photon resonance conditions, leading to markedly different EIT spectra. The M-type configuration exhibits one, two, and three well-resolved transparency windows as successive control fields are introduced. In contrast, the inverted-Y configuration produces broader transparency windows because of the overlap of multiple interference channels, whereas the K-type configuration exhibits only a single EIT window when all control fields are resonant. Multiple transparency windows in the K-type system appear after introducing appropriate coupling-field detunings. Doppler broadening at room temperature significantly broadens the absorption spectrum and reduces the transparency depth, while preserving the number and positions of the EIT windows. These results demonstrate that the coupling scheme plays an important role in determining the formation and evolution of multi-window EIT spectra and identify the characteristics of the three five-level configurations for multi-channel quantum-optical applications, as well as for the experimental observation of EIT spectra in five-level configurations.
We report the experimental observation of a slow-light information conversion via electromagnetically induced transparency (EIT) in a rare-earth-ion-doped solid. Under the EIT-based slow-light regime, by manipulating the spectrum of the control fields, the slowed light pulse is transformed into two different frequency-spatial channels. The pulse shapes and energies in two output channels are further studied. This slow-light information conversion can be used as a controllable frequency-spatial multiplexing of the quantum state of the optical field and will be important in information processing and all-optical networks.