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Physical Review A

Linear and nonlinear crystal optics using the magnetic field of light

Zachary Noel Buckholtz, Deniz D. Yavuz

Published Feb 18, 2020• 3 citations
Publisher

Abstract

We study the $^{7}F_{0}\ensuremath{\rightarrow}^{5}D_{1}$ magnetic-dipole transition in the $4f$ shell of europium ions at a wavelength of 527.5 nm and demonstrate spectral hole burning, ion class selection, and optical pumping to specific ground hyperfine states. We then use the narrow lines of the selected ions to observe linear group delay of a weak probe pulse with a group velocity of $c/3800$. We also demonstrate electromagnetically induced transparency by establishing a $\mathrm{\ensuremath{\Lambda}}$ scheme between the ground hyperfine levels and driving the ions to a dark state.

DOI
10.1103/physreva.101.023831

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We study the 7F0\ensuremath→5D1^{7}F_{0}\ensuremath{\rightarrow}^{5}D_{1}7F0​\ensuremath→5D1​ magnetic-dipole transition in the 4f4f4f shell of europium ions at a wavelength of 527.5 nm and demonstrate spectral hole burning, ion class selection, and optical pumping to specific ground hyperfine states. We then use the narrow lines of the selected ions to observe linear group delay of a weak probe pulse with a group velocity of c/3800c/3800c/3800. We also demonstrate electromagnetically induced transparency by establishing a \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ scheme between the ground hyperfine levels and driving the ions to a dark state.
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 have employed spectral-hole-burning, coherent-transient, and optical-rf double-resonance techniques to measure various parameters associated with the 580.8-nm 7F0^{7}\mathrm{F}_{0}7F0​${\mathrm{\ensuremath{-}}}^{5}$D0{\mathrm{D}}_{0}D0​ transition of Eu3+{\mathrm{Eu}}^{3+}Eu3+ doped into Y2{\mathrm{Y}}_{2}Y2​O3{\mathrm{O}}_{3}O3​. In particular, we have measured the hyperfine splittings of the terminal levels (for both 151Eu^{151}\mathrm{Eu}151Eu and 153Eu^{153}\mathrm{Eu}153Eu), an effective thermalization rate of the ground-state (7{(}^{7}(7F0{\mathrm{F}}_{0}F0​) hyperfine manifold over the temperature range of \ensuremath{\simeq}4--15 K, and the homogeneous linewidth of the optical transition over the range of \ensuremath{\simeq}14--35 K. Large ratios of inhomogeneous to homogeneous linewidth at elevated temperatures (103{10}^{3}103 at 25 K) and long ground-state hyperfine thermalization times (>30 h at 4 K) make this an interesting crystal in the context of spectrally addressable optical memories.
The $^{2}F_{7/2}\ensuremath{\leftrightarrow}^{2}F_{5/2}$ optical transitions of Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+ doped into Y3Al5O12{\mathrm{Y}}_{3}\mathrm{A}{\mathrm{l}}_{5}{\mathrm{O}}_{12}Y3​Al5​O12​ (YAG) were studied for potential quantum information and photonic signal processing applications. Absorption and fluorescence spectroscopy located the energy levels of the ground 2F7/2^{2}F_{7/2}2F7/2​ and excited 2F5/2^{2}F_{5/2}2F5/2​ manifolds, allowing inconsistencies between previous assignments of crystal field splittings in the literature to be resolved. These measurements reveal an unusually large splitting between the first and second levels in both the ground and excited multiplets, potentially providing for reduced sensitivity to thermally induced decoherence and spin-lattice relaxation. Spectral hole burning through two-level saturation was observed, determining the excited state lifetime to be 860 \ensuremath{\mu}s and resolving ambiguities in previous fluorescence measurements that were caused by the large radiation trapping effects in this material. Optical decoherence measurements using two-pulse photon echoes gave a homogeneous linewidth of 18 kHz for an applied magnetic field of 1 T, narrowing to 5 kHz at 2.5 T. The observed decoherence was described by spectral diffusion attributed to $\mathrm{Y}{\mathrm{b}}^{3+}\mathrm{\ensuremath{-}}\mathrm{Y}{\mathrm{b}}^{3+}$ magnetic dipole interactions. Laser absorption determined an inhomogeneous linewidth of 3.6 GHz for this transition in this 0.05%-doped crystal, which is narrower than for any other rare-earth-ion transition previously studied in the YAG host. The temperature dependence of the transition energy and linewidth of the lowest 2F7/2^{2}F_{7/2}2F7/2​ to lowest 2F5/2^{2}F_{5/2}2F5/2​ transition centered at 968.571 nm measured from 4 K to 300 K was well described by phonon scattering at higher temperatures, with an additional anomalous linear temperature-dependent broadening at temperatures below 80 K. Two magnetically inequivalent subgroups of Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+ ions were identified when a magnetic field was applied along the $\ensuremath{\langle}111\ensuremath{\rangle}$ axis, as expected for the D2{D}_{2}D2​ sites in the cubic symmetry crystal, with ground and excited state effective ggg-values of gg=3.40{g}_{\mathrm{g}}=3.40gg​=3.40 (3.34) and ge=1.04{g}_{\mathrm{e}}=1.04ge​=1.04 (2.01), respectively. Together with the convenient diode laser wavelength of this transition, our study suggests that Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+:YAG is a promising material system for spectral hole burning and quantum information applications.
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Europium-doped crystal Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ is an interesting platform for optical quantum memories, due to its long optical and spin coherence times. In this work, we investigate 151Eu3+:Y2SiO5{^{151}\mathrm{Eu}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}151Eu3+:Y2​SiO5​ under the application of magnetic field, a complex system with 36 different optical-hyperfine transitions. We present a simple numerical simulator for calculating the effect of optical pumping schemes that allow the isolation of a single-frequency class of ions, applicable to any multilevel atom with inhomogeneous broadening. Experimentally, we develop methodologies for estimating the magnetic field vector, demonstrating high precision in predicting spectral features based on the known spin Hamiltonians. We measured the optical Rabi frequency of 21 transitions among the 36 possible optical-hyperfine transitions, allowing for the construction of a $6\ifmmode\times\else\texttimes\fi{}6$ branching ratio matrix of relative transition strengths. From the Rabi frequency measurements, we derive the optical dipole moment for the $^{7}F_{0}\ensuremath{\leftrightarrow}^{5}D_{0}$ transition, yielding a value of $(6.94\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}33}\phantom{\rule{0.28em}{0ex}}\mathrm{C}\phantom{\rule{0.16em}{0ex}}\mathrm{m}$. Our results provide a critical test of the spin Hamiltonian models, demonstrating high precision in predicting energy levels and relative transition strengths, which are key abilities for quantum applications with 151Eu3+:Y2SiO5{^{151}\mathrm{Eu}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}151Eu3+:Y2​SiO5​ under magnetic field.
We report an experimental observation of narrow and high-contrast spectra, which are induced by interacting dark resonances and have been predicted in Phys. Rev. A 60, 3225 (1999). Spectra are measured with cold 87Rb{}^{87}\mathrm{Rb}87Rb atoms produced by a magneto-optical trap. In this experimental system, a coupling laser and a weak probe laser form a three-level \ensuremath{\Lambda}-type configuration of electromagnetically induced transparency (EIT); a microwave drives a magnetic-dipole transition between the fourth level and the ground state that is coupled with the excited state by the coupling laser. The observed spectral profile of probe absorption exhibits a very sharp peak emerging inside a narrow EIT dip. Such spectral feature provides more opportunities in manipulating atomic-optical response.