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arXiv:1601.05013 · Physical Review Letters

Ultranarrow Optical Inhomogeneous Linewidth in a Stoichiometric Rare-Earth Crystal

Rose L. Ahlefeldt, Michael Hush, Matthew J. Sellars

Published Dec 15, 2016• 63 citations
arXivHTMLPDF

Abstract

We obtain a low optical inhomogeneous linewidth of 25 MHz in the stoichiometric rare-earth crystal EuCl_{3}·6H_{2}O by isotopically purifying the crystal in ^{35}Cl. With this linewidth, an important limit for stoichiometric rare-earth crystals is surpassed: the hyperfine structure of ^{153}Eu is spectrally resolved, allowing the whole population of ^{153}Eu^{3+} ions to be prepared in the same hyperfine state using hole-burning techniques. This material also has a very high optical density, and can have long coherence times when deuterated. This combination of properties offers new prospects for quantum information applications. We consider two of these: quantum memories and quantum many-body studies. We detail the improvements in the performance of current memory protocols possible in these high optical depth crystals, and describe how certain memory protocols, such as off-resonant Raman memories, can be implemented for the first time in a solid-state system. We explain how the strong excitation-induced interactions observed in this material resemble those seen in Rydberg systems, and describe how these interactions can lead to quantum many-body states that could be observed using standard optical spectroscopy techniques.

DOI
10.1103/physrevlett.117.250504

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We obtain a low optical inhomogeneous linewidth of 25 MHz in the stoichiometric rare-earth crystal EuCl_{3}·6H_{2}O by isotopically purifying the crystal in ^{35}Cl. With this linewidth, an important limit for stoichiometric rare-earth crystals is surpassed: the hyperfine structure of ^{153}Eu is spectrally resolved, allowing the whole population of ^{153}Eu^{3+} ions to be prepared in the same hyperfine state using hole-burning techniques. This material also has a very high optical density, and can have long coherence times when deuterated. This combination of properties offers new prospects for quantum information applications. We consider two of these: quantum memories and quantum many-body studies. We detail the improvements in the performance of current memory protocols possible in these high optical depth crystals, and describe how certain memory protocols, such as off-resonant Raman memories, can be implemented for the first time in a solid-state system. We explain how the strong excitation-induced interactions observed in this material resemble those seen in Rydberg systems, and describe how these interactions can lead to quantum many-body states that could be observed using standard optical spectroscopy techniques.
We report the optical study of europium nitrate hexahydrate crystals Eu(NO 3 ) ⋅ 3 6H 2 O and their deuterated version Eu(NO 3 ) ⋅ 3 6D 2 O conducted at 50 mK. The crystals show sub-GHz inhomogeneous linewidths for the F 0 7 ↔ 5 D 0 transition and optical coherence times up to 136 μs for the non-deuterated crystal and 750 μs for the deuterated one. In addition, using the spectral hole burning technique, the hyperfine splittings in the absence of an external field have been estimated for the ground and optical levels. These results suggest that rare-earth nitrate crystals could represent a promising class of materials for quantum information applications as well as for fundamental physics experiments requiring narrow optical transitions and good coherence properties. • Deuterated and non-deuterated europium nitrate crystals were grown using the slow-cooling method. • Optical coherence times up to 0.75 ms were measured at 50 mK using the photon echo technique. • Sub-GHz optical inhomogeneous linewidths were observed. • The hyperfine splittings of the ground and optical states were assessed via spectral hole burning.
Rare-earth emitters in solids are well suited for implementing efficient, long-lived quantum memory coupled to integrated photonics for scalable quantum technologies. They are typically introduced as dopants in a solid-state host, but this introduces disorder and limits the available density of emitters. Stoichiometric materials can offer high densities with narrow optical linewidths. The regular spacing of emitters also opens possibilities for quantum information processing and collective effects. Here, we show narrow optical linewidths in a layered stoichiometric crystalline material, NaEu(IO_{3})_{4}. We observed an inhomogeneous linewidth of 2.2(1) GHz and a homogeneous linewidth of 120(4) kHz. Using spectral hole-burning techniques, we observe a hyperfine spin lifetime of 1.9(4) s. Furthermore, we demonstrate an atomic frequency comb delay of up to 800 ns.
Dense rare-earth spin ensembles in solids offer strong collective light-matter coupling for scalable quantum technologies but are typically incompatible with long coherence times due to strong dipolar interactions. Here we challenge this paradigm by showing long-lived coherence in such systems. In a stoichiometric EuCl_{3}·6H_{2}O crystal, we achieve hyperfine coherence times T_{2}^{CPMG} of up to 15 s at 4 K, extending the zero-field value T_{2} of 1.28 ms by more than four orders of magnitude using dynamical decoupling at a zero-first-order Zeeman (ZEFOZ) transition. Homogeneous linewidth measurements reveal a substantial suppression of resonant Eu^{3+}-Eu^{3+} spin interactions introduced by the full concentration near the ZEFOZ point. Coherence remains resilient to strong local perturbations, with a 32 ms coherence time for Eu^{3+} ions adjacent to Er^{3+} dopants. These results establish stoichiometric rare-earth crystals as a promising platform for quantum memories and spin-photon interfaces, demonstrating that intrinsically high optical depth and long-lived spin coherence can coexist in a fully concentrated ensemble.
This thesis presents a spectroscopic study of the 7F0 ---t5D0 transition of Eu3+ in EuC13 ·6H2 0, which is used to evaluate the potential performance of a quantum com­ puting system implemented in EuCla·6H2 0 and, more generally, in stoichiometric rare earth crystals. EuC13 ·6H2 0 has one of the narrowest optical inhomogeneous linewidths of any solid but this linewidth is shown to be still much larger than that required for practical quantum computing in a rare earth crystal. To assess the possibility of reducing the linwidth, the contributions of isotopic impurities to both the optical linewidth and line structure were investigated, and ligand isotopes were identified as a major source of both inhomogeneous broadening and structure on the optical transition, suggesting that the linewidth could be substantially reduced by isotopi­ cally purifying EuC13 ·6H20. The effect of ligand isotopes on the optical lifetime and coherence time was also investigated. It was found that fully deuterating the crystal to EuC13·6D20 substantially improves both the lifetime and coherence time. The satellite lines formed in the optical spectrum of a rare earth crystal when it is doped with another rare earth are proposed as qubits. A crucial step in char­ acterising EuCla ·6H20 for quantum computing is associating these satellite lines in EuC13 ·6H2 0 with crystallographic sites. A new method for associating sites with lines, which works for low symmetry crystals such as EuC13·6H20, is presented. This method involves modelling the splitting of the ground state hyperfine levels caused by the magnetic dipole-dipole interaction between a Kramers dopant and the Eu3+ ion. Using this method, most of the outer satellite lines in rare earth doped EuCla·6H2 0 were assigned to crystallographic sites. It has been proposed that the electronic interactions between these satellite lines be used to enact two-qubit gates in a rare earth quantum computer. These interac­ tions were measured between a number of different satellite lines using a new two­ laser spectral holeburning technique. Interactions of up to 46.081±0.005 MHz were observed, and this was the first time that electronic interactions between weakly coupled rare earth ions had been measured. The two most common interactions identified between rare earth ions in solids are electric dipole-dipole and exchange, but the observed interactions are stronger than expected from a electric dipole-dipole model and occur at too large a distance to be superexchange. It is shown that the development of a moderate-sized quantum processor, one with more than 10 qubits, in a stoichiometric rare earth crystal is feasible provided that the optical inhomogeneous linewidth is reduced below 1MHz. Demonstrations of three or four qubit devices should be possible using existing materials.
Slow-light-enhanced Atomic Frequency Comb Quantum Memory in Stoichiometric EuCl3⋅_3 \cdot3​⋅ 6D2_22​O
Rare-earth-doped crystals are promising candidates for quantum storage, yet their performance in free-space configurations is fundamentally restricted by low optical depth. Here, we demonstrate high-efficiency quantum storage in a stoichiometric EuCl3⋅_3 \cdot3​⋅ 6D2_22​O crystal, which intrinsically provides high optical density without the complexity of cavity implementation. We show that in this high-density regime, the system exhibits significant slow-light-like effects, including dispersion-induced echo delays and finesse-dependent echo intensity modulation. We develop a unified theoretical framework showing how absorption and dispersion work in concert to mediate echo generation. We achieve storage efficiencies of 42.9% for classical light and 34.4% for weak coherent pulses, alongside 90% efficiency for slow-light storage. These findings validate EuCl3⋅_3 \cdot3​⋅ 6D2_22​O as a robust platform, establishing a viable pathway for scalable solid-state quantum memory.