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arXiv:2011.05114 · Physical Review A

Optical and spin manipulation of non-Kramers rare-earth ions in a weak magnetic field for quantum memory applications

Jean Etesse, Adrian Holzäpfel, Antonio Ortu, Mikael Afzelius

Published Feb 26, 2021• 19 citations
arXivHTMLPDF

Abstract

Rare-earth ion doped crystals have proven to be solid platforms for implementing quantum memories. Their potential use for integrated photonics with large multiplexing capability and unprecedented coherence times is at the core of their attractiveness. The best performances of these ions are, however, usually obtained when subjected to a DC magnetic field, but consequences of such fields on the quantum memory protocols have only received little attention. In this paper, we focus on the effect of a DC bias magnetic field on the population manipulation of non-Kramers ions with nuclear quadrupole states, both in the spin and optical domains, by developing a simple theoretical model. We apply this model to explain experimental observations in a $^{151}\mathrm{Eu}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ crystal, and highlight specific consequences on the atomic frequency comb spin-wave protocol. The developed analysis should allows predicting optimal magnetic field configurations for various protocols.

DOI
10.1103/physreva.103.022618

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Rare-earth ion doped crystals have proven to be solid platforms for implementing quantum memories. Their potential use for integrated photonics with large multiplexing capability and unprecedented coherence times is at the core of their attractiveness. The best performances of these ions are, however, usually obtained when subjected to a DC magnetic field, but consequences of such fields on the quantum memory protocols have only received little attention. In this paper, we focus on the effect of a DC bias magnetic field on the population manipulation of non-Kramers ions with nuclear quadrupole states, both in the spin and optical domains, by developing a simple theoretical model. We apply this model to explain experimental observations in a 151Eu:Y2SiO5^{151}\mathrm{Eu}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}151Eu:Y2​SiO5​ crystal, and highlight specific consequences on the atomic frequency comb spin-wave protocol. The developed analysis should allows predicting optimal magnetic field configurations for various protocols.
Rare earth ion doped crystals are state-of-the-art platforms for processing quantum information, particularly thanks to their excellent optical and spin coherence properties at cryogenic temperatures. Experimental observations have shown that the application of a static magnetic bias field significantly improves the coherence times in the rare earth ions ensemble, but only a few studies have focused on its dependency as a function of both magnetic field direction and amplitude. This is especially true for magnetic field amplitudes under the mT, and for low magnetic dipole moment ions. In this paper, we investigate the relationship between the magnetic field parameters and the decoherence caused by magnetic dipole-dipole coupling with the nearest-neighbor nuclear spins in the crystal. The primary non-Kramers rare earth ions investigated here are europium and praseodymium, but we also extend our study to the ytterbium Kramers ion due to its low magnetic dipole in the mT range. We perform theoretical investigations and simulations of the energy structure and coherence time evolution and identify good correspondences between experimental and simulated spin echo data. This work allows us to pinpoint the most relevant decoherence mechanisms in the considered magnetic field regime, and to predict favorable magnetic configurations.
Spin dynamics are investigated in several rare-earth-ion-doped crystals, both for so-called Kramers ions and non-Kramers ions. I have studied two illustrative examples of such systems, Neodymium (Kramers) and Europium (non-Kramers). The main motivation behind these studies is the search for long relaxation and coherence times in solid state atomic ensembles. To this end I employ spectroscopic techniques to probe different kinds of interactions and relaxation mechanisms taking place in the samples. I perform spectroscopy of Neodymium (Kramers) in two different crystal lattices, yttrium orthosilicate and yttrium orthovanadate. I propose new methods to improve the relaxation lifetimes, and make precise characterizations of the interactions taking place within the atomic ensemble. In particular we achieve the most precise measurement of a kind of interaction which has received considerable attention recently in other areas of physics, the Dzyaloshinskii-Moriya interaction. These spectroscopic studies are of course of fundamental interest, but they can also be applied to quantum communication and computation. In this context, we were able to increase the efficiency of a quantum memory based on a Kramers ion (Nd) to be on par with the best non-Kramers (Eu,Pr) memories. Using Neodymium ions, I have certified that multi-dimensional entanglement can be stored in a quantum memory. The second part of this thesis concerns the study of Europium (non-Kramers), starting with a characterization of the Zeeman and quadrupole interactions. I believe these studies will pave the way for long duration (100 ms or more) quantum storage in a rare-earth-ion-doped crystal.
Without using any trapping lasers, rare-earth (RE) ions can be doped into some nanofabricated materials in form of nanocrystals in a solid state matrix, thus rendering a natural trap for potential application as a quantum computing device. In particular, passive nuclear spin states of RE ions can be utilized as (i) optical quantum memory (with huge density as yielded from nanocrystals), (ii) qubits by encoding in ground hyperfine states and operated as (iii) two-qubit gate when transferring them to active magnetized electronic states. A feasible implementation of qubits is realised by using those doped RE ions whose open-shell (for inner highly shielded 4f4 f4f shell electrons) energy levels and statevectors are well described by the crystal field (CF) interaction and hyperfine coupling in which the Hamiltonian is composed of various freeion interactions, the CF potential, electronic and nuclear Zeeman effects as well as the hyperfine interaction. For those qubit encoded in the two ground hyperfine states of RE ions, they can have fairly long lifetimes of days and coherence times (from 1.3s for Er3+\mathrm{Er}^{3+}Er3+ to 6 hours for Eu3+\mathrm{Eu}^{3+}Eu3+) due to the unique spectroscopic properties of RE ions. Because of the recent progress in optical single-ion detection for addressing individual qubits with a specific frequency channel, RE ions could be packed in a solid state 3D matrix at nanometer spacing, hence rendering very high qubit densities for quantum memories. Meanwhile, this configure also leads to strong dipole-dipole interactions (or high connectivity) between qubits which are not nearest neighbors. In this study, Kramers ions like 167Er{ }^{167} \mathbf{E r}167Er and 171Yb{ }^{171} \mathbf{Y b}171Yb doped in yttrium orthosilicate Y2SiO5{Y}_{2} {SiO}_{5}Y2​SiO5​ (YSO) nanocrystals will be investigated as a promising system for quantum computing because of their weak spin bath and possibility for being directly milled in single nanocrystals as nano-resonators. By using the famous Wien2k package to carry out the first-principles calculations, we can obtain the CF parameters and hyperfine constants as well as various electronic properties like energy gap and band structure for those Kramers RE ions doped in YSO. We shall present some essential findings from first-principles calculations to obtain various properties of the ground and excited CF and hyperfine states for those RE ions with an aim to optimize RE ions doping in YSO nanocrystals for quantum memories and qubits, contributing to scalable quantum computing architectures.
Rare-earth ion-doped crystals are promising systems for quantum communication and quantum information processing. In particular, paramagnetic rare-earth centers can be utilized to realize quantum coherent interfaces simultaneously for optical and microwave photons. In this paper, we study hyperfine and magnetic properties of a Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ crystal doped with 171Yb3+^{171}\mathrm{Yb}^{3+}171Yb3+ ions. This isotope is particularly interesting since it is the only rare--earth ion having electronic spin S=12S=\frac{1}{2}S=21​ and nuclear spin I=12I=\frac{1}{2}I=21​, which results in the simplest possible hyperfine level structure. In this work, we determine the hyperfine tensors for the ground and excited states on the optical $^{2}\mathrm{F}_{7/2}(0)\ensuremath{\longleftrightarrow}^{2}\mathrm{F}_{5/2}(0)$ transition by combining spectral hole burning and optically detected magnetic resonance techniques. The resulting spin Hamiltonians correctly predict the magnetic-field dependence of all observed optical-hyperfine transitions, from zero applied field up to fields where the Zeeman interaction is dominating the hyperfine interaction. Using the optical absorption spectrum, we can also determine the order of the hyperfine levels in both states. These results pave the way for realizing solid-state optical and microwave quantum memories based on a 171Yb3+:Y2SiO5^{171}\mathrm{Yb}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}171Yb3+:Y2​SiO5​ crystal.
A long-lived quantum memory is a firm requirement for implementing a quantum repeater scheme. Recent progress in solid-state rare-earth-ion-doped systems justifies their status as very strong candidates for such systems. Nonetheless an optical memory based on spin-wave storage at the single-photon level has not been shown in such a system to date, which is crucial for achieving the long storage times required for quantum repeaters. In this paper we show that it is possible to execute a complete atomic frequency comb (AFC) scheme, including spin-wave storage, with weak coherent pulses of $\overline{n}=2.5\ifmmode\pm\else\textpm\fi{}0.6$ photons per pulse. We discuss in detail the experimental steps required to obtain this result and demonstrate the coherence of a stored time-bin pulse. We show a noise level of $(7.1\ifmmode\pm\else\textpm\fi{}2.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ photons per mode during storage, and this relatively low noise level paves the way for future quantum optics experiments using spin waves in rare-earth-doped crystals.
Abstract Quantum memories with long storage times are key elements in long-distance quantum networks. The atomic frequency comb (AFC) memory in particular has shown great promise to fulfill this role, having demonstrated multimode capacity and spin–photon quantum correlations. However, the memory storage times have so-far been limited to about 1 ms, realized in a Eu3+ doped Y2SiO5 crystal at zero applied magnetic field. Motivated by studies showing increased spin coherence times under applied magnetic field, we developed an AFC spin-wave memory utilizing a weak 15 mT magnetic field in a specific direction that allows efficient optical and spin manipulation for AFC memory operations. With this field configuration the AFC spin-wave storage time increased to 40 ms using a simple spin-echo sequence. Furthermore, by applying dynamical decoupling techniques the spin-wave coherence time reaches 530 ms, a 300-fold increase with respect to previous AFC spin-wave storage experiments. This result paves the way towards long duration storage of quantum information in solid-state ensemble memories.