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arXiv:1710.07591 · Physical review. B./Physical review. B

Characterization of the hyperfine interaction of the excited D05 state of Eu3+:Y2SiO5

Emmanuel Zambrini Cruzeiro, Jean Etesse, Alexey Tiranov, Pierre-Antoine Bourdel, Florian Fröwis, Philippe Goldner, Nicolas Gisin, Mikael Afzelius

Published Mar 16, 2018• 22 citations
arXivHTMLPDF

Abstract

We characterize the europium $({\mathrm{Eu}}^{3+})$ hyperfine interaction of the excited state $(^{5}\mathrm{D}_{0})$ and determine its effective spin Hamiltonian parameters for the Zeeman and quadrupole tensors. An optical free induction decay method is used to measure all hyperfine splittings under a weak external magnetic field (up to 10 mT) for various field orientations. On the basis of the determined Hamiltonian, we discuss the possibility to predict optical transition probabilities between hyperfine levels for the $^{7}\mathrm{F}_{0}\ensuremath{\longleftrightarrow}^{5}\mathrm{D}_{0}$ transition. The obtained results provide necessary information to realize an optical quantum memory scheme which utilizes long spin coherence properties of $^{151}\mathrm{Eu}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ material under external magnetic fields.

DOI
10.1103/physrevb.97.094416

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We characterize the europium (Eu3+)({\mathrm{Eu}}^{3+})(Eu3+) hyperfine interaction of the excited state (5D0)(^{5}\mathrm{D}_{0})(5D0​) and determine its effective spin Hamiltonian parameters for the Zeeman and quadrupole tensors. An optical free induction decay method is used to measure all hyperfine splittings under a weak external magnetic field (up to 10 mT) for various field orientations. On the basis of the determined Hamiltonian, we discuss the possibility to predict optical transition probabilities between hyperfine levels for the 7F0\ensuremath⟷5D0^{7}\mathrm{F}_{0}\ensuremath{\longleftrightarrow}^{5}\mathrm{D}_{0}7F0​\ensuremath⟷5D0​ transition. The obtained results provide necessary information to realize an optical quantum memory scheme which utilizes long spin coherence properties of 151Eu3+:Y2SiO5^{151}\mathrm{Eu}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}151Eu3+:Y2​SiO5​ material under external magnetic fields.
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.
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 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.
We present characterization of the hyperfine interaction for the europium in hydrated europium chloride and as a dopant in yttrium orthosilicate. The Zeeman and pseudoquadrupole tensors were determined by measuring the hyperfine splittings while rotating the direction of a weak $(\ensuremath{\sim}300\phantom{\rule{0.3em}{0ex}}\mathrm{G})$ magnetic field. The hyperfine spectra were recorded using Raman-heterodyne spectroscopy, an radio-frequency optical double resonance technique. For both materials magnetic field values were identified where there is no first order Zeeman shift in a europium hyperfine transition. These field insensitive transitions will have application in achieving very long hyperfine coherence times.
This thesis investigates the coherence properties of the hyperfine transitions of the 151Eu3+ ions in Eu3+:Y2SiO5 and evaluates the potential of developing quantum memories using these transitions. Quantum memories for light with long storage times are required for quantum commu- nication applications. For these memories to be useful they need to have storage times long compared to the transmission times across the communication network. For a global optical communication network this requires storage time longer than 100 ms. Rare-earth doped crystals have been identified as a suitable storage material. The storage time of these systems is limited by the coherence time of the hyperfine transitions of the optically active rare-earth ions. In previous work it had been demonstrated that coherence times as long as 1.4 seconds could be achieved for hyperfine transitions in Pr3+:Y2SiO5 by ap- plying a particular magnetic field such that the first order Zeeman shift of the transition nulled. This technique is known as zero first-order Zeeman (ZEFOZ). Due to the relatively large second order Zeeman efficient of the transitions in Pr3+:Y2SiO5, an extension of the coherence time, significantly beyond the 1.4 second mark using ZEFOZ, is not expected. However, it has been predicted that coherence times more than two orders of magnitude longer could be achieved in Eu3+:Y2SiO5 due to the smaller second order Zeeman shifts associated with the relevant hyperfine transitions. The dominant decoherence mechanism for the hyperfine transitions in diluted Eu3+:Y2SiO5 is the magnetic field perturbations caused by the random spin reconfigu- ration of the Y3+ ions in the host. By applying the ZEFOZ technique, previously used in Pr3+:Y2SiO5, the sensitivity of the transition’s frequency to environmental magnetic field perturbations was significantly reduced. Further, this strong ZEFOZ magnetic field was also shown to induce a frozen core around the Eu3+ ion, which resulted in a signifi- cant suppression of the reconfiguration of the nearby Y3+ spins. The combined effect of the reduced sensitivity and frozen core effect allowed a decoherence rate of 8 × 10−5 s−1 over 100 milliseconds to be demonstrated. The observed decoherence rate is at least an order of magnitude lower than that of any other system suitable for an optical quantum memory. Furthermore, by employing dynamic decoherence control, a coherence time of 370 ± 60 minutes was achieved. This 6 hour coherence time observed here opens up the possibility of distributing quantum entanglement via the physical transport of memories as an alternative to optical communications. It was found that even at the critical point alignment the observed coherence times showed that the Y3+ spin flips remain the dominant decoherence mechanism. To aid in the development of future strategies to further extend the coherence time beyond 6 hours, a study of the Y3+ spin dynamics in the frozen core was conducted. Four of the Y3+ sites were resolved and a complete mapping of all frozen-core Y3+ sites was limited by the inhomogeneity of the applied magnetic field. The Rabi frequency, the coherence time and lifetime as well as the interaction strength with the Eu3+ ion of one of these Y3+ ions were measured. The observed lifetime of the Y3+ ion is 27 s, which is four orders of magnitude longer than the low field value. With the technique developed, a detailed understanding of the frozen-core dynamics is possible, which would allow an extension of the hyperfine coherence time of the Eu3+ ion towards the lifetime limit. In summary, this thesis provides a detailed characterisation of the decoherence mecha- nisms of the hyperfine transitions in Eu3+:Y2SiO5. The potential of using rare-earth doped crystals for the long-term storage of quantum information with applications to long-range quantum communications is identified. The demonstrated long coherence time of the quantum transitions for information storage allows a new way of entanglement distribu- tion: entanglement is transported by physically transporting the memory crystal rather than the light. This approach opens a new regime for both quantum communication and fundamental tests of quantum mechanics.
Rare-earth doped crystals are promising systems for quantum information processing. In particular, paramagnetic rare earths could be used to build coherent interfaces with optical and microwave photons. In addition, isotopes with nonzero nuclear spins could provide long-lived states for quantum state storage and processing. Yb3+{\mathrm{Yb}}^{3+}Yb3+ is particularly interesting in this respect since it is the only paramagnetic rare earth with a spin-12\frac{1}{2}21​ isotope, which corresponds to the simplest possible level structure. In this paper, we report on the optical and magnetic properties of Yb3+{\mathrm{Yb}}^{3+}Yb3+ in the two sites of Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​, a commonly used crystal for quantum applications. We measured optical inhomogeneous linewidths, peak absorption coefficients, oscillator strengths, and excited-state lifetimes. The Zeeman tensors were also determined in the ground and excited states, as well as the ground-state hyperfine tensor for the 171Yb3+^{171}\mathrm{Yb}^{3+}171Yb3+ (I=12I=\frac{1}{2}I=21​) isotope. These results suggest that Yb3+{\mathrm{Yb}}^{3+}Yb3+:Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ is a promising material for applications like solid-state optical and microwave quantum memories.