Coherence Time Extension by Large-Scale Optical Spin Polarization in a Rare-Earth Doped Crystal

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Coherence Time Extension by Large-Scale Optical Spin Polarization in a Rare-Earth Doped Crystal

Sacha Welinski, Alexey Tiranov, Moritz Businger, Alban Ferrier, Mikael Afzelius, and Philippe Goldner

Phys. Rev. X 10, 031060 – Published 16 September 2020

Abstract

Optically addressable spins are actively investigated in quantum communication, processing, and sensing. Optical and spin coherence lifetimes, which determine quantum operation fidelity and storage time, are often limited by spin-spin interactions, which can be decreased by polarizing spins. Spin polarization can be achieved using optical pumping, large magnetic fields, or mK-range temperatures. Here, we show that optical pumping of a small fraction of ions with a fixed-frequency laser, coupled with spin-spin interactions and spin diffusion, leads to substantial spin polarization in a paramagnetic rare-earth doped crystal, ${}^{171}{Yb}^{3 +} ∶ Y_{2} {SiO}_{5}$ . Indeed, more than 90% spin polarization has been achieved at 2 K and zero magnetic field. Using this spin polarization mechanism, we further demonstrate an increase in optical coherence lifetime from 0.3 ms to 0.8 ms, due to a strong decrease in spin-spin interactions. This effect opens the way to new schemes for obtaining long optical and spin coherence lifetimes in various solid-state systems such as ensembles of rare-earth ions or color centers in diamond, which are of interest for a broad range of quantum technologies.

Received 10 December 2019
Revised 2 July 2020
Accepted 27 July 2020

DOI:https://doi.org/10.1103/PhysRevX.10.031060

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Optical coherence Quantum information processing Spin dynamics

Rare-earth doped crystals

Optical pumping

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Sacha Welinski ^1,*, Alexey Tiranov ^2,†, Moritz Businger², Alban Ferrier ^1,3, Mikael Afzelius², and Philippe Goldner^1,‡

¹Chimie ParisTech, PSL University, CNRS, Institut de Recherche de Chimie Paris, 75005 Paris, France
²Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
³Sorbonne Universités, Faculté des Sciences et Ingénierie, UFR 933, 75005 Paris, France

^*Present address: Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA.
^†Present address: The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark.
^‡philippe.goldner@chimieparistech.psl.eu

Popular Summary

Spins that can be manipulated by optical signals are among the most promising systems for technologies such as quantum sensing or quantum communication. For example, such optically active spins offer a bridge between light-based qubits, which can convey quantum information over long distances, and stationary spin-based qubits, which can act as quantum processors and memories. Here, we propose a novel scheme to significantly increase the so-called coherence lifetime of the spin and optical superposition states, a crucial parameter that should be as long as possible for high-fidelity quantum operations.

Coherence lifetimes, which are a measure of state stability, are often limited by magnetic noise caused by flipping spins. Techniques to reduce it are generally complex: They may use magnetic fields of several tesla or temperatures below 100 mK. Under such conditions, spins become highly polarized and magnetic noise is strongly reduced.

In this work, we propose a novel scheme to achieve noise-free systems that combines two effects. Optical excitation polarizes a small number of spins by population transfer through an excited state, and then spin-spin interactions diffuse this polarization to the other spins. We investigate this process in a rare-earth, ion-doped crystal. At a temperature of 2 K and zero magnetic field, we polarize a large ensemble of spins to over 90%, even though only 0.5% of spins are optically excited. This large-scale polarization results in a significant extension of optical coherence lifetime, thus confirming the drastic reduction of magnetic noise.

We believe that this scheme can be applied to a broad range of solid-state systems to achieve similar improvement in spin and optical coherence lifetimes for high-performance quantum technologies.

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Vol. 10, Iss. 3 — July - September 2020

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Figure 1
Diffusion enhanced optical pumping (DEOP) in ${}^{171}{Yb}^{3 +} ∶ Y_{2} {SiO}_{5}$ . (a) DEOP mechanism: Optically pumped spins (red circles) initially surrounded by spins in thermal equilibrium (blue circles) gradually polarize neighboring spins and spins that are further apart (yellow circles) through flip-flop interactions. (b) Energy diagram showing the ${}^{171}{Yb}^{3 +}$ hyperfine structure. (c) Absorption spectrum without (purple) and after 20 s of optical pumping (orange). The OP is along the $| 4 g ⟩ \to | 1 e ⟩$ transition [red arrow in panels (b) and (c)]. (d) Ground-state spin populations $k_{i g}$ , normalized by thermal equilibrium values, over the volume addressed by the laser without OP (top, purple, $k_{i g} = 1$ ) and after OP (bottom, orange, $k_{1 g}$ , $k_{2 g}$ , $k_{3 g}$ , $k_{4 g} = 1.67 \pm 0.30$ , $1.28 \pm 0.36$ , $1.01 \pm 0.12$ , $0.04 \pm 0.04$ ). (e) Enlarged regions 1 and 2 in panel (c) showing a narrow hole at the laser frequency ( $| 4 g ⟩ \to | 1 e ⟩$ ) and a corresponding antihole ( $| 2 g ⟩ \to | 3 e ⟩$ ).
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Figure 2
Dynamics of DEOP and spin-lattice relaxation. (a) Absorption profile around the $| 4 g ⟩ \leftrightarrow | 1 e ⟩$ transition after 0 s, 1 s, 3 s, 5 s, 7 s, 10 s, 30 s, and 40 s of OP at $- 0.17 GHz$ (light blue arrow). The whole inhomogeneously broadened absorption decreases when pumping duration increases. The laser creates a narrow spectral hole at $- 0.17 GHz$ , which is clearly seen for pump duration between 1 and 7 s. The small side hole at $+ 0.5 GHz$ originates from the $| 3 g ⟩$ level and should therefore appear as an antihole. This is explained by a fast relaxation between the $| 4 g ⟩$ and $| 3 g ⟩$ levels by flip-flop processes [32]. The absorption centered at $+ 0.655 MHz$ corresponds to the $| 3 g ⟩ \leftrightarrow | 1 e ⟩$ transition. (b) Normalized level $| 4 g ⟩$ population $k_{4 g}$ as a function of OP duration for different laser frequencies shown in panel (a) by color-coded arrows. Solid lines are exponential fits to the data (see text). (c) Spin- $1 / 2$ model scheme (see text). (d) Level $| 4 g ⟩$ normalized steady-state populations ( $k_{4 g}^{\infty}$ , red circles) and polarization rate ( $R_{P}$ , blue circles) as a function of the fraction of pumped ions (see text). Solid lines correspond to fits using a spin- $1 / 2$ model and rate equations. (e) Relaxation time $1 / R_{c}$ as a function of temperature deduced from absorption recovery after OP is stopped. The lines are fits using direct and two-phonon processes (see text). All error bars correspond to a 95% confidence interval.
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Figure 3
Optical coherence lifetime under DEOP. (a) Absorption spectra after 0, 1, and 10 s of OP at $- 1.44 GHz$ . Inset: Normalized ground-state populations $k_{1 g}$ , $k_{2 g}$ , $k_{3 g}$ , $k_{4 g} = 0.02 \pm 0.02$ , $2.30 \pm 0.12$ , $0.02 \pm 0.02$ , $1.70 \pm 0.06$ . (b) Absorption spectra after 0, 1, and 10 s of OP at $+ 2.67 GHz$ . Inset: Normalized ground-state populations $k_{1 g}$ , $k_{2 g}$ , $k_{3 g}$ , $k_{4 g} = 0.02 \pm 0.02$ , $0.02 \pm 0.02$ , $1.95 \pm 0.10$ , $2.05 \pm 0.08$ . (c) Photon echo decays under DEOP for the $| 4 g ⟩ \leftrightarrow | 1 e ⟩$ transition measured at $- 4.6 GHz$ [arrow in panels (a) and (b)]. Decay colors and numbers correspond to spectra in panels (a) and (b); solid lines are exponential fits to the data. (d) Optical coherence times $T_{2, o}$ deduced from fits in panel (c) (color-coded). All error bars correspond to a 95% confidence interval.
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Figure 4
Optical homogeneous linewidth $Γ_{h, o}$ of the $| 4 g ⟩ \leftrightarrow | 1 e ⟩$ transition at $- 4.6 GHz$ as a function of pumping time under DEOP. Optical pumping is set at $- 1.44 GHz$ [see Fig. 3]. The area under the curves represents contributions to $Γ_{h, o}$ from ${}^{171}{Yb}^{3 +}$ in site 2 (blue), other centers including ${}^{171}{Yb}^{3 +}$ in site 1 (orange), and the excited-state lifetime (yellow). The line drawn through experimental data points is a guide to the eye.
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