Enhancing Spin Coherence in Optically Addressable Molecular Qubits through Host-Matrix Control

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Enhancing Spin Coherence in Optically Addressable Molecular Qubits through Host-Matrix Control

S. L. Bayliss, P. Deb, D. W. Laorenza, M. Onizhuk, G. Galli, D. E. Freedman, and D. D. Awschalom

Phys. Rev. X 12, 031028 – Published 18 August 2022

See synopsis: Shielding Qubits with Chemistry

Abstract

Optically addressable spins are a promising platform for quantum information science due to their combination of a long-lived qubit with a spin-optical interface for external qubit control and readout. The ability to chemically synthesize such systems—to generate optically addressable molecular spins—offers a modular qubit architecture which can be transported across different environments and atomistically tailored for targeted applications through bottom-up design and synthesis. Here, we demonstrate how the spin coherence in such optically addressable molecular qubits can be controlled through engineering their host environment. By inserting chromium (IV)-based molecular qubits into a nonisostructural host matrix, we generate noise-insensitive clock transitions, through a transverse zero-field splitting, that are not present when using an isostructural host. This host-matrix engineering leads to spin-coherence times of more than $10 μ s$ for optically addressable molecular spin qubits in a nuclear and electron-spin-rich environment. We model the dependence of spin coherence on transverse zero-field splitting from first principles and experimentally verify the theoretical predictions with four distinct molecular systems. Finally, we explore how to further enhance optical-spin interfaces in molecular qubits by investigating the key parameters of optical linewidth and spin-lattice relaxation time. Our results demonstrate the ability to test qubit structure-function relationships through a tunable molecular platform and highlight opportunities for using molecular qubits for nanoscale quantum sensing in noisy environments.

Received 18 March 2022
Revised 16 June 2022
Accepted 1 July 2022

DOI:https://doi.org/10.1103/PhysRevX.12.031028

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)

Chemical Physics & Physical Chemistry Quantum engineering Quantum information processing Spintronics

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

synopsis

Shielding Qubits with Chemistry

Published 18 August 2022

The spin state of molecular qubits can be made more stable by changing the chemical environment in which the qubits sit.

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Authors & Affiliations

S. L. Bayliss ^1,2,*, P. Deb ^1,3,*, D. W. Laorenza ^4,5,*, M. Onizhuk ^1,6, G. Galli ^1,6,7, D. E. Freedman ^4,†, and D. D. Awschalom ^1,3,7,‡

¹Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
²James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, United Kingdom
³Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
⁴Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁵Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
⁶Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA
⁷Center for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA

^*These authors contributed equally to this work.
^†danna@mit.edu
^‡awsch@uchicago.edu

Popular Summary

Quantum bits (qubits) are the building blocks for quantum information science, an emerging field that seeks to use quantum-mechanical properties to advance areas from secure communication to biological sensing. The spins of electrons are attractive qubits, as they can preserve quantum states over long timescales and be controlled with light. Housing such optically active spins in molecules offers opportunities to chemically design qubits for bespoke applications. The key to unlocking this potential is to draw on the versatility of molecular systems to enhance qubit properties. Here, we enhance the timescale over which optically active molecular qubits can preserve quantum superpositions (the coherence time) by engineering the molecular packing around the qubit.

The environment around a qubit creates noise—from the fluctuating magnetic fields of atomic nuclei, for example—which limits the qubit’s coherence. One approach to mitigate this decoherence is to reduce the noise sources. However, this strategy is not always possible or convenient. We use an alternative approach: We create optically addressable molecular qubits that are intrinsically less sensitive to noise by chemically controlling their molecular packing. Using host-matrix control, we alter the qubit’s symmetry, resulting in a qubit that is intrinsically protected from magnetic-field noise. This effect significantly enhances coherence without the need to reduce environmental noise.

Such noise-protected molecular qubits, which can be remotely controlled with light, hold promise for applications in nanoscale sensing in intrinsically noisy environments such as biological cells. Here, the versatility enabled by chemically synthesized qubits appears particularly exciting for future advancements.

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Vol. 12, Iss. 3 — July - September 2022

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Images

Figure 1
Host-matrix engineering of optically addressable molecular qubits. (a) Molecular structure of $1 − Cr$ (determined from single-crystal x-ray diffraction) with laser excitation and emission outlined. Hydrogen atoms are omitted for clarity. (b) Single-crystal packing diagram of $1 − Cr$ in its isostructural host, $1 − Sn$ (red, left), and nonisostructural host, $2 − Sn$ (blue, right), showing only positions of metal centers. The cell volumes for the representations of $1 − Sn$ and $2 − Sn$ are 9 and $10 {nm}^{3}$ , respectively. Below each cell, we show the molecular structures of the tin host, with hydrogen atoms omitted for clarity. The resulting ground-state spin structures (bottom) show the clock transition ( $E > 0$ ) induced in $2$ . (c) Energy level diagram of chromium molecular color centers, highlighting resonant excitation to, and photoluminescence (PL) from, the $S = 0$ excited state, and zero-field splitting of the ground-state spin sublevels. (d) PL and photoluminescence excitation (PLE) spectra of $2$ at 4 K.
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Figure 2
Host-matrix engineered clock transitions in $2$ . (a) Continuous-wave optically detected magnetic resonance performed on a single crystal of $2$ as a function of the magnetic field and microwave frequency overlaid with simulated spin transition frequencies (dashed lines). The ODMR spectrum yields $D = 5.55 GHz$ and $E = 1.85 GHz$ . (b) Calculated spin-sublevel energies as a function of the magnetic field highlighting their magnetic-field insensitivity. (c) Pulsed ODMR at zero magnetic field demonstrating an optical contrast of approximately 40%. Inset: pulsed ODMR sequence comprising optical initialization (init), microwave, and optical readout (read) pulses.
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Figure 3
Host and chemical tuning of transverse zero-field splitting to enhance coherence. (a) Molecular structures of the host matrix for $1$ , $2$ , and $3$ with their simulated spin energy levels as a function of the magnetic field. (b) Hahn-echo traces for single crystals of $1$ , $2$ , and $3$ at zero magnetic field. (c) Zero-field spin coherence as a function of the transverse zero-field splitting along with the theoretical dependence calculated from first-principles gCCE methods (using the large $D$ limit; see Supplemental Material). (d) Experimental and calculated $T_{2}$ as a function of the magnetic field.
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Figure 4
Extracting the homogeneous optical linewidth for $2$ . (a) ODMR showing the relevant microwave transitions ( $B \sim 70 mT$ ). (b) Schematic of the two-color experiments showing a fixed laser tone $f_{L}$ , along with a sideband detuned by $Δ f_{L}$ , which is swept. (c) PL as a function of $Δ f_{L}$ with and without a microwave drive ( $f_{M W, 2} ≃ 4.6 GHz$ ). (d) ODMR as a function of $Δ f_{L}$ for applied microwave tones at $f_{M W, 2}$ and $f_{M W, 3}$ ( $≃ 8.3 GHz$ ) with fits yielding a homogeneous optical linewidth of $≃ 3 GHz$ .
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Figure 5
Enhanced optical contrast and spin-lattice relaxation time for host-matrix engineered molecular qubits. (a) Optical-spin initialization observed as a reduction in PL over the course of an applied laser pulse. (b) Spin-lattice relaxation time measured by an all-optical sequence comprising initialization and readout laser pulses, separated by a variable relaxation time $T$ .
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