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Implementing a quantum memory at microwave frequencies with Bismuth donors in silicon

Audrey Bienfait, Tristan Lorriaux, Yutian Wen, V. Ranjan, D. Vion, Emmanuel Flurin, Benjamin Huard, Patrice Bertet

Published Nov 6, 2024• 0 citations
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Ensembles of bismuth-donor spins in silicon are promising storage elements for microwave quantum memories due to their long coherence times, which exceed seconds. The operation of an efficient quantum memory requires the achievement of critical coupling between the spin ensemble and a suitable high-quality factor resonator---this in turn requires a thorough understanding of the line shapes for the relevant spin-resonance transitions, particularly considering the influence of the resonator itself on line broadening. Here, we present pulsed electron-spin-resonance measurements of ensembles of bismuth donors in natural silicon, above which niobium superconducting resonators have been patterned. By studying spin transitions across a range of frequencies and fields, we identify distinct line-broadening mechanisms and, in particular, those that can be suppressed by operating at magnetic-field-insensitive ``clock transitions.'' Given the donor concentrations and resonator used here, we measure a cooperativity $C\ensuremath{\sim}0.2$ and based on our findings we discuss a route to achieve unit cooperativity, as required for a quantum memory.

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Spins in nuclear-spin-free solid state systems such as isotopically purified 28Si have seen extensive research as candidates for quantum information storage and processing, thanks to their long spin coherence lifetimes [1]. Strongly coupling such spins to a high Q superconducting resonator provides a route to develop microwave quantum memories. Bismuth donor spins can be tuned to so-called ‘clock transitions’, which, due to their insensitivity to magnetic field noise, can have electron spin coherence times as long as 3 seconds [2]. The system also possesses ‘hyperfine clock transitions’, which are insensitive to changes in the hyperfine coupling constant, and which may mitigate the effects of strain on the transition. Achieving coupling to such transitions requires resonators which are both magnetic-field resilient, and frequency tuneable. This thesis outlines the work done towards realising a quantum memory using Bi donors in silicon, from resonator design and fabrication, coupling these to implanted Bi spins in silicon and tuning to various clock transitions, through to storage and retrieval of few-photon excitations in a spin ensemble and their retrieval over 100 ms later.

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The realization of a quantum computer represents a tremendous scientific and technological challenge due to the extreme fragility of quantum information. The physical support of information, namely the quantum bit or qubit, must at the same time be strongly coupled to other qubits by gates to compute information, and well decoupled from its environment to keep its quantum behavior. An interesting physical system for realizing such qubits are magnetic impurities in semiconductors, such as bismuth donors in silicon. Indeed, spins associated to bismuth donors can reach an extremely long coherence time - of the order of seconds. Yet it is extremely difficult to establish and control efficient gates between these spins. Here we demonstrate a protocol where single bismuth donors can coherently transfer their quantum information to a superconducting flux qubit, which acts as a mediator or quantum bus. This superconducting device allows to connect distant spins on-demand with little impact on their coherent behavior. Donor spin impurities in silicon are promising qubit candidates, but efficient control and coupling of distant spins remains a key challenge. In this work, the authors experimentally demonstrate coherent coupling between a superconducting flux qubit and individual bismuth donor spins in silicon.

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Ensembles of bismuth-donor spins in silicon are promising storage elements for microwave quantum memories due to their long coherence times, which exceed seconds. The operation of an efficient quantum memory requires the achievement of critical coupling between the spin ensemble and a suitable high-quality factor resonator---this in turn requires a thorough understanding of the line shapes for the relevant spin-resonance transitions, particularly considering the influence of the resonator itself on line broadening. Here, we present pulsed electron-spin-resonance measurements of ensembles of bismuth donors in natural silicon, above which niobium superconducting resonators have been patterned. By studying spin transitions across a range of frequencies and fields, we identify distinct line-broadening mechanisms and, in particular, those that can be suppressed by operating at magnetic-field-insensitive ``clock transitions.'' Given the donor concentrations and resonator used here, we measure a cooperativity $C\ensuremath{\sim}0.2$ and based on our findings we discuss a route to achieve unit cooperativity, as required for a quantum memory.
Spins in nuclear-spin-free solid state systems such as isotopically purified 28Si have seen extensive research as candidates for quantum information storage and processing, thanks to their long spin coherence lifetimes [1]. Strongly coupling such spins to a high Q superconducting resonator provides a route to develop microwave quantum memories. Bismuth donor spins can be tuned to so-called ‘clock transitions’, which, due to their insensitivity to magnetic field noise, can have electron spin coherence times as long as 3 seconds [2]. The system also possesses ‘hyperfine clock transitions’, which are insensitive to changes in the hyperfine coupling constant, and which may mitigate the effects of strain on the transition. Achieving coupling to such transitions requires resonators which are both magnetic-field resilient, and frequency tuneable. This thesis outlines the work done towards realising a quantum memory using Bi donors in silicon, from resonator design and fabrication, coupling these to implanted Bi spins in silicon and tuning to various clock transitions, through to storage and retrieval of few-photon excitations in a spin ensemble and their retrieval over 100 ms later.
The realization of a quantum computer represents a tremendous scientific and technological challenge due to the extreme fragility of quantum information. The physical support of information, namely the quantum bit or qubit, must at the same time be strongly coupled to other qubits by gates to compute information, and well decoupled from its environment to keep its quantum behavior. An interesting physical system for realizing such qubits are magnetic impurities in semiconductors, such as bismuth donors in silicon. Indeed, spins associated to bismuth donors can reach an extremely long coherence time - of the order of seconds. Yet it is extremely difficult to establish and control efficient gates between these spins. Here we demonstrate a protocol where single bismuth donors can coherently transfer their quantum information to a superconducting flux qubit, which acts as a mediator or quantum bus. This superconducting device allows to connect distant spins on-demand with little impact on their coherent behavior. Donor spin impurities in silicon are promising qubit candidates, but efficient control and coupling of distant spins remains a key challenge. In this work, the authors experimentally demonstrate coherent coupling between a superconducting flux qubit and individual bismuth donor spins in silicon.