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Coupling superconducting resonators to bismuth donor spins in silicon for quantum memory applications

James O’Sullivan

Published Jan 1, 2020• 0 citations
OpenAlex

Abstract

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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Spin-Resonance Linewidths of Bismuth Donors in Silicon Coupled to Planar Microresonators

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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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Quantum control of donor spins in silicon and their environment

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Donors in silicon, which combine an electron and nuclear spin, are some of the most promising candidates for quantum information. The electron spin has been proposed as a register with fast manipulation and the nuclear spin as a memory with long coherence times. However, this division reduces the complexity of the donor system, in particular behaviors emerging from their interaction. In natural silicon, there is also the presence of 29Si nuclear spins in the donor environment; though they are generally seen as a source of decoherence, they are quantum systems that can be investigated too. The main subject of this thesis is the study of the interactions between these various spins, using different methods to probe and control them. I first concentrate on the coupling between the donor and the 29Si spins. This coupling can be perturbed by the application of dynamical decoupling on the donor electron spin, whose evolution can be made sensitive to the number of 29Si spins interacting together. I then propose an error correction scheme using the donor and 29Si spins, showing key requirements such as coherence times and methods for manipulation and initialization. Secondly, I focus on the donor itself, in a regime where the hyperfine and Zeeman couplings compete with each other. Here, the spin transitions can have different sensitivities to the magnetic environment, and can even be suppressed to first order, resulting in coherence times up to seconds with electron spin-like manipulation times. Controlling this sensitivity was also used to probe the effect of the donor on the 29Si spin bath evolution. Finally, I use electric fields to modulate the hyperfine coupling within the donor. I first characterize the spins’ sensitivity to the electric field, and then demonstrate electrical switching of the nuclear spin response to an external magnetic excitation.

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Solid-state spin ensembles addressed via superconducting circuits are promising candidates for quantum memory applications, offering multimodal storage capability and second-long coherence times at their clock transition. Implementing practical memory schemes requires dynamic control over both the resonator frequency and bandwidth. In this letter, we report measurements of a superconducting resonator whose frequency can be tuned by passing a DC current through the high-kinetic-inductance thin film, and whose bandwidth can be tuned by parametric coupling to a low-Q buffer resonator. Using this resonator, we address an ensemble of bismuth donors at their clock transition, measuring a Hahn-echo coherence time of 450 ms. We demonstrate RF driving of the bismuth donor hyperfine transitions, as well as dynamic bandwidth control of the resonator.

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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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Majid Mohammady

A promising platform for quantum information processing is that of silicon impurities, where the quantum states are manipulated by magnetic resonance. Such systems, in abstraction, can be considered as a nucleus of arbitrary spin coupled to an electron of spin one-half via an isotropic hyperfine interaction. We therefore refer to them as "nuclear-electronic spin systems". The traditional example, being subject to intensive experimental studies, is that of phosphorus doped silicon (Si:P) which couples a spin one-half electron to a nucleus of the same spin, with a hyperfine strength of 117.5 MHz. More recently, bismuth doped silicon (Si:Bi) has been suggested as an alternative instantiation of nuclear-electronic spin systems, differing from Si:P by its larger nuclear spin and hyperfine strength of 9/2 and 1.4754 GHz respectively. The aim of this thesis has been to develop a model that is capable of predicting the magnetic resonance properties of nuclear-electronic spin systems. The theoretical predictions of this model have been tested against experimental data collected on Si:Bi at 4.044 GHz, and have proven quite successful. Furthermore, the larger nuclear spin and hyperfine strength of Si:Bi, compared with that of Si:P, are predicted to offer advantages for quantum information processing. Most notable amongst these is that magnetic field-dependent two-dimensional decoherence free subspaces, called optimal working points, have been identified to exist in Si:Bi, but not Si:P.

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arXiv:2005.09275•Physical Review Letters•Nov 20, 2020•30 citations
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.
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.
Donors in silicon, which combine an electron and nuclear spin, are some of the most promising candidates for quantum information. The electron spin has been proposed as a register with fast manipulation and the nuclear spin as a memory with long coherence times. However, this division reduces the complexity of the donor system, in particular behaviors emerging from their interaction. In natural silicon, there is also the presence of 29Si nuclear spins in the donor environment; though they are generally seen as a source of decoherence, they are quantum systems that can be investigated too. The main subject of this thesis is the study of the interactions between these various spins, using different methods to probe and control them. I first concentrate on the coupling between the donor and the 29Si spins. This coupling can be perturbed by the application of dynamical decoupling on the donor electron spin, whose evolution can be made sensitive to the number of 29Si spins interacting together. I then propose an error correction scheme using the donor and 29Si spins, showing key requirements such as coherence times and methods for manipulation and initialization. Secondly, I focus on the donor itself, in a regime where the hyperfine and Zeeman couplings compete with each other. Here, the spin transitions can have different sensitivities to the magnetic environment, and can even be suppressed to first order, resulting in coherence times up to seconds with electron spin-like manipulation times. Controlling this sensitivity was also used to probe the effect of the donor on the 29Si spin bath evolution. Finally, I use electric fields to modulate the hyperfine coupling within the donor. I first characterize the spins’ sensitivity to the electric field, and then demonstrate electrical switching of the nuclear spin response to an external magnetic excitation.
Solid-state spin ensembles addressed via superconducting circuits are promising candidates for quantum memory applications, offering multimodal storage capability and second-long coherence times at their clock transition. Implementing practical memory schemes requires dynamic control over both the resonator frequency and bandwidth. In this letter, we report measurements of a superconducting resonator whose frequency can be tuned by passing a DC current through the high-kinetic-inductance thin film, and whose bandwidth can be tuned by parametric coupling to a low-Q buffer resonator. Using this resonator, we address an ensemble of bismuth donors at their clock transition, measuring a Hahn-echo coherence time of 450 ms. We demonstrate RF driving of the bismuth donor hyperfine transitions, as well as dynamic bandwidth control of the resonator.
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.
A promising platform for quantum information processing is that of silicon impurities, where the quantum states are manipulated by magnetic resonance. Such systems, in abstraction, can be considered as a nucleus of arbitrary spin coupled to an electron of spin one-half via an isotropic hyperfine interaction. We therefore refer to them as "nuclear-electronic spin systems". The traditional example, being subject to intensive experimental studies, is that of phosphorus doped silicon (Si:P) which couples a spin one-half electron to a nucleus of the same spin, with a hyperfine strength of 117.5 MHz. More recently, bismuth doped silicon (Si:Bi) has been suggested as an alternative instantiation of nuclear-electronic spin systems, differing from Si:P by its larger nuclear spin and hyperfine strength of 9/2 and 1.4754 GHz respectively. The aim of this thesis has been to develop a model that is capable of predicting the magnetic resonance properties of nuclear-electronic spin systems. The theoretical predictions of this model have been tested against experimental data collected on Si:Bi at 4.044 GHz, and have proven quite successful. Furthermore, the larger nuclear spin and hyperfine strength of Si:Bi, compared with that of Si:P, are predicted to offer advantages for quantum information processing. Most notable amongst these is that magnetic field-dependent two-dimensional decoherence free subspaces, called optimal working points, have been identified to exist in Si:Bi, but not Si:P.