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arXiv:2007.07600 · Physical Review Applied

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

James O’Sullivan, Oscar W. Kennedy, Christoph W. Zollitsch, Mantas Šimėnas, Christopher N. Thomas, Leonid V. Abdurakhimov, Stafford Withington, John J. L. Morton

Published Dec 16, 2020• 21 citations

Abstract

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.

DOI: 10.1103/physrevapplied.14.064050

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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.

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 authors demonstrate the selective addressability of two nearly degenerate clock transitions in bismuth-doped

{}^{28}

Si without tuning the magnetic field or microwave frequency. Rather, they vary the microwave polarization between clockwise and counterclockwise circular polarizations, which can be done rapidly. To generate the circularly polarized microwaves, a superconducting coplanar waveguide microresonator was oriented inside a tunable dielectric resonator such that their microwave magnetic fields can be superimposed to give any arbitrary microwave polarization. This work not only opens up additional states near the Si:Bi clock transition, which can be used for different quantum computing schemes, it also demonstrates a clever method for generating arbitrarily polarized microwaves.

The efficient transfer of quantum states into a long-lived storage unit such as solid-state spin ensembles is widely recognized as a critical challenge with significant implications for quantum communication, sensing and computing applications. Here, we experimentally investigate the interaction of propagating squeezed microwaves with an electron spin resonance transition in order to evaluate the use of spin ensembles as quantum memories for GHz signals. We generate continuous variable microwave states with a squeezing of up to 5dB below the vacuum level and let this signal interrogate a spin ensemble, which is inductively coupled to a lumped element superconducting microwave resonator with a cooperativity of C=0.3. Analyzing this signal using Wigner tomography, we observe a transfer efficiency of around 61% between the squeezed microwaves and the spin excitation. We successfully model our experimental results with a dedicated steady-state model based on the quantum input-output formalism and provide guidance for design parameters required to enable spin-based quantum memories.

Hybrid quantum systems with high-T

_c

superconducting resonators

Superconducting microwave resonators are crucial elements of microwave circuits, offering a wide range of potential applications in modern science and technology. While conventional low-T[Formula: see text] superconductors are mainly employed, high-T[Formula: see text] cuprates could offer enhanced temperature and magnetic field operating ranges. Here, we report the realization of [Formula: see text] superconducting coplanar waveguide resonators, and demonstrate a continuous evolution from a lossy undercoupled regime, to a lossless overcoupled regime by adjusting the device geometry, in good agreement with circuit model theory. A high-quality factor resonator was then used to perform electron spin resonance measurements on a molecular spin ensemble across a temperature range spanning two decades. We observe spin-cavity hybridization indicating coherent coupling between the microwave field and the spins in a highly cooperative regime. The temperature dependence of the Rabi splitting and the spin relaxation time point toward an antiferromagnetic coupling of the spins below 2 K. Our findings indicate that high-Tc superconducting resonators hold great promise for the development of functional circuits. Additionally, they suggest novel approaches for achieving hybrid quantum systems based on high-T[Formula: see text] superconductors and for conducting electron spin resonance measurements over a wide range of magnetic fields and temperatures.