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arXiv:1601.05735 · Physical review. B./Physical review. B

Addressing spin transitions on Bi209 donors in silicon using circularly polarized microwaves

Takashi Yasukawa, Anthony J. Sigillito, Brendon C. Rose, Alexei M. Tyryshkin, S. A. Lyon

Published Mar 25, 2016• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.93.121306

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The authors demonstrate the selective addressability of two nearly degenerate clock transitions in bismuth-doped 28{}^{28}28Si 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.
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.
We demonstrate the use of high-Q superconducting coplanar waveguide (CPW) microresonators to perform rapid manipulations on a randomly distributed spin ensemble using very low microwave power (400 nW). This power is compatible with dilution refrigerators, making microwave manipulation of spin ensembles feasible for quantum computing applications. We also describe the use of adiabatic microwave pulses to overcome microwave magnetic field (B1) inhomogeneities inherent to CPW resonators. This allows for uniform control over a randomly distributed spin ensemble. Sensitivity data are reported showing a single shot (no signal averaging) sensitivity to 107 spins or 3×104spins/Hz with averaging.
We demonstrate the use of high-Q superconducting coplanar waveguide (CPW) microresonators to perform rapid manipulations on a randomly distributed spin ensemble using very low microwave power (400 nW). This power is compatible with dilution refrigerators, making microwave manipulation of spin ensembles feasible for quantum computing applications. We also describe the use of adiabatic microwave pulses to overcome microwave magnetic field (B1) inhomogeneities inherent to CPW resonators. This allows for uniform control over a randomly distributed spin ensemble. Sensitivity data are reported showing a single shot (no signal averaging) sensitivity to 107 spins or 3×104spins/Hz with averaging.
In this work, we demonstrate the use of frequency-tunable superconducting NbTiN coplanar waveguide microresonators for multi-frequency pulsed electron spin resonance (ESR) experiments. By applying a bias current to the center pin, the resonance frequency (∼7.6 GHz) can be continuously tuned by as much as 95 MHz in 270 ns without a change in the quality factor of 3000 at 2 K. We demonstrate the ESR performance of our resonators by measuring donor spin ensembles in silicon and show that adiabatic pulses can be used to overcome magnetic field inhomogeneities and microwave power limitations due to the applied bias current. We take advantage of the rapid tunability of these resonators to manipulate both phosphorus and arsenic spins in a single pulse sequence, demonstrating pulsed double electron-electron resonance. Our NbTiN resonator design is useful for multi-frequency pulsed ESR and should also have applications in experiments where spin ensembles are used as quantum memories.
The nitrogen vacancy (NV) center in diamond is promising as an electron spin qubit due to its long-lived coherence and optical addressability. The ground state is a spin triplet with two levels $({m}_{s}=\ifmmode\pm\else\textpm\fi{}1)$ degenerate at zero magnetic field. Polarization-selective microwave excitation is an attractive method to address the spin transitions independently since this allows operation down to zero magnetic field. Using a resonator designed to produce circularly polarized microwaves, we have investigated the polarization selection rules of the NV center. We first apply this technique to NV ensembles in [100]- and [111]-oriented samples. Next, we demonstrate an imaging technique, based on optical polarization dependence, which allows rapid identification of the orientations of many single NV centers. Finally, we test the microwave polarization selection rules of individual NV centers of known orientation.