High-fidelity adiabatic inversion of a ³¹P electron spin qubit in natural silicon

Abstract

The main limitation to the high-fidelity quantum control of spins in semiconductors is the presence of strongly fluctuating fields arising from the nuclear spin bath of the host material. We demonstrate here a substantial improvement in single-qubit inversion fidelities for an electron spin qubit bound to a 31 P atom in natural silicon, by applying adiabatic sweeps instead of narrow-band pulses. We achieve an inversion fidelity of 97%, and we observe signatures in the spin resonance spectra and the spin coherence time that are consistent with the presence of an additional exchange-coupled donor. This work highlights the effectiveness of simple adiabatic inversion techniques for spin control in fluctuating environments. P donor electron 7 and nuclear 8 spins in silicon. In any III-V semiconductor, as well as in natural Si, the fluctuating nuclear spin environment is the main factor limiting spin coherence times 9,10 and, importantly, the fidelity of quantum gate operations, with typical fidelities in the range of 55%-75%. 4,7 This is insufficient for fault-tolerant qubit operations, which require fidelities in excess of 99% even in the most optimistic schemes.11 Group IV semiconductors such as Si and C possess spin-zero nuclear isotopes, which can be artificially enriched to create a nearly spin-free environment for spin qubits. Indeed 28 Si has been termed a "semiconductor vacuum" 12 for this reason. Ensemble spin resonance of 31 P donors in isotopically pure 28 Si has shown extraordinarily long coherence times, T 2e % 10 s for the electron 13 and T 2n % 3 h for the nucleus, 14 and it is certainly an exciting prospect to adopt isotopically pure substrates for nanoscale qubit devices. However, the production of nuclear spin-zero environments in isotopically purified semiconductors other than silicon is relatively undeveloped 15 or impossible because of the lack of suitable isotopes. Therefore, methods to maximize qubit control fidelities in the presence of a nuclear spin environment will remain important.In this Letter, we present how adiabatic frequency sweeps can be utilized to control the spin of an electron bound to a single 31 P donor with high-fidelity, in spite of the fluctuating nuclear spins from the 4.7% 29 Si (spin 1/2) in natural silicon. For an inhomogeneously broadened electron spin resonance (ESR) transition at $36 GHz with a linewidth of $12 MHz, we achieved an average electron spin inversion fidelity as high as F I ¼ 97 6 2%, insensitive to fluctuations of the background nuclear field. The method of adiabatic passage has been widely applied in nuclear magnetic resonance 16 and to some extent also in ESR. 17 Recent progress in high-frequency electronics and the very active research field of spin-based quantum computation have reignited the interest in this topic, with applications as ultra-wideband inversion, 18 geometric phase gates, 19 and even the inversion of single electron spins in diamond. 20,21 Our single qubit, however, is operated at much higher frequencies (36 GHz in the present work) t...

Addressable electron spin resonance using donors and donor molecules in silicon

“…Our microwave ESR pulses are applied with a nominal power at the signal generator of +5 dBm (we estimate ~60 dB attenuation at the device) for 150 μs and modulated with a linear frequency chirp of ±20 MHz. This adiabatic passage pulse ( 24 ) inverts the electron spin eigenstates irrespective of the exact pulse duration or precise instantaneous resonance frequency, enhancing our spin resonance signal ( 25 ). The spin resonance spectrum of the single donor (1P) is shown in Fig.…”

Exploring quantum chaos with a single nuclear spin

“…A pulse with linearly increasing frequency is applied that adiabatically inverts the electron state if its resonance frequency lies within the frequency range. 87 The bias voltage is then modified to ensure that the electron can only tunnel back onto the SET island if its spin state has successfully been flipped, which is measured as a finite SET current.…”

Coherent Control of a SingleSi29Nuclear Spin Qubit

“…This allows us to read the 29 Si spin state in the same way as the 31 P spin [3]. Here we apply adiabatic frequency sweeps [26] over the first half of the ν e2 resonance, i.e. from far-detuned to a point mid-way between the two peaks.…”