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arXiv:2206.00399 · Physical review. B./Physical review. B

Electrically driven spin resonance with bichromatic driving

Zoltán György, András Pályi, Gábor Széchenyi

Published Oct 17, 2022• 10 citations
arXivHTMLPDF

Abstract

Electrically driven spin resonance (EDSR) is an established tool for controlling semiconductor spin qubits. Here, we theoretically study a frequency-mixing variant of EDSR, where two driving tones with different drive frequencies are applied, and the resonance condition connects the spin Larmor frequency with the sum of the two drive frequencies. Focusing on flopping-mode operation of a single electron in a double quantum dot with spin-orbit interaction, we calculate the parameter dependence of the Rabi frequency and the Bloch-Siegert shift. A shared-control spin qubit architecture could benefit from this bichromatic EDSR scheme, as it enables simultaneous single-qubit gates.

DOI
10.1103/physrevb.106.155412

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Electrically driven spin resonance (EDSR) is an established tool for controlling semiconductor spin qubits. Here, we theoretically study a frequency-mixing variant of EDSR, where two driving tones with different drive frequencies are applied, and the resonance condition connects the spin Larmor frequency with the sum of the two drive frequencies. Focusing on flopping-mode operation of a single electron in a double quantum dot with spin-orbit interaction, we calculate the parameter dependence of the Rabi frequency and the Bloch-Siegert shift. A shared-control spin qubit architecture could benefit from this bichromatic EDSR scheme, as it enables simultaneous single-qubit gates.
Germanium quantum dot hole spin qubits are compatible with fully electrical control and are progressing toward multi-qubit operations. However, their coherence is limited by charge noise and driving field induced frequency shifts, and the resulting ensemble 1/f1/f1/f dephasing. Here we theoretically demonstrate that a bichromatic driving scheme cancels the second order frequency shift from the control field without sacrificing the electric dipole spin resonance (EDSR) rate, and without additional gate design or microwave engineering. Based on this property, we further demonstrate that bichromatic control creates a wide operating window that reduces sensitivity to quasi-static charge noise and thus enhances single qubit gate fidelity. This method provides a low-power route to a stabler frequency operation in germanium hole spin qubits and is readily transferable to other semiconductor spin qubit platforms.
In electric dipole spin resonance (EDSR), a single spin is electrically driven in the field gradient produced by a micromagnet. While EDSR has enabled high fidelity gate operations in many devices, there are reports of unexpected non-linearities in the Rabi frequency as a function of microwave drive amplitude. We carefully measure the response of Loss-DiVincenzo (LD) single spin qubits to resonant drives as well as simultaneous resonant and off-resonant drives, as would be encountered in a realistic quantum processor. With the microwave amplitude carefully calibrated, we find that the Rabi frequency scales linearly with drive amplitude, even when all three spins are driven simultaneously. We also determine that heating-induced resonance frequency shifts from off-resonant drives are comparable to typical temporal drifts. Our results indicate that the previously observed nonlinear response is not a general feature of LD spin qubits.
Hole spin qubits in semiconductor quantum dots (QDs) enable high-fidelity all-electric control, but conventional electric dipole spin resonance (EDSR) can require substantial rf drive power at the low magnetic fields that are favorable for qubit coherence and readout. In planar Ge hole spin qubits, this can reach -27 dBm at the device, posing challenges for scalable architectures due to heating and crosstalk. Here, we demonstrate a flopping-mode (FM) qubit in Ge, where a single spin is delocalized in a double QD, combining first-order protection against charge noise with exceptionally efficient electric driving. By mapping out coherence sweet-spots as a function of magnetic field orientation we achieve T2∗=1.4μsT_2^*= 1.4μ\mathrm{s}T2∗​=1.4μs, T2Hahn=11.5μsT_2^{\mathrm{Hahn}}= 11.5 μ\mathrm{s}T2Hahn​=11.5μs, T2φ,CPMG32=130μsT^{φ, \mathrm{CPMG32}}_2= 130 μ\mathrm{s}T2φ,CPMG32​=130μs, and T1=226μsT_1= 226 μ\mathrm{s}T1​=226μs, and a single-qubit gate fidelity of up to 99.76%\%% for a gate time tXπ=88t_{Xπ} = 88tXπ​=88 ns. Importantly, these results are obtained at a nearly in-plane magnetic field of 5 mT using only -52 dBm drive power at the device. We further find that qubit relaxation in this regime is consistent with a two-photon Orbach process, providing a route for further optimization. Our results demonstrate that FM-EDSR supports ultra-low-power, high-fidelity single-qubit operations, improvements that could benefit scalable hole-spin-based architectures and hybrid spin-photon interfaces.
The ggg-tensor formalism is a powerful method for describing the electrical driving of semiconductor spin qubits. However, up to now, this technique has only been applied to the simplest qubit dynamics, resonant monochromatic driving by a single gate. Here we study the description of (i) monochromatic driving using two driving gates and bichromatic driving via (ii) one or (iii) two gates. Assuming a general Hamiltonian with qubit states well separated from excited orbital states, we find that when (i) two driving gates are used for monochromatic driving or (ii) a single one for bichromatic, the ggg-tensor formalism successfully captures the leading-order dynamics. We express the Rabi frequency and the Bloch-Siegert shift using the ggg-tensor and its first and second derivatives with respect to the gate voltage. However, when (iii) bichromatic driving is realized using two distinct driving gates, we see a breakdown of ggg-tensor formalism: the Rabi frequency cannot be expressed using the ggg-tensor and its derivatives. We find that beyond the ggg-tensor and its derivatives, three additional parameters are needed to capture the dynamics. We demonstrate our general results by assuming an electron (hole) confined in a circular quantum dot, subjected to Rashba spin-orbit interaction.
Dynamic qubit routing is emerging as a promising architectural path for semiconductor quantum processors. Charge carriers can be rapidly moved around on a chip using traveling-wave potentials known as conveyors, preserving the spin state with high fidelity. Originally developed for spin transport, conveyor-mode shuttling may also offer opportunities for performing qubit operations directly controlled by the motion itself. Here, we demonstrate coherent single- and two-qubit control by conveyor-mode electron shuttling, using two conceptually different approaches. First, conveyor electric-dipole spin resonance (conveyor EDSR) achieves high-fidelity rotations by resonantly shuttling spins through transverse magnetic-field gradients at their mean Larmor frequency. Second, conveyor diabatic gates exploit quantization-axis tilts for tunable bang-bang control. Combining diabatic conveyor transport with exchange activation controlled by the motion directly yields a variety of effective two-qubit interactions selectable via the shuttling speed and distance. These experimental results motivate an architectural paradigm of reconfigurable and transport-driven spin qubits.
There have been impressive breakthroughs in semiconductor quantum dots in recent years, with single- and two-qubit gate fidelities matching other leading platforms and scalability still remaining a relative strength; however, due to qubit wiring considerations, mobile electron architectures have been proposed to facilitate upward scaling, and this opens the possibility of enlarging the motional amplitude for electric-dipole spin resonance (EDSR)-based qubit manipulation. In this work, we examine and demonstrate the possibility of significantly outperforming static-EDSR-type single-qubit pulsing by taking advantage of greater spatial mobility to achieve higher Rabi frequencies and reduce the effect of charge noise. Our theoretical results indicate that fidelities are ultimately bottlenecked by spin-valley physics, which can be suppressed through the use of quantum optimal control. We demonstrate that, across different potential regimes and competing physical models, shuttling-based single-qubit gates retain significant advantages over existing alternatives.