Session B07: Electron and Hole Based Spin Qubits in Heterostructures

Electric dipole-induced spin resonance of holes in Ge/Si nanowires

Electric dipole-induced spin resonance (EDSR) forms a basic tool in quantum information processing with spin qubits. It enables electrically driven quantum gates and forms a way to accurately probe the energy spectrum of spin qubits. We demonstrate EDSR of hole spins confined in a double quantum dot in a Ge/Si nanowire. The spin-orbit interaction of hole spins in this system has a unique character, as it is predicted to be very strong, potentially enabling GHz Rabi oscillation frequencies, as well as electrically tunable. Recent experiments support this with a demonstration of a 30 nm spin-orbit length and Rabi frequencies exceeding 400 MHz.

Here we perform hole spin spectroscopy through the measurement of EDSR transitions between double dot spin states under various resonance conditions. In particular, we characterize the hole g-tensor as well as the direction of the effective spin-orbit magnetic field through an investigation of EDSR transitions as a function of the magnitude and orientation of an applied external magnetic field . Knowledge of these parameters allows tuning the system towards optimized Rabi oscillation frequencies and minimized decoherence.   

Electric control of the single hole g-factor by 400% in a silicon MOS quantum dot.

Holes in silicon quantum dots are attracting significant attention for their potential use as fast, highly coherent spin qubits [1]. However, there are still gaps in the understanding of the physics of hole spins. For example, the full effects of confinement and spin-orbit coupling on hole spin states remains an open problem. Studies of the Lande g-tensor are valuable for characterizing this underlying spin physics, however most studies of holes have been performed in an unknown orbital configuration where spin-orbit coupling can lead to complex non-trivial spin effects. Studies of a single hole in a known and reproducible orbital state can therefore provide valuable insight into the complex spin physics.

In this work we confine a single hole in a known orbital state [2] and study the Lande g-tensor using a 3D vector magnet. We compare the g-tensor for different confinement profiles and find the g-tensor can be strongly modulated and even rotated by up to 30 degrees. These results show that the anisotropy of the single hole g-tensor is due to symmetries in the tunable electric confinement. This tunability can be harnessed for further use of holes in spin qubit applications.

[1] C. Kloeffel et al., Phys. Rev. B 88, 241405 (2013)
[2] S. D. Liles et al., Nature Communications 9 (2018)   

Fast and tunable Rabi oscillations of hole spins in Ge/Si nanowires

The strong confinement of holes to one dimension in Ge/Si core/shell nanowires gives rise to direct Rashba spin-orbit interaction which is predicted to be both very strong and electric field tunable. The full electrical control promises to switch the spin-orbit interaction either on, enabling fast qubit operations, or off, protecting the spin state in order to achieve an increased qubit lifetime. These properties make Ge/Si nanowires a very promising system for the implementation of hole spin qubits. Recent experiments have found a spin-orbit interaction length on the order of only 30 nm, paving the way to very fast spin manipulation by electric dipole spin resonance. This mechanism allows us to drive very fast Rabi oscillations above 400 MHz at a Larmor frequency of 3.4 GHz, thus entering the strong driving regime. Furthermore, we find the Rabi oscillation frequency as well as the g-factor to be highly tunable with small changes in gate voltages, indicating the feasibility to electrically control the spin-orbit interaction strength.
  

Towards scalable hole spin qubits in silicon

Since the first proof-of-concept demonstration of a silicon hole spin qubit based on industry-standard CMOS technology [1], our research efforts have focused on acquiring a better understanding of the mechanism for electric-field-driven hole-spin manipulation [2], as well as on the development of spin readout based on rf gate reflectometry [3]. All of these studies were carried out on p-type silicon-nanowire devices with two crossing gates in series. Here we report the first implementation of hole-qubit functionality in a face-to-face gate geometry [4]. This more scalable geometry can be regarded as the elementary building block of a one-dimensional chain of qubits were each qubit on the chain is read through a facing helper quantum dot via the Pauli spin blockade mechanism and rf gate reflectometry [5].

References:
[1] A. Crippa et al., Nature Communications 10, 2776 (2019).
[2] A. Crippa et al., Physical Review Letters 120, 137702 (2018).
[3] S. De Franceschi et al., Technical Digest - IEDM, 13.4.1–13.4.4 (2017).
[4] R. Maurand et al., Nature Communications, 3–8(2016).
[5] B. Voisin et al., Nano Letters 14, 2094–2098 (2014).   

Hole spin echo envelope modulations

An anisotropic hyperfine coupling can give rise to a substantial spin-echo envelope modulation that can be Fourier-analyzed to accurately reveal the hyperfine tensor. We give a general theoretical analysis for hole-spin-echo envelope modulation (HSEEM), and apply this analysis to the specific case of a boron-acceptor hole spin in silicon [1]. For boron acceptor spins in unstrained silicon, both the hyperfine and Zeeman Hamiltonians are approximately isotropic leading to negligible envelope modulations. In contrast, in strained silicon, where light-hole spin qubits can be energetically isolated, we find the hyperfine Hamiltonian and g-tensor are sufficiently anisotropic to give spin-echo-envelope modulations. We show that there is an optimal magnetic-field orientation that maximizes the visibility of envelope modulations in this case. Based on microscopic estimates of the hyperfine coupling, we find that the maximum modulation depth can be substantial, reaching ∼ 10%, at a moderate laboratory magnetic field, B < 200 mT.

[1] P. Philippopoulos et al., Phys. Rev. B, 100, 125402 (2019).   

Effects of Valley-Orbit Coupling on the Exchange Interaction in a Si/SiGe Double Quantum Dots

We investigate the effects of the phase and magnitude of the valley orbit coupling on the tunnel coupling matrix elements and the exchange interaction in a Si double quantum dot. Our results show that a difference in the phase between the two quantum dots modifies the single-electron tunnel coupling between different valley eigenstates. In particular, valley-blockade between the ground valleys of individual dots could be obtained when the valley phase difference between the dots is π. For the two-electron case, exchange interaction at the symmetric point (zero detuning) is suppressed when valley phase difference is finite, and reaches its minimum value when the phase difference is 180 degrees. The energy spectrum at finite detuning also depends on the magnitudes and phases of the valley orbit couplings of the two dots. Our results shed new lights on the controllability of Silicon based spin qubit for its application in quantum information processing.   

Singlet-triplet splitting of two electrons in a Si/SiGe quantum dot

We theoretically study the effects of quantum dot confinement strength on the singlet-triplet (ST) splitting of two-electron dots in Si/SiGe quantum wells. Our analysis includes valley effects and disorder at the quantum well interface by combining full configuration interaction (FCI) scheme with tight-binding (TB) calculations. While TB provides an accurate description of single-electron wave functions by taking microscopic effects like interface disorder into account, and captures the valley physics of silicon, FCI allows us to calculate multielectron energies and corresponding wave functions by including the effects of electron-electron interactions. We show that these interactions can have unexpectedly strong or unexpectedly weak effects on the ST splitting, depending on the confinement strength and anisotropy.   

Operation of a four-qubit device in isotopically enriched Si/SiGe

Quantum processors based on electron spins in silicon are rapidly becoming a strong contender in the race to build a quantum computer. Over the past few years, quantum-dot spin qubits have been shown to offer high fidelity single-qubit [1] and two-qubit [2-5] control at levels approaching the fault tolerant threshold. However, most experiments have been conducted in one-qubit, or two-qubit devices. Recently, we have demonstrated operation of a four-qubit device in isotopically enriched Si/SiGe [6]. Here we outline improvements to our four-qubit device design and present new data on one- and two-qubit operation in the device including recent randomized benchmarking results.
[1] Yoneda et al., Nat. Nanotech. 13, 102 (2018)
[2] Zajac et al., Science 359, 439 (2018)
[3] Watson et al., Nature 555, 633 (2018)
[4] Huang et al., Nature 569, 532 (2019)
[5] Xue et al., Phys. Rev. X 9, 021011 (2019)
[6] Sigillito et al., Phys. Rev. Applied 6, 061006 (2019)   

Coherent spectroscopy of a Si/SiGe double quantum dot molecule

We report the wideband microwave spectroscopy of a gate-defined double quantum dot qubit. The double quantum dot, operated with a total of five electrons, has a series of molecular energy levels that can be manipulated coherently. Working in the (4,1)-(3,2) charge configuration, we use a two-step Ramsey pulse sequence to characterize the energy levels of the (3,2) charge configuration as a function of the double-dot detuning. Using this procedure, we demonstrate differences in the dispersion for two closely spaced levels (<2GHz separation in energy). We present measurements of the broadband spectrum, discovering seven energy levels that can be addressed coherently, each with distinct Rabi oscillation characteristics. The double quantum dot is formed in an undoped Si/SiGe heterostructure using an overlapping gate architecture [1]. The measurements are acquired using a tunable latched measurement scheme similar to that in Ref. [2], made possible by the presence of independent reservoirs and corresponding tunnel barriers for each quantum dot.

[1] Zajac, D. et al., Appl. Phys. Lett. 106, 223507 (2015)
[2] S. A. Studenikin et al. Appl. Phys. Let., 101, 23 (2012)   

Towards coupled valley qubits in silicon

Valley states in silicon are a promising candidate for encoding qubits in gate-defined quantum dots due to their protection against charge noise, fast operation times, and ability to operate without a magnetic field. Recently, two-axis quantum control of a valley qubit using gate pulse sequences with X and Z rotations, occurring within a fast operation time of 300 ps, has been demonstrated [1]. In this talk, we present our progress on coupling two such valley qubits. We have fabricated a device consisting of two double-quantum dots on a SiGe heterostructure for our experiments. We further measure the capacitive coupling between the two double dots in the few electron region, showing sufficiently large and tunable coupling. By exploiting this electrostatic interaction, we discuss our plan for employing the two coupled valley qubits to realize a two-qubit logic gate.

[1] Nicholas E. Penthorn, Joshua S. Schoenfield, John D. Rooney, Lisa F. Edge, and HongWen Jiang, “Two-axis quantum control of a fast valley qubit in silicon”, npj Quantum Information, in press (2019).   

Hyperfine effects in a single hole GaAs/AlGaAs double quantum dot device

Hole spin qubits are attractive because, compared to electrons, they are predicted theoretically to have significantly weaker interactions with host nuclei, resulting in longer coherence times [1]. As a result it is more challenging to quantify hyperfine (hf) effects with holes. In Ref. [2], in a quantum point contact device, Dynamic Nuclear Polarization (DNP) through the hf interaction with holes was undetectable. In this work, we detect and explore small DNP effects in a single hole GaAs/AlGaAs gated DQD device using a modified EDSR technique [3]. As compared to our previous studies [3], the device is tuned to a much smaller inter-dot coupling regime to minimize spin-orbit effects and to make nuclear spin effects detectable.
[1] Philippopoulos, et al. PRB 100, 125402 (2019);
[2] Keane, et al., Nano Lett. 11, 3147 (2011);
[2] Studenikin et al., http://meetings.aps.org/Meeting/MAR19/Session/H35.13   

A realistic GaAs-spin qubit device for a classical error-corrected quantum memory and beyond

Based on numerically-optimized real-device gates and parameters we study the performance of the phase-flip (repetition) code on a linear array of GaAs quantum dots hosting singlet-triplet qubits. We first examine the expected performance of the code using simple error models of circuit-level and phenomenological noise, reporting a.o. a 3% circuit-level depolarizing noise threshold. We then perform density-matrix simulations using a maximum-likelihood and minimum-weight matching decoder to study the effect of real-device dephasing, read-out error, quasi-static as well as fast gate noise. Considering the trade-off between qubit read-out time versus dephasing time (T2), we identify a sub-threshold region for the phase-flip code which lies within experimental reach.   

Devloping atom-based solid-state quantum simulators: understanding charge-stability diagrams of dopant arrays in Si

Atomically precise fabrication of dopant arrays in Si provides exciting opportunities to perform quantum simulations and to study the dynamics of engineered quantum systems. Here we describe theoretical simulations done for two-dimensional arrays of dopants in Si used to implement an extended range Fermi-Hubbard model. Simulations are done with and without atom disorder, as a function of the electron-electron interaction to test the limits of weak and strong interaction, and with and without a spin/valley degree of freedom. Results are used to understand charge-stability diagrams, recently obtained for two-dimensional arrays of dopants in Si. The nature of transport through these arrays depends critically on the ratio of the inter-dopant tunneling to tunnel coupling of the dopants to the source and drain. We consider n x m arrays of different sizes to identify the array states that are probed in transport. We further consider the effect of array orientation relative to the source and drain on the tunnel coupling and on the capacitive coupling to side gates. Implications for using dopant arrays as a quantum lab on a chip are discussed.   

Controlling textured hole spins in InAs quantum dots with oscillating electric fields

Recently, we have shown that hole spins in InAs quantum dots (QDs) exhibit spatially dependent texture, caused by the spin-orbit properties of the material and the geometry of the dot. Utilizing this spin texture, we demonstrated the ability to flip the overall hole spin by reversing the in-plane electrical bias across the dot. To fully capture the spin texture of the hole states, we used an atomistic tight-binding model that is able to resolve the wavefunction at the atomic level. However, atomistic tight-binding calculations are computationally expensive. Here, we present a reduced Hamiltonian capable of describing the evolution of the lowest hole state tight-binding wavefunctions, simulating the effect of oscillating electric fields, while fully preserving the effects of the spin texture. We calculate the timescale at which the spatial texture of the hole spin evolves, how the spin texture changes as the field oscillates, and how oscillating fields drive the overall net spin. We briefly discuss how our results can be used to design new control schemes for holes in QDs.