We investigate the energy spectra of three electrons in SiGe/Si/SiGe equilateral triangular and symmetric linear triple quantum dots in the presence of magnetic (in either Faraday or Voigt configuration) and electric fields with single valley approximation by using the real-space configuration interaction method. The strong electron-electron Coulomb interaction, which is crucial to the energy spectra, is explicitly calculated whereas the weak spin-orbit coupling is treated perturbatively. In both equilateral triangular and symmetric linear triple quantum dots, we find doublet-quartet transition of ground-state spin configuration by varying dot size or interdot distance in the absence of external fields. This transition has not been reported in the literature on triple quantum dots. In the magnetic-field (Faraday configuration) dependence of energy spectra, we find anticrossings with large energy splittings between the energy levels with the same spin state in the absence of the spin-orbit coupling. This anticrossing behavior originates from the triple quantum dot confinement potential. In addition, with the inclusion of the spin-orbit coupling, we find that all the intersections shown in the equilateral triangular case become anticrossing whereas only part of the intersections in symmetric linear case show anticrossing behavior in the presence of magnetic field in either the Faraday or Voigt configuration. All the anticrossing behaviors are analyzed based on symmetry consideration. Moreover, we show that the electric field can effectively influence the energy levels and the charge configurations.
Valley splitting in Si quantum dots embedded in SiGe
我们研究嵌入到Si_{0.75} Ge_{0.25}缓冲器中的Si量子点的能谱，使用原子数值计算与量子位实现相关的尺寸。最低轨道态的谷简并度被提升，谷分裂随单层频率的变化而变化。对于点厚度<6 nm valley splitting is found to be >150 μ eV。利用原子计算的独特优势，我们分析了缓冲区无序对谷分裂的影响。缓冲区中的无序导致谷分裂被抑制2.5倍，对于不同的无序实现，分裂波动约20 ueV。通过这些模拟，我们可以指导未来的实验进入低设备到设备波动的区域。
We study double quantum dots in a Ge/SiGe heterostructure and test their maturity towards singlet-triplet ($S-T_0$) qubits. We demonstrate a large range of tunability, from two single quantum dots to a double quantum dot. We measure Pauli spin blockade and study the anisotropy of the $g$-factor. We use an adjacent quantum dot for sensing charge transitions in the double quantum dot at interest. In conclusion, Ge/SiGe possesses all ingredients necessary for building a singlet-triplet qubit.
Electron spins in Si/SiGe quantum wells suffer from nearly degenerate conduction band valleys, which compete with the spin degree of freedom in the formation of qubits. Despite attempts to enhance the valley energy splitting deterministically, by engineering a sharp interface, valley splitting fluctuations remain a serious problem for qubit uniformity, needed to scale up to large quantum processors. Here, we elucidate and statistically predict the valley splitting by the holistic integration of 3D atomic-level properties, theory and transport. We find that the concentration fluctuations of Si …
Excitation intensity dependence of photoluminescence spectra of SiGe quantum dots grown on prepatterned Si substrates: Evidence for biexcitonic transition
Electron spins in silicon have long coherence times and are a promising qubit platform. However, electric field noise in semiconductors poses a challenge for most single- and multi-qubit operations in quantum-dot spin qubits. Here, we investigate the dependence of low-frequency charge noise spectra on temperature and aluminum-oxide gate dielectric thickness in Si/SiGe quantum dots with overlapping gates. We find that charge noise increases with aluminum oxide thickness. We also find strong dot-to-dot variations in the temperature dependence of the noise magnitude and spectrum. These findings s…
Recently, lithographic quantum dots in strained-Ge/SiGe have become a promising candidate for quantum computation, with a remarkably quick progression from demonstration of a quantum dot to qubit logic demonstrations. Here we present a measurement of the out-of-plane $g$-factor for single-hole quantum dots in this material. As this is a single-hole measurement, this is the first experimental result that avoids the strong orbital effects present in the out-of-plane configuration. In addition to verifying the expected $g$-factor anisotropy between in-plane and out-of-plane magnetic ($B$)-fields,…
The valley degree of freedom presents challenges and opportunities for silicon spin qubits. An important consideration for singlet-triplet states is the presence of two distinct triplets, comprised of valley vs. orbital excitations. Here we show that both of these triplets are present in the typical operating regime, but that only the valley-excited triplet offers intrinsic protection against charge noise. We further show that this protection arises naturally in dots with stronger confinement. These results reveal an inherent advantage for silicon-based multi-electron qubits.
Quantum dot arrays are a versatile platform for the implementation of spin qubits, as high-bandwidth sensor dots can be integrated with single-, double- and triple-dot qubits yielding fast and high-fidelity qubit readout. However, for undoped silicon devices, reflectometry off sensor ohmics suffers from the finite resistivity of the two-dimensional electron gas (2DEG), and alternative readout methods are limited to measuring qubit capacitance, rather than qubit charge. By coupling a surface-mount resonant circuit to the plunger gate of a high-impedance sensor, we realized a fast charge sensing…
We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of ma…
Low-Noise Quantum Dots in Ultra-Shallow Ge/SiGe Heterostructures for Prototyping Hybrid Semiconducting-Superconducting Devices
Institute of Science and Technology Austria（奥地利科学与技术研究所）；Catalan Institute of Nanoscience and Nanotechnology – ICN2 (CSIC and BIST)（加泰罗尼亚纳米科学技术研究所（CSIC和BIST））
Interactions between electrons can strongly affect the shape and functionality of multi-electron quantum dots. The resulting charge distributions can be localized, as in the case of Wigner molecules, with consequences for the energy spectrum and tunneling to states outside the dot. The situation is even more complicated for silicon dots, due to the interplay between valley, orbital, and interaction energy scales. Here, we study two-electron wavefunctions in electrostatically confined quantum dots formed in a SiGe/Si/SiGe quantum well at zero magnetic field, using a combination of tight-binding…
Even as today's most prominent spin-based qubit technologies are maturing in terms of capability and sophistication, there is growing interest in exploring alternate material platforms that may provide advantages, such as enhanced qubit control, longer coherence times, and improved extensibility. Recent advances in heterostructure material growth have opened new possibilities for employing hole spins in semiconductors for qubit applications. Undoped, strained Ge/SiGe quantum wells are promising candidate hosts for hole spin-based qubits due to their low disorder, large intrinsic spin-orbit cou…
We implement a technique for measuring the singlet-triplet energy splitting responsible for spin-to-charge conversion in semiconductor quantum dots. This method, which requires fast, single-shot charge measurement, reliably extracts an energy in the limits of both large and small splittings. We perform this technique on an undoped, accumulation-mode Si/SiGe triple-quantum dot and find that the measured splitting varies smoothly as a function of confinement gate biases. Not only does this demonstration prove the value of having an $in~situ$ excited-state measurement technique as part of a stand…
Electron spins in silicon quantum dots are promising qubits due to their long coherence times, scalable fabrication, and potential for all-electrical control. However, charge noise in the host semiconductor presents a major obstacle to achieving high-fidelity single- and two-qubit gates in these devices. In this work, we measure the charge-noise spectrum of a Si/SiGe singlet-triplet qubit over nearly 12 decades in frequency using a combination of methods, including dynamically-decoupled exchange oscillations with up to 512 π pulses during the qubit evolution. The charge noise is colored across…
Motivated by recent experiments of Zajac et al. [arXiv:1708.03530], we theoretically describe high-fidelity two-qubit gates using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We use a combination of analytical calculations and numerical simulations to provide the optimal pulse sequences and parameter settings for the gate operation. We present a novel synchronization method which avoids detrimental spin flips during the gate operation and provide details about phase mismatches accumulated during the two-qubit gates which occur due…
Silicon spin qubits show great promise as a scalable qubit platform for fault-tolerant quantum computing. However, fast high-fidelity readout of charge and spin states, which is required for quantum error correction, has remained elusive. Radio-frequency reflectometry enables rapid high-fidelity readout of GaAs spin qubits, but the relatively large resistances and capacitances of accumulation-mode Si quantum dot devices have made radio-frequency reflectometry challenging in these platforms. In this work, we implement radio-frequency reflectometry in a Si/SiGe quantum dot device with overlappin…
Silicon quantum dot qubits must contend with low-lying valley excited states which are sensitive functions of the quantum well heterostructure and disorder; quantifying and maximizing the energies of these states are critical to improving device performance. We describe a spectroscopic method for probing excited states in isolated Si/SiGe double quantum dots using standard baseband pulsing techniques, easing the extraction of energy spectra in multiple-dot devices. We use this method to measure dozens of valley excited state energies spanning multiple wafers, quantum dots, and orbital states, …
We theoretically investigate the energy of the ground state exciton confined to two-dimensional (2D) monolayers with circular shape. Within an effective mass approach employing a nonlocal screening effect on the Coulomb potential energy, we demonstrate how the exciton energy is correlated with the radius of the circle, electron-hole reduced mass, and 2D susceptibility. In addition, we show that a dead layer around the circle edge, into which the electron-hole pair cannot penetrate, is necessary for understanding the energy shift recently observed in monolayer WSe2 quantum dots.
We present a detailed investigation of different excitonic states weakly confined in single GaAs/AlGaAs quantum dots obtained by the Al droplet-etching method. For our analysis we make use of temperature-, polarization- and magnetic field-dependent $μ$-photoluminescence measurements, which allow us to identify different excited states of the quantum dot system. Besides that, we present a comprehensive analysis of g-factors and diamagnetic coefficients of charged and neutral excitonic states in Voigt and Faraday configuration. Supported by theoretical calculations by the Configuration interacti…
We investigate the effects of the orientation of the magnetic field and the orientation of a quantum dot, with respect to crystallographic coordinates, on the quality of an electrically controlled qubit realized in a gated semiconductor quantum dot. We find that, due to the anisotropy of the spin-orbit interactions, varying the two orientations it is possible to tune the qubit in the sense of optimizing the ratio of its couplings to phonons and to a control electric field. We find conditions under which such optimal setup can be reached by solely reorienting the magnetic field, and when a spec…
Silicon-germanium heterostructures have successfully hosted quantum dot qubits, but the intrinsic near-degeneracy of the two lowest valley states poses an obstacle to high fidelity quantum computing. We present a modification to the Si/SiGe heterostructure by the inclusion of a spike in germanium concentration within the quantum well in order to increase the valley splitting. The heterostructure is grown by chemical vapor deposition and magnetospectroscopy is performed on gate-defined quantum dots to measure the excited state spectrum. We demonstrate a large and widely tunable valley splitting…
