Teck Seng Koh

Tunable Spin Loading and T-1 of a Silicon Spin Qubit Measured by Single-Shot Readout

The remarkable properties of silicon have made it the central material for the fabrication of current microelectronic devices. Silicon’s fundamental properties also make it an attractive option for the development of devices for spintronics [1] and quantum information processing [2–5]. The ability to manipulate and measure spins of single electrons is crucial for these applications. Here we report the manipulation and measurement of a single spin in a quantum dot fabricated in a silicon/silicon-germanium heterostructure. We demonstrate that the rate of loading of electrons into the device can be tuned over an order of magnitude using a gate voltage, that the spin state of the loaded electron depends systematically on the loading voltage level, and that this tunability arises because electron spins can be loaded through excited orbital states of the quantum dot. The longitudinal spin relaxation time T1 is measured using single-shot pulsed techniques [6] and found to be ∼ 3 seconds at a field of 1.85 Tesla. The demonstration of single spin measurement as well as a long spin relaxation time and tunability of the loading are all favorable properties for spintronics and quantum information processing applications. Silicon is a material in which spin qubits are expected to have long coherence times, thanks to the predominance of a spin-zero nuclear isotope and relatively weak spin-orbit coupling. However, silicon quantum dots have yet to demonstrate the reproducibility and controllability achieved in gallium arsenide devices [7–10]. Here, we demonstrate the control and manipulation of spin states of single electrons in a silicon/silicon-germanium (Si/SiGe) quantum dot and report the first single-shot measurements of the longitudinal spin relaxation time T1 in such devices. We also show that the presence of a relatively low-lying spin-split orbital excited state in the dot can be exploited to increase the speed and tunability of the loading of spins into the dot. Our results demonstrate that Si/SiGe quantum dots can be fabricated that are sufficiently tunable to enable single-electron manipulation and measurement, and that long spin relaxation times are consistent with the orbital and/or valley excitation energies in these systems. The measurements we report were performed on a gate-defined quantum dot with the gate configuration shown in Fig. 1a, tuned to be in the single-dot regime. The dot is measured at low temperature and in a parallel magnetic field. As shown in Fig. 1b, an electron can be loaded into one of four energy eigenstates; we denote 2.0 1.0 0.0 B (T) -0.158 -0.152

Fast Hybrid Silicon Double-Quantum-Dot Qubit

We propose a quantum dot qubit architecture that has an attractive combination of speed and fabrication simplicity. It consists of a double quantum dot with one electron in one dot and two electrons in the other. The qubit itself is a set of two states with total spin quantum numbers S(2)=3/4 (S=1/2) and S(z)=-1/2, with the two different states being singlet and triplet in the doubly occupied dot. Gate operations can be implemented electrically and the qubit is highly tunable, enabling fast implementation of one- and two-qubit gates in a simpler geometry and with fewer operations than in other proposed quantum dot qubit architectures with fast operations. Moreover, the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices.

Fast coherent manipulation of three-electron states in a double quantum dot

An important goal in the manipulation of quantum systems is the achievement of many coherent oscillations within the characteristic dephasing time T2(*). Most manipulations of electron spins in quantum dots have focused on the construction and control of two-state quantum systems, or qubits, in which each quantum dot is occupied by a single electron. Here we perform quantum manipulations on a system with three electrons per double quantum dot. We demonstrate that tailored pulse sequences can be used to induce coherent rotations between three-electron quantum states. Certain pulse sequences yield coherent oscillations fast enough that more than 100 oscillations are visible within a T2(*) time. The minimum oscillation frequency we observe is faster than 5 GHz. The presence of the third electron enables very fast rotations to all possible states, in contrast to the case when only two electrons are used, in which some rotations are slow.

Coherent quantum oscillations and echo measurements of a Si charge qubit

Fast quantum oscillations of a charge qubit in a double quantum dot fabricated in a Si/SiGe heterostructure are demonstrated and characterized experimentally. The measured inhomogeneous dephasing time T ∗ 2 ranges from 127 ps to ∼2.1 ns; it depends substantially on how the energy difference of the the two qubit states varies with external voltages, consistent with a decoherence process that is dominated by detuning noise (charge noise that changes the asymmetry of the qubit’s double-well potential). In the regime with the shortest T ∗ 2 , applying a charge-echo pulse sequence increases the measured inhomogeneous decoherence time from 127 ps to 760 ps, demonstrating that low-frequency noise processes are an important dephasing mechanism.

Pulse-Gated Quantum-Dot Hybrid Qubit

A quantum-dot hybrid qubit formed from three electrons in a double quantum dot has the potential for great speed, due to the presence of level crossings where the qubit becomes chargelike. Here, we show how to exploit the level crossings to implement fast pulsed gating. We develop one- and two-qubit dc quantum gates that are simpler than the previously proposed ac gates. We obtain closed-form solutions for the control sequences and show that the gates are fast (subnanosecond) and can achieve high fidelities.

High-fidelity gates in quantum dot spin qubits

Significance This paper addresses a critical issue in the development of a practical quantum computer using semiconducting quantum dots: the achievement of high-fidelity quantum gates in the presence of environmental noise. The paper shows how to maximize the fidelity, which is the key figure of merit, for several different implementations of quantum gates in semiconducting quantum dot qubits. The paper also shows how to optimize the fidelity over the various control parameters, and that the different implementations display an unexpected commonality in how the fidelity depends on these parameters. The optimum fidelity for a given implementation is determined by experimental constraints on the control parameters, which are different for different qubit designs. Several logical qubits and quantum gates have been proposed for semiconductor quantum dots controlled by voltages applied to top gates. The different schemes can be difficult to compare meaningfully. Here we develop a theoretical framework to evaluate disparate qubit-gating schemes on an equal footing. We apply the procedure to two types of double-dot qubits: the singlet–triplet and the semiconducting quantum dot hybrid qubit. We investigate three quantum gates that flip the qubit state: a DC pulsed gate, an AC gate based on logical qubit resonance, and a gate-like process known as stimulated Raman adiabatic passage. These gates are all mediated by an exchange interaction that is controlled experimentally using the interdot tunnel coupling g and the detuning ϵ, which sets the energy difference between the dots. Our procedure has two steps. First, we optimize the gate fidelity (f) for fixed g as a function of the other control parameters; this yields an that is universal for different types of gates. Next, we identify physical constraints on the control parameters; this yields an upper bound that is specific to the qubit-gate combination. We show that similar gate fidelities should be attainable for singlet-triplet qubits in isotopically purified Si, and for hybrid qubits in natural Si. Considerably lower fidelities are obtained for GaAs devices, due to the fluctuating magnetic fields ΔB produced by nuclear spins.

Pauli spin blockade and lifetime-enhanced transport in a Si/SiGe double quantum dot

We analyze electron-transport data through a Si/SiGe double quantum dot in terms of spin blockade and lifetime-enhanced transport LET, which is transport through excited states that is enabled by long spinrelaxation times. We present a series of low-bias voltage measurements showing the sudden appearance of a strong tail of current that we argue is an unambiguous signature of LET appearing when the bias voltage becomes greater than the singlet-triplet splitting for the 2,0 electron state. We present eight independent data sets, four in the forward-bias spin-blockade regime and four in the reverse-bias lifetime-enhanced transport regime and show that all eight data sets can be fit to one consistent set of parameters. We also perform a detailed analysis of the reverse-bias LET regime, using transport rate equations that include both singlet and triplet transport channels. The model also includes the energy-dependent tunneling of electrons across the quantum barriers and resonant and inelastic tunneling effects. In this way, we obtain excellent fits to the experimental data, and we obtain quantitative estimates for the tunneling rates and transport currents throughout the reverse-bias regime. We provide a physical understanding of the different blockade regimes and present detailed predictions for the conditions under which LET may be observed.

Single-Shot Measurement of One and Two-Electron Spin States in Si/SiGe Gated Quantum Dots

In this talk we discuss recent experiments involving single-shot measurements of electron spins in both a single-spin basis and a two-electron spin basis. In both cases, to measure the spin state we use a spin-to-charge conversion technique based on the energy difference between the two spin states. For single spins, this approach involves applying a magnetic field large enough that the Zeeman splitting between up and down spins Ez = gμBB is larger than the electron temperature T. Here g ≅ 2 is the g-factor, μB is the Bohr magneton, B is the magnetic field, and T ≅ 140 mK for the single-spin experiments. For measurements of two-electron spin states, we make use of the energy difference between singlet and triplet states with two electrons in a single dot; in this case, we require the singlet-triplet splitting to be larger than the temperature T, which was less than 50 mK for the two-electron measurements.