Gate-Sensing Coherent Charge Oscillations in a Silicon Field-Effect Transistor

Coherent charge oscillations in a bilayer graphene double quantum dot

The coherent dynamics of a quantum mechanical two-level system passing through an anti-crossing of two energy levels can give rise to Landau-Zener-Stückelberg-Majorana (LZSM) interference. LZSM interference spectroscopy has proven to be a fruitful tool to investigate charge noise and charge decoherence in semiconductor quantum dots (QDs). Recently, bilayer graphene has developed as a promising platform to host highly tunable QDs potentially useful for hosting spin and valley qubits. So far, in this system no coherent oscillations have been observed and little is known about charge noise in this material. Here, we report coherent charge oscillations and [Formula: see text] charge decoherence times in a bilayer graphene double QD. The charge decoherence times are measured independently using LZSM interference and photon assisted tunneling. Both techniques yield [Formula: see text] average values in the range of 400-500 ps. The observation of charge coherence allows to study the origin and spectral distribution of charge noise in future experiments.

Probing Two Driven Double Quantum Dots Strongly Coupled to a Cavity

We experimentally and theoretically study a driven hybrid circuit quantum electrodynamics (cQED) system beyond the dispersive coupling regime. Treating the cavity as part of the driven system, we develop a theory applicable to such strongly coupled and to multiqubit systems. The fringes measured for a single driven double quantum dot (DQD)-cavity setting and the enlarged splittings of the hybrid Floquet states in the presence of a second DQD are well reproduced with our model. This opens a path to study Floquet states of multiqubit systems with arbitrarily strong coupling and reveals a new perspective for understanding strongly driven hybrid systems.

Multi-Dimensional Quantum Capacitance of the Two-Site Hubbard Model: The Role of Tunable Interdot Tunneling

Few-electron states confined in quantum-dot arrays are key objects in quantum computing. The discrimination between these states is essential for the readout of a (multi-)qubit state, and can be achieved through a measurement of the quantum capacitance within the gate-reflectometry approach. For a system controlled by several gates, the dependence of the measured capacitance on the direction of the oscillations in the voltage space is captured by the quantum capacitance matrix. Herein, we apply this tool to study a double quantum dot coupled to three gates, which enable the tuning of both the bias and the tunneling between the two dots. Analytical solutions for the two-electron case are derived within a Hubbard model, showing the overall dependence of the quantum capacitance matrix on the applied gate voltages. In particular, we investigate the role of the tunneling gate and reveal the possibility of exploiting interdot coherences in addition to charge displacements between the dots. Our results can be directly applied to double-dot experimental setups, and pave the way for further applications to larger arrays of quantum dots.

Single-Shot Readout of a Driven Hybrid Qubit in a GaAs Double Quantum Dot

We report a single-shot-based projective readout of a semiconductor hybrid qubit formed by three electrons in a GaAs double quantum dot. Voltage-controlled adiabatic transitions between the qubit operations and readout conditions allow high-fidelity mapping of quantum states. We show that a large ratio both in relaxation time vs tunneling time (≈50) and singlet-triplet splitting vs thermal energy (≈20) allows energy-selective tunneling-based spin-to-charge conversion with a readout visibility of ≈92.6%. Combined with ac driving, we demonstrate high visibility coherent Rabi and Ramsey oscillations of a hybrid qubit in GaAs. Further, we discuss the generality of the method for use in other materials, including silicon.

Epitaxial Growth of Ordered In-Plane Si and Ge Nanowires on Si (001)

Controllable growth of wafer-scale in-plane nanowires (NWs) is a prerequisite for achieving addressable and scalable NW-based quantum devices. Here, by introducing molecular beam epitaxy on patterned Si structures, we demonstrate the wafer-scale epitaxial growth of site-controlled in-plane Si, SiGe, and Ge/Si core/shell NW arrays on Si (001) substrate. The epitaxially grown Si, SiGe, and Ge/Si core/shell NW are highly homogeneous with well-defined facets. Suspended Si NWs with four {111} facets and a side width of about 25 nm are observed. Characterizations including high resolution transmission electron microscopy (HRTEM) confirm the high quality of these epitaxial NWs.

Quantum Interferometry with a g-Factor-Tunable Spin Qubit

We study quantum interference effects of a qubit whose energy levels are continuously modulated. The qubit is formed by an impurity electron spin in a silicon tunneling field-effect transistor, and it is read out by spin blockade in a double-dot configuration. The qubit energy levels are modulated via its gate-voltage-dependent g factors, with either rectangular, sinusoidal, or ramp radio frequency waves. The energy-modulated qubit is probed by the electron spin resonance. Our results demonstrate the potential of spin qubit interferometry implemented in a silicon device and operated at a relatively high temperature.

Floquet Spectroscopy of a Strongly Driven Quantum Dot Charge Qubit with a Microwave Resonator

We experimentally investigate a strongly driven GaAs double quantum dot charge qubit weakly coupled to a superconducting microwave resonator. The Floquet states emerging from strong driving are probed by tracing the qubit-resonator resonance condition. In this way, we probe the resonance of a qubit that is driven in an adiabatic, a nonadiabatic, or an intermediate rate, showing distinct quantum features of multiphoton processes and a fringe pattern similar to Landau-Zener-Stückelberg interference. Our resonant detection scheme enables the investigation of novel features when the drive frequency is comparable to the resonator frequency. Models based on the adiabatic approximation, rotating wave approximation, and Floquet theory explain our experimental observations.

Landau-Zener-Stückelberg-Majorana Interferometry of a Single Hole

We perform Landau-Zener-Stückelberg-Majorana (LZSM) spectroscopy on a system with strong spin-orbit interaction (SOI), realized as a single hole confined in a gated double quantum dot. Analogous to electron systems, at a magnetic field B=0 and high modulation frequencies, we observe photon-assisted tunneling between dots, which smoothly evolves into the typical LZSM funnel-shaped interference pattern as the frequency is decreased. In contrast to electrons, the SOI enables an additional, efficient spin-flip interdot tunneling channel, introducing a distinct interference pattern at finite B. Magnetotransport spectra at low-frequency LZSM driving show the two channels to be equally coherent. High-frequency LZSM driving reveals complex photon-assisted tunneling pathways, both spin conserving and spin flip, which form closed loops at critical magnetic fields. In one such loop, an arbitrary hole spin state is inverted, opening the way toward its all-electrical manipulation.

Palladium gates for reproducible quantum dots in silicon

We replace the established aluminium gates for the formation of quantum dots in silicon with gates made from palladium. We study the morphology of both aluminium and palladium gates with transmission electron microscopy. The native aluminium oxide is found to be formed all around the aluminium gates, which could lead to the formation of unintentional dots. Therefore, we report on a novel fabrication route that replaces aluminium and its native oxide by palladium with atomic-layer-deposition-grown aluminium oxide. Using this approach, we show the formation of low-disorder gate-defined quantum dots, which are reproducibly fabricated. Furthermore, palladium enables us to further shrink the gate design, allowing us to perform electron transport measurements in the few-electron regime in devices comprising only two gate layers, a major technological advancement. It remains to be seen, whether the introduction of palladium gates can improve the excellent results on electron and nuclear spin qubits defined with an aluminium gate stack.

Symmetry-Breaking Assisted Landau-Zener Transitions in Rydberg Atoms

We report the observation of a controlled Landau-Zener transition (LZT) in Rydberg atoms by breaking the symmetry of the underlying Hamiltonian. For a nonhydrogenic Rydberg atom inside a changing electric (F) field, a LZT occurs between the avoided crossing energy levels of neighboring Rydberg states only for a sufficiently high changing rate. If a transverse magnetic (B) field is applied as we implement, the atomic level symmetry is broken, which causes the Stark manifolds denoted by a different |m| (m is the magnetic quantum number) to interact with each other. The mixed state levels end up pushing the adiabatically repelled target states closer and additionally they serve as stepping stones for the sequential LZTs between the neighboring sublevels. Such a feature significantly decreases the changing rate required for an efficient LZT inside a pure electric field. We report experimental observations that support the above scenario. It opens a versatile approach for engineering a controlled LZT in more general systems.

Hole Spin Resonance and Spin-Orbit Coupling in a Silicon Metal-Oxide-Semiconductor Field-Effect Transistor

We study hole spin resonance in a p-channel silicon metal-oxide-semiconductor field-effect transistor. In the subthreshold region, the measured source-drain current reveals a double dot in the channel. The observed spin resonance spectra agree with a model of strongly coupled two-spin states in the presence of a spin-orbit-induced anticrossing. Detailed spectroscopy at the anticrossing shows a suppressed spin resonance signal due to spin-orbit-induced quantum state mixing. This suppression is also observed for multiphoton spin resonances. Our experimental observations agree with theoretical calculations.

Quantum state readout of individual quantum dots by electrostatic force detection

Electric charge detection by atomic force microscopy (AFM) with single-electron resolution (e-EFM) is a promising way to investigate the electronic level structure of individual quantum dots (QDs). The oscillating AFM tip modulates the energy of the QDs, causing single electrons to tunnel between QDs and an electrode. The resulting oscillating electrostatic force changes the resonant frequency and damping of the AFM cantilever, enabling electrometry with a single-electron sensitivity. Quantitative electronic level spectroscopy is possible by sweeping the bias voltage. Charge stability diagram can be obtained by scanning the AFM tip around the QD. e-EFM technique enables to investigate individual colloidal nanoparticles and self-assembled QDs without nanoscale electrodes. e-EFM is a quantum electromechanical system where the back-action of a tunneling electron is detected by AFM; it can also be considered as a mechanical analog of admittance spectroscopy with a radio frequency resonator, which is emerging as a promising tool for quantum state readout for quantum computing. In combination with the topography imaging capability of the AFM, e-EFM is a powerful tool for investigating new nanoscale material systems which can be used as quantum bits.

Level Spectrum and Charge Relaxation in a Silicon Double Quantum Dot Probed by Dual-Gate Reflectometry

We report on dual-gate reflectometry in a metal-oxide-semiconductor double-gate silicon transistor operating at low temperature as a double quantum dot device. The reflectometry setup consists of two radio frequency resonators respectively connected to the two gate electrodes. By simultaneously measuring their dispersive responses, we obtain the complete charge stability diagram of the device. Electron transitions between the two quantum dots and between each quantum dot and either the source or the drain contact are detected through phase shifts in the reflected radio frequency signals. At finite bias, reflectometry allows probing charge transitions to excited quantum-dot states, thereby enabling direct access to the energy level spectra of the quantum dots. Interestingly, we find that in the presence of electron transport across the two dots the reflectometry signatures of interdot transitions display a dip-peak structure containing quantitative information on the charge relaxation rates in the double quantum dot.