Single-electron Regime Research Articles

Understanding conditions for the single electron regime in 28 nm FD-SOI quantum dots: Interpretation of experimental data with 3D quantum TCAD simulations

Single electrons trapped in quantum dots hosted in silicon nanostructures are a promising platform for the implementation of quantum technologies. In this study, we investigated the required conditions to attain the single-electron regime in an Ultra-Thin Body and Buried oxide (UTBB) Fully Depleted Silicon-On-Insulator (FD-SOI) quantum dot device fabricated using the standard manufacturing process of STMicroelectronics. The cryogenic temperature operation of the quantum dot device is simulated and analyzed using the 3D Quantum Technology Computer Aided Design (QTCAD) software developed by Nanoacademic Technologies, achieving convergence down to 1.4 K. We report here simulations exploring single-electron occupancy of a single side-gate activated corner quantum dot and compare them to experimental data collected from the measurements on a device with the same geometry.

Colloquium: Advances in automation of quantum dot devices control.

Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of individual electrostatic and dynamical voltages that must be carefully set to localize the system into the single-electron regime and to realize good qubit operational performance. The mapping of requisite QD locations and charges to gate voltages presents a challenging classical control problem. With an increasing number of QD qubits, the relevant parameter space grows sufficiently to make heuristic control unfeasible. In recent years, there has been considerable effort to automate device control that combines script-based algorithms with machine learning (ML) techniques. In this Colloquium, a comprehensive overview of the recent progress in the automation of QD device control is presented, with a particular emphasis on silicon- and GaAs-based QDs formed in two-dimensional electron gases. Combining physics-based modeling with modern numerical optimization and ML has proven effective in yielding efficient, scalable control. Further integration of theoretical, computational, and experimental efforts with computer science and ML holds vast potential in advancing semiconductor and other platforms for quantum computing.

Passage of a vortex electron over an inclined grating

We study Smith-Purcell radiation from a conducting grating generated by an inclined passage of a shaped electron wave packet with an electric quadrupole moment in the nonparaxial regime. Spreading of an asymmetric wave packet induces quadrupole corrections to the radiation field. Although the nonparaxial corrections stay small, they are dynamically enhanced during the interaction of the electron with the grating whose length exceeds the Rayleigh length of the packet. To simplify the possible experimental setup where such effects could be measured, we study the dependence of these effects on the inclination angle, i.e., the angle between the mean velocity of the packet and the surface of the grating. There is a minimal angle such that the multipole expansion always stays valid at the grating surface. In such a regime, the quadrupole contribution to the Smith-Purcell radiation can become the leading one, which represents a quantum effect impossible for classical pointlike electrons. Thus, the impact of the wave-packet shape (vortex structure or nonspherical shape) can be observed experimentally by comparing the radiation for different orientations of the grating in the single-electron regime.

3D integration and measurement of a semiconductor double quantum dot with a high-impedance TiN resonator

One major challenge to scaling quantum dot qubits is the dense wiring requirements, making it difficult to envision fabricating large 2D arrays of nearest-neighbor-coupled qubits necessary for error correction. We describe a method to ameliorate this issue by spacing out the qubits using superconducting resonators facilitated by 3D integration. To prove the viability of this approach, we use integration to couple an off-chip high-impedance TiN resonator to a double quantum dot in a Si/SiGe heterostructure. Using the resonator as a dispersive gate sensor, we tune the device down to the single electron regime with an SNR = 5.36. Characterizing the individual systems shows 3D integration can be done while maintaining low-charge noise for the quantum dots and high-quality factors for the superconducting resonator (single photon QL = 2.14 × 104 with Qi ≈ 3 × 105), necessary for readout and high-fidelity two-qubit gates.

Spin-valley coupling in single-electron bilayer graphene quantum dots

Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems, is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enable to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in bilayer graphene quantum dots in the single-electron regime. By making use of highly-tunable double quantum dot devices we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of ≈ 60 μeV. Furthermore, we find an upper limit of a potentially disorder-induced mixing of the K and K^{prime} states below 20 μeV.

Dispersive sensing of charge states in a bilayer graphene quantum dot

We demonstrate dispersive readout of individual charge states in a gate-defined few-electron quantum dot in bilayer graphene. We employ a radio frequency reflectometry circuit, where an LC resonator with a resonance frequency close to 280 MHz is directly coupled to an Ohmic contact of the quantum dot device. The detection scheme based on changes in the quantum capacitance operates over a wide gate-voltage range and allows us to probe excited states down to the single-electron regime. Crucially, the presented sensing technique avoids the use of an additional, capacitively coupled quantum device such as a quantum point contact or single electron transistor, making dispersive sensing particularly interesting for gate-defined graphene quantum dots.

Algorithm for automated tuning of a quantum dot into the single-electron regime

We report an algorithm designed to perform computer-automated tuning of a single quantum dot with a charge sensor. The algorithm performs an adaptive measurement sequence of sub-sized stability diagrams until the single-electron regime is identified and reached. For each measurement, the signal processing module removes the physical background of the charge sensor to generate a binary image of charge transitions. Then, the image analysis module identifies the position and number of lines using two line detection schemes that are robust to noise and missing data.

Single-Electron Double Quantum Dots in Bilayer Graphene.

We present transport measurements through an electrostatically defined bilayer graphene double quantum dot in the single-electron regime. With the help of a back gate, two split gates, and two finger gates, we are able to control the number of charge carriers on two gate-defined quantum dots independently between zero and five. The high tunability of the device meets requirements to make such a device a suitable building block for spin-qubits. In the single-electron regime, we determine interdot tunnel rates on the order of 2 GHz. Both, the interdot tunnel coupling as well as the capacitive interdot coupling increase with dot occupation, leading to the transition to a single quantum dot. Finite bias magneto-spectroscopy measurements allow to resolve the excited-state spectra of the first electrons in the double quantum dot and are in agreement with spin and valley conserving interdot tunneling processes.

Site-Selective Quantum Control in an Isotopically Enriched Si28/Si0.7Ge0.3 Quadruple Quantum Dot

Silicon spin qubits are a promising quantum computing platform offering long coherence times, small device sizes, and compatibility with industry-backed device fabrication techniques. In recent years, high fidelity single-qubit and two-qubit operations have been demonstrated in Si. Here, we demonstrate coherent spin control in a quadruple quantum dot fabricated using isotopically enriched 28Si. We tune the ground state charge configuration of the quadruple dot down to the single electron regime and demonstrate tunable interdot tunnel couplings as large as 20 GHz, which enables exchange-based two-qubit gate operations. Site-selective single spin rotations are achieved using electric dipole spin resonance in a magnetic field gradient. We execute a resonant-CNOT gate between two adjacent spins in 270 ns.

A low-disorder metal-oxide-silicon double quantum dot

One of the biggest challenges impeding the progress of metal-oxide-silicon (MOS) quantum dot devices is the presence of disorder at the Si/SiO2 interface which interferes with controllably confining single and few electrons. In this work, we have engineered a low-disorder MOS quantum double-dot device with critical electron densities, i.e., the lowest electron density required to support a conducting pathway, approaching critical electron densities reported in high quality Si/SiGe devices and commensurate with the lowest critical densities reported in any MOS device. Utilizing a nearby charge sensor, we show that the device can be tuned to the single-electron regime where charging energies of ≈8 meV are measured in both dots, consistent with the lithographic size of the dot. Probing a wide voltage range with our quantum dots and charge sensor, we detect three distinct electron traps, corresponding to a defect density consistent with the ensemble measured critical density. Low frequency charge noise measurements at 300 mK indicate a 1/f noise spectrum of 3.4 μeV/Hz1∕2 at 1 Hz and magnetospectroscopy measurements yield a valley splitting of 110 ± 26 μeV. This work demonstrates that reproducible MOS spin qubits are feasible and represent a platform for scaling to larger qubit systems in MOS.

Calculation of a capacitively-coupled floating gate array toward quantum annealing machine

Quantum annealing machines based on superconducting qubits, which have the potential to solve optimization problems faster than digital computers, are of great interest not only to researchers but also to the general public. In this paper, we propose a quantum annealing machine based on a semiconductor floating gate (FG) array. The purpose of using the architecture of nand flash memories is to reuse a mature technology to create large arrays of silicon qubits. Current high-density nand flash memories use sufficiently small FG cells to make the number of electrons stored in each cell small and countable. The high packing density of these cells creates mutual capacitive couplings that can be used to generate cell-to-cell interactions. We explore these characteristics to derive an Ising Hamiltonian for the FG system in the single-electron regime. Considering the size of a cell (10 nm), the ideal operation temperature of a quantum annealer based on FG cells is estimated to be approximately that of liquid nitrogen. Assuming the parameters of a commercial 64 Gbit nand, we estimate that it is possible to create 2-megabyte (MB) qubit systems solely using conventional fabrication processes. Our proposal demonstrates that a large qubit system can be obtained as a natural extension of the miniaturization of commercial-grade electronics, although more effort will likely be required to achieve high-quality qubits.

Sub-cycle optical phase control of nanotunnelling in the single-electron regime

Carrier-envelope-phase control of the electronic current over a laterally confined tunnelling gap a few nanometres wide yields current densities above 50 MA cm–2 driven by picojoule-level optical pulses at room temperature.

Computer-automated tuning of semiconductor double quantum dots into the single-electron regime

We report the computer-automated tuning of gate-defined semiconductor double quantum dots in GaAs heterostructures. We benchmark the algorithm by creating three double quantum dots inside a linear array of four quantum dots. The algorithm sets the correct gate voltages for all the gates to tune the double quantum dots into the single-electron regime. The algorithm only requires (1) prior knowledge of the gate design and (2) the pinch-off value of the single gate T that is shared by all the quantum dots. This work significantly alleviates the user effort required to tune multiple quantum dot devices.

The Use of a Standard Source of Synchrotron Radiation for Calibration of the Sensitivity of a Telescope with CCD Array and High Angular Resolution

A method involving the use of a primary standard source of synchrotron radiation for precision calibration of the sensitivity of telescopes equipped with a CCD array and high angular resolution is considered. The method is based on precision reproduction of the spectral energy characteristics, the Gaussian distribution of the spectral density of the irradiance over a radiating region, and the stability and reproducibility of the characteristics of synchrotron radiation in a single-electron regime.

Femtosecond single-electron diffraction.

Ultrafast electron diffraction allows the tracking of atomic motion in real time, but space charge effects within dense electron packets are a problem for temporal resolution. Here, we report on time-resolved pump-probe diffraction using femtosecond single-electron pulses that are free from intra-pulse Coulomb interactions over the entire trajectory from the source to the detector. Sufficient average electron current is achieved at repetition rates of hundreds of kHz. Thermal load on the sample is avoided by minimizing the pump-probe area and by maximizing heat diffusion. Time-resolved diffraction from fibrous graphite polycrystals reveals coherent acoustic phonons in a nanometer-thick grain ensemble with a signal-to-noise level comparable to conventional multi-electron experiments. These results demonstrate the feasibility of pump-probe diffraction in the single-electron regime, where simulations indicate compressibility of the pulses down to few-femtosecond and attosecond duration.

Compression of single-electron pulses with a microwave cavity

Few-femtosecond to attosecond electron pulses are required for advancing ultrafast diffraction and microscopy to the regime of electrons in motion. Here, we report the combination of a single-electron source with a microwave cavity for pulse compression. In such an arrangement, the electron pulses can become significantly shorter than the laser pulses used for electron generation. This comes at the expense of an increase in energy spread. We report the use of an energy analyzer for characterizing microwave-compressed single-electron pulses. Phase effects, linearity, focal distances, incoming pulse durations and laser–microwave jitter are measured for three different synchronization approaches. The results demonstrate the applicability of a microwave cavity in the single-electron regime and identify jitter as the current limitation on the way to few-femtosecond, eventually attosecond pulses of single electrons.

On the small-signal theory of stimulated Cherenkov emission in dielectric-lined waveguides

The growth characteristics of a two-dimensional Cherenkov free-electron laser (CFEL) in the small-signal low gain regime are studied for both single-electron and collective models. In the single-electron regime, for a thick enough beam, we prove that the gain of the CFEL can be increased by a factor of 2 than that obtained for an infinitely thin electron beam. Thus, the Cherenkov laser should be considered as a hybrid longitudinal/transverse free-electron laser device in general. In the collective-regime, we demonstrate the damping effects of Coulomb collisions among electrons on the amplification characteristics of a Cherenkov laser.

Growth and optical properties of axial hybrid III–V/silicon nanowires

Hybrid silicon nanowires with an integrated light-emitting segment can significantly advance nanoelectronics and nanophotonics. They would combine transport and optical characteristics in a nanoscale device, which can operate in the fundamental single-electron and single-photon regime. III-V materials, such as direct bandgap gallium arsenide, are excellent candidates for such optical segments. However, interfacing them with silicon during crystal growth is a major challenge, because of the lattice mismatch, different expansion coefficients and the formation of antiphase boundaries. Here we demonstrate a silicon nanowire with an integrated gallium-arsenide segment. We precisely control the catalyst composition and surface chemistry to obtain dislocation-free interfaces. The integration of gallium arsenide of high optical quality with silicon is enabled by short gallium phosphide buffers. We anticipate that such hybrid silicon/III-V nanowires open practical routes for quantum information devices, where for instance electronic and photonic quantum bits are manipulated in a III-V segment and stored in a silicon section.

Implementation of 4-bit Reversible Parallel Adder Using Nanoelectronic Single-Electron Circuitry

Single-Electron devices imply the possibility to control the movement and position of a single electron or a few electrons thereby reducing the device size and power consumption. A single-electron transistor can be operated as a switch with the transition of the gate voltage between two appropriate values thereby modifying conventional logic design into the single-electron regime by simply exchanging MOSFETs with SETs. Single-electron logic circuits can thus be employed to perform arithmetic functions, thereby making single-electron technology viable to realize high density low power consumping VLSI circuits. In the present work a single electron logic based high speed power efficient 4-bit reversible binary parallel adder is designed, implemented and its performance studied on its simulated model.

Spin-dependent transport through interacting graphene armchair nanoribbons

We investigate spin effects in transport across fully interacting, finite-size graphene armchair nanoribbons (ACNs) contacted to collinearly spin-polarized leads. In such systems, the presence of short-range Coulomb interaction between bulk states and states localized at the ribbon ends leads to novel spin-dependent phenomena. Specifically, the total spin of the low-energy many-body states is conserved during tunneling but that of the bulk and end states is not. As a consequence, in the single-electron regime, dominated by Coulomb blockade phenomena, we find pronounced negative differential conductance features for ACNs contacted to parallel polarized leads. These features are, however, absent in an anti-parallel contact configuration, which in turn leads, within a certain gate and bias voltage region, to a negative tunneling magneto-resistance. Moreover, we analyze the changes in the transport characteristics under the influence of an external magnetic field.