Interdot Capacitance Research Articles

In situ Tuning of the Electric-Dipole Strength of a Double-Dot Charge Qubit: Charge-Noise Protection and Ultrastrong Coupling

Semiconductor quantum dots in which electrons or holes are isolated via electrostatic potentials generated by surface gates are promising building blocks for semiconductor-based quantum technology. Here, we investigate double-quantum-dot (DQD) charge qubits in GaAs capacitively coupled to high-impedance superconducting quantum interference device array and Josephson-junction array resonators. We tune the strength of the electric-dipole interaction between the qubit and the resonator in situ using surface gates. We characterize the qubit-resonator coupling strength, the qubit decoherence, and the detuning noise affecting the charge qubit for different electrostatic DQD configurations. We find all quantities to be systematically tunable over more than one order of magnitude, resulting in reproducible decoherence rates Γ2/2π<5 MHz in the limit of high interdot capacitance. In the opposite limit, by reducing the interdot capacitance, we increase the DQD electric-dipole strength and, therefore, its coupling to the resonator. Employing a Josephson-junction array resonator with an impedance of approximately 4 kΩ and a resonance frequency of ωr/2π∼5.6 GHz, we observe a coupling strength of g/2π∼630 MHz, demonstrating the possibility to operate electrons hosted in a semiconductor DQD in the ultrastrong-coupling regime (USC). The presented results are essential for further increasing the coherence of quantum-dot-based qubits and investigating USC physics in semiconducting QDs.6 MoreReceived 26 October 2021Revised 3 April 2022Accepted 26 May 2022DOI:https://doi.org/10.1103/PhysRevX.12.031004Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum information architectures & platformsQuantum information processingQuantum information with hybrid systemsQuantum information with solid state qubitsQuantum Information

(Invited) Evaluation of Coupled Triple Quantum Dots with Compact Device Structure

Semiconductor multiple-quantum-dot devices have been attracted as a single-electron pump and quantum bits (qubits) [1, 2]. In particular, silicon-based coupled-quantum-dot has been paid attentions for the applications as qubits in solid state quantum computers due to their long coherent time of electron spins [3]. In the previous reports, these devices have been demonstrated by the use of two-dimensional electron gas (2DEG) and multiple control gates, where many gates were used to form tunnel barriers. This device concept makes it difficult to integrate quantum dots (QDs) due to the interference of many gates. For the applications in quantum computing, development of coupled QDs with a smaller number of control gates is considered. We have already succeeded in the fabrication of serially coupled Si triple-quantum-dots (TQD) by pattern-dependent oxidation (PADOX) method [4] and additional oxidation of the silicon nanowire on a SOI wafer with three control gates [5, 6]. The formation of a Si TQD, where each QD is formed just under each control gate, was confirmed experimentally. The equivalent circuit of the fabricated TQD is shown in Fig. 1 (a). The device has nine gate capacitances and two inter-dot coupling capacitances. It is crucial to know these capacitances for controlling the potential and the number of electrons of each dot. It is well known that the nine gate capacitances can be evaluated from the stability diagram that consists of boundary of the charge transition in the QDs. If the distance between the three gates is relatively long enough to ignore the influence of non-adjacent QD, it is easy to get the stability diagrams of charges. However, when the TQD become compact in size, the outer QD cannot be ignored because the center gate strongly couples to all three QDs, i.e., C 23 or C 21 is comparable to C 22. The stability diagram of such TQD usually shows very complicated behavior because three boundaries of the charge transition lines of individual QDs are superimposed. Fig. 1(b) shows the stability diagram which is the contour plot of current of TQD at 10 K simulated as a function of the two gate voltages V 1 and V 2 by the use of Monte Carlo method. Green dotted lines in the figures are the boundaries of charge transition of QD3, which are difficult to determine from the diagram. In addition, the coupling capacitance between the QDs also makes the stability diagrams complicate. Figs. 1(c) and (d) show stability diagrams of the TQD when the coupling capacitances, C 2 and C 3, become larger. As shown in the figures, the current peaks (white regions) are split as coupling capacitance C 2 and C 3 increase.In this study, we propose a simple analyzing method to evaluate the TQD by defining the contributions from each QD in stability diagrams. In order to divide the complicated stability diagram of TQD into the diagram of each QD, we employ the simultaneous scanning of three gate voltages with different sweeping ratios [7]. The effectiveness of the method is also confirmed even when the inter-dot coupling capacitance is large as shown in Fig. 1(c) and (d). The analysis using this method was applied to a Si TQD device fabricated on SOI wafer and successfully achieved the nine gate capacitances of the TQD. Acknowledgement This work was partly supported by JSPS KAKENHI (nos. 25420279, 26630141, 15H01706, 16H04339 and 16K18073). References H. Pothier, et al.: “Single electron pump fabricated with ultrasmall normal tunnel junction,” Physica B, 169, 573 1991. W. G. van der Wiel, et al.: “Electron transport through double quantum dots,” Rev. Mod. Phys, 75, 1 2002. B. M. Maune, et al.: “Coherent singlet-triplet oscillations in a silicon-based double quantum dot,” Nature, 481, 344 2012. Y. Takahashi, et al.: “Fabrication technique for Si single-electron transistor operating at room temperature,” Electron. Lett. 31, 136 1995. T. Uchida, et al.: “Coupling capacitance between double quantum dots tunable by the number of electrons in Si quantum dots,” J. Appl. Phys. 117, 084316 2015. T. Uchida, et al.: “Fabrication and evaluation of series-triple quantum dots by thermal oxidation of silicon nanowire,” AIP Advances. 5, 117144 2015. T. Uchida, et al.: “Capacitance evaluation of compact silicon triple quantum dots by simultaneous gate voltage sweeping,” J. Appl. Phys. 120, 234502 2016. Figure 1

Two laterally arranged quantum dot systems with strong capacitive interdot coupling

A method has been developed to form two quantum dot systems in lateral arrangement in a two-dimensional electron system of a GaAs–AlGaAs heterostructure with strong capacitive interdot coupling. In the authors’ design, the interdot capacitance can reach more than one-third of the single-dot capacitance while tunneling between the dots is excluded. This has been achieved by a floating metallic electrode covering both quantum dots, a method already used in split-gate designs before. Here, however, they have reduced the capacitive coupling of this floating gate to other electrodes in the surroundings by an etching technique to obtain a large interdot coupling.

Coulomb blockade, current and shot noise in parallel double metallic quantum dotstructures

We systematically study sequential electron tunnelling through parallel double metallicquantum dot structures, focusing on the role of inter-dot coupling and parameterasymmetry. It is shown that the evolution of Coulomb blockade charging diagrams, inducedby only the inter-dot capacitance, describes the existing experimental data quite well. Boththe inter-dot capacitance and the resistance strongly affect the shot noise, making itsuper-Poissonian even in fully symmetric structures. An asymmetry of parameters,enhancing the role of inter-dot coupling, may produce a variety of current–voltagecharacteristics behaviours, including negative differential conductance regions, and a verylarge noise. For all structures studied the noise is shown to be more sensitive thanthe conductance to the inter-dot coupling as well as the parameter asymmetry.

Cotunnelling versus sequential tunnelling in Coulomb blockade metallic double quantumdot structures

The cotunnelling is systematically studied in comparison to sequential tunnelling inCoulomb blockade metallic double quantum dot structures, using the standardmaster equation approach. In the case of zero gate voltage, we are able to deriveanalytical expressions of threshold voltages for both tunnelling processes:Vth(s) for the sequentialtunnelling and Vth(2) for the lowest-order inelastic macroscopic quantum tunnelling (cotunnelling). Taking intoaccount the gate and temperature effects, numerical solutions of the master equationshow that an increase of the inter-dot capacitance leads to a decrease of the ratioVth(2)/Vth(s) and at the same time to a decrease of cotunnelling conductance compared to the sequentialone. An oscillation of cotunnelling conductance is observed in classical Coulomb blockedregions. In comparison with the sequential tunnelling conductance spectroscopy, the peakheight of cotunnelling conductance is about three orders of magnitude smaller and the peakspacing distribution is far from regular. Increase of temperature raises the current anddestroys the Coulomb gap. Its relative influence is more important at lower bias.

Capacitively coupled quantum dots as a single-electron switch

A double quantum dot in a GaAs/AlGaAs heterostructure with strong interdot capacitance but no interdot tunneling can be constructed using a floating metal gate that covers both dots and an etched trench between the dots that prevents tunneling. The interdot capacitance C INT=0.34 C Σ between Dots 1 and 2, measured using the Coulomb blockade, was significantly larger than that measured for similar dots without a floating gate. When a single electron is added to Dot 1 the charge couples to Dot 2, and vice versa, causing the Coulomb blockade peaks to split. The change in dot conductance from peak splitting can be as large as two orders of magnitude, allowing the double dot to be used as a single-electron switch. The split conductance peaks observed for weak tunneling from each dot to its leads were fit by a thermally broadened line shape, and good agreement with the data was found. Charge fluctuations induced by stronger tunneling from Dot 2 to its leads softened the splitting transition on Dot 1 that was maintained in the weak tunneling regime. Under the same conditions the splitting for Dot 2 remained sharp.

Strongly capacitively coupled quantum dots

Double quantum dots were formed in a gated GaAs/AlGaAs heterostructure with negligible interdot tunneling; strong capacitive coupling was provided by a floating interdot capacitor. The interdot capacitance was measured to be 0.28CΣ, where CΣ is the single-dot capacitance. Coulomb blockade conductance images for both dots versus side gate voltages at 70 mK show a hexagonal pattern of peaks; the double dot acts as a single-electron current switch. For weak tunneling, the conductance peaks of both dots fit thermally broadened line shapes. Charge fluctuations produced by strong tunneling on one dot are induced on the second, filling in its peak splitting.

Effect of phase breaking on ac transport through a quantum dot dimer

The ac response of a coupled double quantum dot system involving a phase-breaking effect is studied. We calculate the ac conductance based on the nonequilibrium Green's-function formalism. Some parasitic and gate capacitances are included in our model, thus the displacement current is considered, and the overall charge and current conservation are fulfilled. In our results the double resonant structure of the conductance is observed. We find that the electron-phonon interaction has a significant effect on the ac conductance both for low and high temperatures. Due to the phase-breaking effect of electron-phonon scattering, the resonant conductance peak is suppressed very seriously, and the second peak of the ac conductance may disappear completely. However, for the nonresonant situation, the conductance is enhanced for small frequencies. Furthermore, we study the effect of the capacitances on the ac conductance, and find that, for small frequencies, the capacitances have a small effect on the real part of the admittance. On the imaginary part of the admittance, all the capacitances except for the interdot capacitance have a considerable effect. For high frequencies all the capacitances have a considerable effect on the ac conductance.

Conductance peak splitting in hole transport through a SiGe double quantum dot

We have observed the splitting of Coulomb oscillation peaks in coupled Si0.9Ge0.1 double quantum dots at 4.2 K. The quantum dots are formed by trench isolation, which means that the dots can be made much smaller than possible with the surface-gated approach. A dot diameter of 50 nm or less increases the charging energy and, therefore, the operating temperature of the device compared to previous approaches. A simulation of the results using parameters calculated from the lithographic dimensions of the device shows that a good fit to the experimental data can be achieved with a realistic interdot capacitance value.

Transport through double quantum dots

We study transport through two quantum dots in series. Electron-electron interactions are taken into account in the capacitive model with an additional interdot capacitance. The tunneling rates between the dots and the outside reservoirs are assumed to be weak, therefore we treat it perturbatively and derive a master equation. The interdot tunneling is treated in two limits: weak interdot tunneling is included perturbatively, whereas in the opposite limit we assume that there is only one level in the dot in the relevant energy range such that the Hamiltonian of the dots can be diagonalized exactly. We calculate the current through the structure as a function of the two gate voltages. The well-known Coulomb oscillations of a single dot are changed into a characteristic structure of boomerang-like shape. The transport and gate voltages can be time-dependent, and in this case we find that the dependence of the Coulomb oscillations on the two gate voltages allows us to identify which level dominates the transport.

Single electron switching in a parallel quantum dot

Low-temperature conductance measurements have been performed upon a parallel quantum-dot configuration defined in the two-dimensional electron gas of a GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructure. The observed Coulomb-blockade oscillations of the conducting dot exhibit pronounced periodic shifts as a consequence of the tunable coupling to the nonconducting dot. We show that the transport is essentially determined by the interdot capacitance and that the addition of a single electron to the nonconducting dot can switch the device conductance from a maximum to a Coulomb-blockade minimum.

Coulomb Blockade of Two Quantum Dots in Series

A Coulomb blockade of two quantum dots in series has been investigated. Despite the two dots being connected by tunneling barrier, no electrostatic interaction is observed in the conductance. This result is consistent with numerical calculations performed by using experimental parameters. The interaction is reduced in a system where the ratio of inter-dot capacitance and the total capacitance is small.

Stochastic Coulomb blockade in a double-dot system.

Coulomb blockade in a system of two dots connected in series is qualitatively different from that of a single dot. We show that, although the conductance G of a double-dot system reveals oscillations with the gate-induced potential ${\mathit{V}}_{\mathit{g}}$, a typical period of these oscillations changes with the temperature. If the capacitance ratio ${\mathit{C}}_{1}$/${\mathit{C}}_{2}$ for the dots is an irrational number, the system of peaks in G(${\mathit{V}}_{\mathit{g}}$) becomes increasingly sparse as the temperature decreases. Both the peak-to-peak distance and the activation energies of the conductance at the peaks that persist are random. However, the distribution function of activation energies calculated for a large interval of ${\mathit{V}}_{\mathit{g}}$ has a universal shape and may be considered as a characteristic pattern of a double-dot system. If the ratio ${\mathit{C}}_{1}$/${\mathit{C}}_{2}$ is small, there is a substantial range of intermediate temperatures in which the ordinary periodic Coulomb oscillations are restored. Numerical simulations show that for observation of both stochastic and regular Coulomb blockade for the same sample at different temperatures it is enough to have the ratio ${\mathit{C}}_{1}$/${\mathit{C}}_{2}$\ensuremath{\le}0.5. The existence of a small interdot capacitance C\ensuremath{\ll}${\mathit{C}}_{1}$,${\mathit{C}}_{2}$ is shown to cause, at the lowest temperatures, a splitting of the conductance peaks that persist into doublets with a constant spacing ${\mathit{e}}^{2}$C/${\mathit{C}}_{1}$${\mathit{C}}_{2}$.