Quantum Dot Arrays Research Articles

Two-dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands

The mobility edge (ME) that marks the energy separating extended and localized states is a most important concept in understanding the metal-insulator transition induced by disordered or quasiperiodic potentials. MEs have been extensively studied in three-dimensional disorder systems and one-dimensional quasiperiodic systems. However, the studies of MEs in two-dimensional (2D) systems are rare. Here, we propose a class of 2D vertex-decorated Lieb lattice models with quasiperiodic potentials only acting on the vertices of the Lieb lattice or extended Lieb lattices. By mapping these models to the 2D Aubry-Andr\'e model, we obtain exact expressions of MEs and the localization lengths of localized states, and further demonstrate that the flat bands remain unaffected by the quasiperiodic potentials. Finally, we propose a highly feasible scheme to experimentally realize our model in a quantum dot array. Our results open the door to studying and realizing exact MEs and robust flat bands in 2D systems.

Theory of multidimensional quantum capacitance and its application to spin and charge discrimination in quantum dot arrays

Quantum states of a few-particle system capacitively coupled to a metal gate can be discriminated by measuring the quantum capacitance, which can be identified with the second derivative of the system energy with respect to the gate voltage. This approach is here generalized to the multivoltage case, through the introduction of the quantum capacitance matrix. The matrix formalism allows us to determine the dependence of the quantum capacitance on the direction of the voltage oscillations in the parameter space and to identify the optimal combination of gate voltages. As a representative example, this approach is applied to the case of a quantum dot array, described in terms of a Hubbard model. Here, we first identify the potentially relevant regions in the multidimensional voltage space with the boundaries between charge stability regions, determined within a semiclassical approach. Then, we quantitatively characterize such boundaries by means of the quantum capacitance matrix. Altogether, this provides a procedure for optimizing the discrimination between states with different particle numbers and/or total spins.

Probing two-qubit capacitive interactions beyond bilinear regime using dual Hamiltonian parameter estimations

We report the simultaneous operation and two-qubit-coupling measurement of a pair of two-electron spin qubits, actively decoupled from quasi-static nuclear noise in a GaAs quadruple quantum dot array. Coherent Rabi oscillations of both qubits (decay time ≈2 μs; frequency few MHz) are achieved by continuously tuning their drive frequency using rapidly converging real-time Hamiltonian estimators. We observe strong two-qubit capacitive interaction (>190 MHz), combined with detuning pulses, inducing a state-conditional frequency shift. The two-qubit capacitive interaction is beyond the bilinear regime, consistent with recent theoretical predictions. We observe a high ratio (>16) between coherence and conditional phase-flip time, which supports the possibility of generating high-fidelity and fast quantum entanglement between encoded spin qubits using a simple capacitive interaction.

Gate-Induced Trans-Dimensionality of Carrier Distribution in Bilayer Lateral Heterosheet of MoS2 and WS2 for Semiconductor Devices with Tunable Functionality

Using the metal–organic chemical vapor deposition technique, we synthesized a bilayer lateral heterostucture of MoS2 and WS2, each of which layers consist of alternately arranged nanostrips of MoS2 and WS2. Transmission electron microscope images exhibit a checked pattern contrast, reflecting the three distinct interlayer metal arrangements of Mo/Mo, W/Mo (Mo/W), and W/W stacking. Theoretical calculations based on the density functional theory elucidated that the bilayer lateral heterostructure of MoS2 and WS2 exhibits complexed type-II band edge alignments depending on the interlayer metal arrangement: The conduction band edge is located at the Mo atom in a Mo/Mo sector, while the valence band edge is located at the W atom in a W/W sector. According to the complexed band edge alignment, the field-induced carrier injection behavior in the bilayer heterosheet composed of MoS2 and WS2 strips shows gate-induced trans-dimensionality, where the accumulated carrier distributions continuously vary from zero- to two-dimensional based on the applied gate voltage. Tunable carrier dimensionality can be applicable for wide areas of electronics, such as quantum dot arrays with tunable dot–dot interaction.

Formation of an Extended Quantum Dot Array Driven and Autoprotected by an Atom-Thick h-BN Layer.

Engineering quantum phenomena of two-dimensional nearly free electron states has been at the forefront of nanoscience studies ever since the first creation of a quantum corral. Common strategies to fabricate confining nanoarchitectures rely on manipulation or on applying supramolecular chemistry principles. The resulting nanostructures do not protect the engineered electronic states against external influences, hampering the potential for future applications. These restrictions could be overcome by passivating the nanostructures with a chemically inert layer. To this end we report a scalable segregation-based growth approach forming extended quasi-hexagonal nanoporous CuS networks on Cu(111) whose assembly is driven by an autoprotecting h-BN overlayer. We further demonstrate that by this architecture both the Cu(111) surface state and image potential states of the h-BN/CuS heterostructure are confined within the nanopores, effectively forming an extended array of quantum dots. Semiempirical electron-plane-wave-expansion simulations shed light on the scattering potential landscape responsible for the modulation of the electronic properties. The protective properties of the h-BN capping are tested under various conditions, representing an important step toward the realization of robust surface state based electronic devices.

Electrohydrodynamically Printed High‐resolution Arrays Based on Stabilized CsPbBr3 Quantum Dot Inks

AbstractHigh‐resolution perovskite quantum dots (PeQDs) arrays printed by electrohydrodynamic (EHD) inkjet printing show great application prospects in fields of micro‐display. Commonly, EHD inkjet requires a polar system for printing but it easily quenches the PeQDs. Meanwhile, the mismatch of solvent parameters causes uneven surface morphology and printing instability. In this work, a morphology uniformization strategy of a nonpolar binary solvent system of 1,3,5‐triethylbenzene and n‐tetradecane is proposed to prepare the didodecyldimethylammonium bromide (DDAB)/PbBr2 passivated PeQDs inks. When the solvent volume ratio is 5:5, the photoluminescence quantum yield (PLQY) of the ink reaches 94.06%. Benefiting from the match of boiling point, surface tension, and dielectric constant of ink, after the EHD inkjet printing, the line width of continuous smooth line arrays is as narrow as 2.0 µm and the coffee effect of dot arrays is well inhibited. Meanwhile, derived from the strong electrostatic interaction between the π‐electron structure of 1,3,5‐triethylbenzene and DDA+, the ink exhibits high stability. Moreover, the high‐resolution logo and miniature quick responsecode by EHD inkjet printing reach 22 718 dpi, far higher than that of the reported micro‐LED. This work paves the way for high‐resolution pixel arrays of micro‐display.

Gate reflectometry in dense quantum dot arrays

Silicon quantum devices are maturing from academic single- and two-qubit devices to industrially-fabricated dense quantum-dot (QD) arrays, increasing operational complexity and the need for better pulsed-gate and readout techniques. We perform gate-voltage pulsing and gate-based reflectometry measurements on a dense 2 × 2 array of silicon QDs fabricated in a 300 mm-wafer foundry. Utilizing the strong capacitive couplings within the array, it is sufficient to monitor only one gate electrode via high-frequency reflectometry to establish single-electron occupation in each of the four dots and to detect single-electron movements with high bandwidth. A global top-gate electrode adjusts the overall tunneling times, while linear combinations of side-gate voltages yield detailed charge stability diagrams. To test for spin physics and Pauli spin blockade at finite magnetic fields, we implement symmetric gate-voltage pulses that directly reveal bidirectional interdot charge relaxation as a function of the detuning between two dots. Charge sensing within the array can be established without the involvement of adjacent electron reservoirs, important for scaling such split-gate devices towards longer 2 × N arrays. Our techniques may find use in the scaling of few-dot spin-qubit devices to large-scale quantum processors.

Quantum Radiating Arrays and Their Directivity: A Dynamical Open System Approach

We investigate the directive properties of radiating quantum antennas comprised of coupled two-level (qubit) systems interacting with bosonic modes and excited by classical fields. A directivity formula inspired by classical antenna theory is proposed. The density operator of a coupled two-level quantum dot (qubit) array, excited by classical external signals with variable amplitude and phase, is evolved in time using the Gorini–Kossakowski–Sudarshan–Lindblad master equation. We illustrate the method in a numerical example where it is shown that manipulating the phase excitations of individual quantum dots may significantly enhance the directive radiation properties of the quantum dot antenna system.

Electron charge sensor with hole current operating at cryogenic temperature

When silicon-on-insulator p-type MOSFET (SOI-PMOS) functions like a capacitor-less 1T-DRAM cell, it is possible for the number of electrons to be sensed at cryogenic temperatures (5 K). We developed a structure that combines silicon-on-insulator n-type MOSFETs (SOI-NMOS) and SOI-PMOS with multiple gates to form a silicon quantum-dot array. In this structure, a variable number of electrons is injected into the SOI-PMOS body by means of the bucket-brigade operation of SOI-NMOS connected in series. The channel-hole current was changed by the injected electrons due to the body bias effect in SOI-PMOS, and the change appeared to be step-like, which suggests a dependence on the elementary charge.

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.

Arrays of size-dispersed ZnSe quantum dots as artificial antennas: Role of quasi-coherent regime and in-gap states of excitons for enhanced light harvesting and energy transfer

Densely packed thin films of semiconductor quantum dots (QDs) shows specific the optoelectronic properties originate from the QDs coupling that may pave the way for new controllable building blocks for quantum technologies and light-harvesting complexes in natural photosynthetic systems and photovoltaic cells. In this work we were compared the optical properties and an excitonic energy transfer (EET) process in an aqueous solutions and dense packed films of ZnSe QDs with a narrow size distribution. An unexpectedly large nonlinear increase in the photoluminescence (PL) intensity was detected in QDs films with the decrease of an excitation energy that can be explained by resonantly transferred of EET through the quantum states. We found that with decreasing of the excitation energy form of quasi-coherent regime of excitons and the quantum and surface PL emission increases by a factor ∼10 and ∼6, respectively, due to increasing the EET rate.

Optical Loss in Microdisk Lasers With Dense Quantum Dot Arrays

We discuss the origin of optical losses in microdisk lasers with a dense array of InGaAs quantum dots in the active region. In particular, we study the effect of microlaser diameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {D}$ </tex-math></inline-formula> variation from 15 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$200~\mu \text{m}$ </tex-math></inline-formula> on optical losses of different nature. A strong dependence of the lasing wavelength on the diameter is observed: the blue-shift with decreasing disk size implies an increase in optical losses, although in the case of an ideal cylinder, a noticeable optical loss should appear only at diameters comparable to the wavelength of light. A comparison of the spectral characteristics of microlasers with those of broad-area stripe lasers, for which optical loss can be easily found, gives a tool to evaluate optical loss in microdisk lasers, which was found to be unexpectedly high. It changes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\propto }\mathbf {D}^{\mathbf {-1}}$ </tex-math></inline-formula> from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 100$ </tex-math></inline-formula> cm−1 in the smallest microlasers to ~ 5 cm−1 in the largest ones. Several possible physical mechanisms of the appearance of optical losses in microlasers are considered, such as radiative loss due to the curvature of the cylindrical cavity, free carrier absorption, light scattering due to roughness of the side walls, and absorption of light in the near-surface region. The latter type of optical loss was found to be the dominant one and can explain the experimental results once the absorbing layer with a thickness of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2~\mu \text{m}$ </tex-math></inline-formula> was suggested. Using the Gaussian approximation for Using the Gaussian approximation for the gain spectrum, the wavelength-loss relationship was simulated and a good agreement with the experimental dependence was found. The variation of the experimental results on optical loss for nominally identical microlasers was attributed to the variation of the scattering loss. The same reason can explain the scatter of the slope efficiency, which varies from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim ~0.03$ </tex-math></inline-formula> to 0.25 W/A being governed by the ratio of the scattering loss to the surface absorption loss.

Linear arrays of InGaAs quantum dots on nanostructured GaAs-on-Si substrates

Linear arrays of high-quality quantum dots (QD) integrated in Si are an ideal platform in exploring the manipulation and transmission of quantum information. Understanding QD self-organization mechanisms on substrates compatible with Si technology is therefore of great practical importance. Here we demonstrate the epitaxial growth of linear arrays of InAs and InGaAs QDs from As2 and In molecular beams on bare and GaAs-coated Si(001) substrates, patterned by high-resolution laser interference nanolithography. Atomic force microscopy, in combination with high-resolution scanning and transmission electron microscopies, show that these arrays exhibit an improvement in growth selectivity, lateral order and size uniformity of the QDs when a pseudomorphic 1 nm-thick GaAs buffer layer is grown prior to InAs deposition. In addition, preferential nucleation of InxGa1-xAs QDs along the 〈110〉 -oriented edges of the nanostructured GaAs-on-Si(001) substrate results from In adatom migration from (111) to (001) nanofacets and the erosion of the wetting and buffer layers caused by the Ga-In intermixing at the step edge during the Stranski-Krastanov transition. These are key elements in the formation of linear arrays of coherent QDs, which differ in morphology and structure from those obtained on both GaAs(001) and Si(001) planar surfaces.

Tunable spectral narrowing enabling the functionality of graphene qubit circuits at room temperature

Electrically controllable quantum coherence in quantum dot clusters and arrays based on graphene stripes with zigzag atomic edges (ZZ-stripes) is studied using the Dirac equation and S-matrix technique. We find that respective multiqubit circuits promise stable operation up to room temperatures when the coherence time is prolonged up by a few orders of magnitude through the intrinsic spectral narrowing owing to electron transport between at bands in adjacent sections. Respectively, the coupling of qubits to a noisy environment is diminished, while the inelastic electron-phonon scattering is suppressed. The Stark splitting technique enables a broad range of operations such as all{electrical tuning of the energy level positions and width, level splitting, controlling of the inter-qubit coupling, and the coherence time. At the resonant energies, the phase coherence spreads over thousands of periods. Such phenomena potentially can be utilized in quantum computing and communication applications at room temperature.

Single-electron pump in a quantum dot array for silicon quantum computers

It is necessary to load single electrons into individual quantum dots (QDs) in an array for implementing fully scalable silicon-based quantum computers. However, this single-electron loading would be impacted by the variability of the QD characteristics, and suppressing this variability is highly challenging even in the state-of-the-art silicon front-end process. Here, we used a single-electron pump (SEP) for loading single electrons into a QD array as a preparatory step to use electrons as spin qubits. We used parallel gates in the QD array as a SEP and demonstrated 100 MHz operation with an accuracy of 99% at 4 K. By controlling the timing of a subsequent gate synchronously as a shutter, we found that the jitter representing electron transfer was less than 10 ns, which would be acceptable for a typical operating speed of around 1 MHz for silicon qubits.

Fabrication of quantum dot and ring arrays by direct laser interference patterning for nanophotonics

Abstract Epitaxially grown semiconductor quantum dots (QDs) and quantum rings (QRs) have been demonstrated to be excellent sources of single photons and entangled photon pairs enabling applications within quantum photonics. The emerging field of QD-based nanophotonics requires the deterministic integration of single or multiple QD structures into photonic architectures. However, the natural inhomogeneity and spatial randomness of self-assembled QDs limit their potential, and the reliable formation of homogeneous and ordered QDs during epitaxy still presents a challenge. Here, we demonstrate the fabrication of regular arrays of single III–V QDs and QRs using molecular beam epitaxy assisted by in situ direct laser interference patterning. Both droplet epitaxy (DE) GaAs/AlGaAs QDs and QRs and Stranski–Krastanov (SK) InAs/GaAs QDs are presented. The resulting QD structures exhibit high uniformity and good optical quality, in which a record-narrow photoluminescence linewidth of ∼17 meV from patterned GaAs QD arrays is achieved. Such QD and QR arrays fabricated through this novel optical technique constitute a next-generation platform for functional nanophotonic devices and act as useful building blocks for the future quantum revolution.

Certain exact many-body results for Hubbard model ground states testable in small quantum dot arrays

We present several interesting phenomena related to flatband ferromagnetism in the Hubbard model. The first is a mathematical theorem stating certain conditions under which a flatband ferromagnetic must necessarily be degenerate with a nonferromagnetic state. This theorem is generally applicable and geometry-independent, but holds only for a small number of holes in an otherwise filled band. The second phenomenon is a peculiar example where the intuition fails that particles prefer to doubly occupy low-energy states before filling higher-energy states. Lastly, we show a pattern of ferromagnetism which appears in small pentagonal and hexagonal plaquettes at filling factors of roughly 3/10 and 1/4. These examples require only a small number of lattice sites, and may be observable in quantum dot arrays currently available as laboratory spin qubit arrays.

A Multiscale Simulation Approach for Germanium-Hole-Based Quantum Processor

A multiscale simulation method is developed to model a quantum dot (QD) array of germanium (Ge) holes for quantum computing. Guided by three-dimensional numerical quantum device simulations of QD structures, an analytical model of the tunnel coupling between the neighboring hole QDs is obtained. Two-qubit entangling quantum gate operations and quantum circuit characteristics of the QD array processor are then modeled. Device analysis of two-qubit Ge hole quantum gates demonstrates faster gate speed, smaller process variability, and less stringent requirement of feature size, compared to its silicon counterpart. The multiscale simulation method allows assessment of the quantum processor circuit performance from a bottom-up, physics-informed perspective. Application of the simulation method to the Ge QD array processor indicates its promising potential for preparing high-fidelity ansatz states in quantum chemistry simulations.

Microfluidic static droplet generated quantum dot arrays as color conversion layers for full-color micro-LED displays.

This paper presents an easy and intact process based on microfluidics static droplet array (SDA) technology to fabricate quantum dot (QD) arrays for full-color micro-LED displays. A minimal sub-pixel size of 20 μm was achieved, and the fluorescence-converted red and green arrays provide good light uniformity of 98.58% and 98.72%, respectively.

Model for speed performance of quantum-dot waveguide photodiode

A model is proposed that makes it possible to analytically analyze the speed performance of a waveguide p-i-n photodiode with a light-absorbing region representing a multilayered array of quantum dots separated by undoped spacers. It is shown that there is an optimal number of layers of quantum dots, as well as an optimal thickness of the spacers, which provide the widest bandwidth. The possibility of achieving a frequency range (at the level of -3 dB) above 20 GHz for waveguide photodiodes based on InGaAs/GaAs quantum well-dots is shown Keywords: photodiode, quantum dots, speed.