Interdot Tunnel Coupling Research Articles

A 2 × 2 quantum dot array with controllable inter-dot tunnel couplings

The interaction between electrons in arrays of electrostatically defined quantum dots is naturally described by a Fermi-Hubbard Hamiltonian. Moreover, the high degree of tunability of these systems makes them a powerful platform to simulate different regimes of the Hubbard model. However, most quantum dot array implementations have been limited to one-dimensional linear arrays. In this letter, we present a square lattice unit cell of 2 × 2 quantum dots defined electrostatically in an AlGaAs/GaAs heterostructure using a double-layer gate technique. We probe the properties of the array using nearby quantum dots operated as charge sensors. We show that we can deterministically and dynamically control the charge occupation in each quantum dot in the single- to few-electron regime. Additionally, we achieve simultaneous individual control of the nearest-neighbor tunnel couplings over a range of 0–40 μeV. Finally, we demonstrate fast (∼1 μs) single-shot readout of the spin state of electrons in the dots through spin-to-charge conversion via Pauli spin blockade. These advances pave the way for analog quantum simulations in two dimensions, not previously accessible in quantum dot systems.

The role of the tunneling matrix element and nuclear reorganization in the design of quantum-dot cellular automata molecules

Mixed-valence molecules provide an implementation for a high-speed, energy-efficient paradigm for classical computing known as quantum-dot cellular automata (QCA). The primitive device in QCA is a cell, a structure with multiple quantum dots and a few mobile charges. A single mixed-valence molecule can function as a cell, with redox centers providing quantum dots. The charge configuration of a molecule encodes binary information, and device switching occurs via intramolecular electron transfer between dots. Arrays of molecular cells adsorbed onto a substrate form QCA logic. Individual cells in the array are coupled locally via the electrostatic electric field. This device networking enables general-purpose computing. Here, a quantum model of a two-dot molecule is built in which the two-state electronic system is coupled to the dominant nuclear vibrational mode via a reorganization energy. This model is used to explore the effects of the electronic inter-dot tunneling (coupling) matrix element and the reorganization energy on device switching. A semi-classical reduction of the model also is made to investigate the competition between field-driven device switching and the electron-vibrational self-trapping. A strong electron-vibrational coupling (high reorganization energy) gives rise to self-trapping, which inhibits the molecule's ability to switch. Nonetheless, there remains an expansive area in the tunneling-reorganization phase space where molecules can support adequate tunneling. Thus, the relationship between the tunneling matrix element and the reorganization energy affords significant leeway in the design of molecules viable for QCA applications.

Cotunneling spin blockade observed in a three-terminal triple quantum dot

We prepare a triple quantum dot with a separate contact lead to each dot to study Pauli spin blockade in the tunnel-coupled three dots in a row. We measure the tunneling current flowing between the center dot and either the left or right dot with the left and right leads as a common source and the center lead as a drain. In the biased stability diagram, we establish Pauli spin blockade in the respective neighboring dots, with features similarly obtained in double quantum dot systems. We further realize Pauli spin blockade with two different conditions by tuning the inter-dot coupling gates: strong and weak inter-dot tunnel coupling regimes. In the strong-coupling regime we observe significant suppression of co-tunneling through the respective double dots due to Pauli spin blockade. We reveal the influence from the third dot in the triple dot device on this co-tunneling Pauli spin blockade and clarify that the co-tunneling Pauli spin blockade is lifted by the resonant coupling of excited states to the third dot level as well as spin exchange of the left and right dots with the adjacent reservoir.

SU(4) Kondo entanglement in double quantum dot devices

We analyze, from a quantum information theory perspective, the possibility of realizing a SU(4) entangled Kondo regime in semiconductor double quantum dot devices. We focus our analysis on the ground state properties and consider the general experimental situation where the coupling parameters of the two quantum dots differ. We model each quantum dot with an Anderson type Hamiltonian including an interdot Coulomb repulsion and tunnel couplings for each quantum dot to independent fermionic baths. We find that the spin and pseudospin entanglements can be made equal, and the SU(4) symmetry recovered, if the gate voltages are chosen in such a way that the average charge occupancies of the two quantum dots are equal, and the double occupancy on the double quantum dot is suppressed. We present density matrix renormalization group numerical results for the spin and pseudospin entanglement entropies, and analytical results for a simplified model that captures the main physics of the problem.

A triangular triple quantum dot with tunable tunnel couplings

A two-dimensional arrangement of quantum dots (QDs) with finite inter-dot tunnel coupling provides a promising platform for studying complicated spin correlations as well as for constructing large-scale quantum computers. Here, we fabricate a tunnel-coupled triangular triple QD with a novel gate geometry in which three dots are defined by positively biasing the surface gates. At the same time, the small area in the center of the triangle is depleted by negatively biasing the top gate placed above the surface gates. The size of the small center depleted area is estimated from the Aharonov–Bohm oscillation measured for the triangular channel but incorporating no gate-defined dots, with a value consistent with the design. With this approach, we can bring the neighboring gate-defined dots close enough to one another to maintain a finite inter-dot tunnel coupling. We finally confirm the presence of the inter-dot tunnel couplings in the triple QD from the measurement of tunneling current through the dots in the stability diagram. We also show that the charge occupancy of each dot and that the inter-dot tunnel couplings are tunable with gate voltages.

Coherent shuttle of electron-spin states

We demonstrate a coherent spin shuttle through a GaAs/AlGaAs quadruple-quantum-dot array. Starting with two electrons in a spin-singlet state in the first dot, we shuttle one electron over to either the second, third, or fourth dot. We observe that the separated spin-singlet evolves periodically into the m = 0 spin-triplet and back before it dephases due to nuclear spin noise. We attribute the time evolution to differences in the local Zeeman splitting between the respective dots. With the help of numerical simulations, we analyze and discuss the visibility of the singlet-triplet oscillations and connect it to the requirements for coherent spin shuttling in terms of the inter-dot tunnel coupling strength and rise time of the pulses. The distribution of entangled spin pairs through tunnel coupled structures may be of great utility for connecting distant qubit registers on a chip.

Magnetic field evolution of spin blockade in Ge/Si nanowire double quantum dots

We perform transport measurements on double quantum dots defined in Ge/Si core/shell nanowires and focus on Pauli spin blockade in the regime where tens of holes occupy each dot. We identify spin blockade through the magnetic field dependence of leakage current. We find both a dip and a peak in the leakage current at zero field. We analyze this behavior in terms of the quantum dot parameters such as coupling to the leads, interdot tunnel coupling as well as spin-orbit interaction. We find a lower bound for spin-orbit interaction with $l_{\rm so}=500$ nm. We also extract large and anisotropic effective Land$\rm \acute{e}$ g-factors, with larger g-factors in the direction perpendicular to the nanowire axis in agreement with previous studies and experiments but with larger values reported here.

Thermoelectric transport through a T-shaped DQD connected to ferromagnetic and superconducting electrodes

We theoretically analyze the properties of thermoelectric transport through a T-shaped DQD connected to ferromagnetic and superconducting electrodes by means of nonequilibrium Green function formalism. The influences of the superconducting gap, interdot tunneling coupling and asymmetry parameter on the thermoelectric properties are discussed. The large thermoelectric efficiency can be obtained by choosing small polarization of ferromagnetic electrode, small asymmetry parameter (<1), appropriately large gap and appropriately interdot coupling, which can be used as the optimal schemes for obtaining high thermoelectric efficiency in the device.

Pulse propagation through a dielectric slab doped with a triple quantum dot nanostructure

The propagation of an electromagnetic pulse through a dielectric slab doped with a triple quantum dot (QD) nanostructure has been discussed in the presence of electron tunneling. We include the effect of an incoherent pump field in the transmission and reflection of a pulse in a triple QD. It is shown that the reflected and transmitted pulses can be switched from subluminal to superluminal light propagation by changing either the rate of the incoherent pump field or the inter-dot tunneling between QD1, QD2 and QD3 in a slab. Furthermore, it is demonstrated that the inter-dot tunnel coupling can significantly affect the behavior of optical bistability (OB) and optical multi-stability (OM) in a dielectric slab. The obtained results can be used for the development of new types of nanoelectronic devices for realizing the switching process.

Extracting inter-dot tunnel couplings between few donor quantum dots in silicon

The long term scaling prospects for solid-state quantum computing architectures relies heavily on the ability to simply and reliably measure and control the coherent electron interaction strength, known as the tunnel coupling, tc. Here, we describe a method to extract the tc between two quantum dots (QDs) utilising their different tunnel rates to a reservoir. We demonstrate the technique on a few donor triple QD tunnel coupled to a nearby single-electron transistor (SET) in silicon. The device was patterned using scanning tunneling microscopy-hydrogen lithography allowing for a direct measurement of the tunnel coupling for a given inter-dot distance. We extract and between each of the nearest-neighbour QDs which are separated by 14.5 nm and 14.0 nm, respectively. The technique allows for an accurate measurement of tc for nanoscale devices even when it is smaller than the electron temperature and is an ideal characterisation tool for multi-dot systems with a charge sensor.

Thermoelectric transport through a zigzag like chain: Influence of the chain length, the interdot tunneling and the intradot Coulomb interaction

We have studied the thermoelectric transport through a zigzaglike chain in the linear response regime using the non-equilibrium Green's function method. This model consists of the main zigzaglike chain and the side radicals coupled with the main chain at the next-near-neighbor sites. The finite-scale effect on the thermoelectric properties has been studied, our results show that thermoelectric efficiency can be enhanced by increasing the chain length. The thermopower and the figure of merit can be enhanced by strengthening the interdot tunneling coupling between the main chain and the side radicals. However, increase of the interdot tunneling coupling in the main chain can weaken the thermoelectric efficiency. Moreover, the thermoelectric efficiency is also strongly dependent on the intradot Coulomb interaction. These results can provide a guidance for the synthesis of thermal devices with high thermoelectric efficiency.

Spin-Orbit Coupling at the Level of a Single Electron.

We utilize electron counting techniques to distinguish a spin-conserving fast tunneling process and a slower process involving spin flips in AlGaAs/GaAs-based double quantum dots. By studying the dependence of the rates on the interdot tunnel coupling of the two dots, we find that as many as 4% of the tunneling events occur with a spin flip related to spin-orbit coupling in GaAs. Our measurement has a fidelity of 99% in terms of resolving whether a tunneling event occurred with a spin flip or not.

Characterization of a gate-defined double quantum dot in a Si/SiGe nanomembrane

We report the fabrication and characterization of a gate-defined double quantum dot formed in a Si/SiGe nanomembrane. In the past, all gate-defined quantum dots in Si/SiGe heterostructures were formed on top of strain-graded virtual substrates. The strain grading process necessarily introduces misfit dislocations into a heterostructure, and these defects introduce lateral strain inhomogeneities, mosaic tilt, and threading dislocations. The use of a SiGe nanomembrane as the virtual substrate enables the strain relaxation to be entirely elastic, eliminating the need for misfit dislocations. However, in this approach the formation of the heterostructure is more complicated, involving two separate epitaxial growth procedures separated by a wet-transfer process that results in a buried non-epitaxial interface 625 nm from the quantum dot. We demonstrate that in spite of this buried interface in close proximity to the device, a double quantum dot can be formed that is controllable enough to enable tuning of the inter-dot tunnel coupling, the identification of spin states, and the measurement of a singlet-to-triplet transition as a function of an applied magnetic field.

Nonlinear Faraday rotation in electromagnetically induced transparency medium of semiconductor three quantum dots

In the past few years, many interesting optical phenomena, such as electromagnetically induced transparency, coherent optical control of a biexciton, slow light and optical solitons, have been investigated in single quantum dot (QD). However, in an actual semiconductor device there exist many quantum dots (QDs). Recently, QD molecule, which is comprised of double semiconductor QDs coupled by tunneling coupling, has been proposed. In this new semiconductor structure, many complex but interesting phenomena have been discovered. In fact, three QD molecules may also be composed of three QDs, which can be coupled by interdot tunneling coupling. For the three semiconductor QDs molecules, the influence of the interdot tunneling coupling strength must be considered. So, in this paper, with considering that a weak, -linear-polarized probe field can form left- and right-polarized components under the control of the parallel magnetic field, and when they are combined with the tunneling coupling among the QDs, an electromagnetically induced transparency medium of a five-level M configuration semiconductor three QDs is proposed. Subsequently, the nonlinear Faraday rotation in the semiconductor three QDs is analytically studied. For the linear case, the linear dispersion relation is driven by a method of multiple scales. Then, by studying the linear optical properties, it is found that the system exhibits a single tunneling induced transparency window due to the quantum destructive interference effect driven by the interdot tunneling coupling under appropriate conditions, and the width of the tunneling induced transparency window can be effectively controlled by the strength of the interdot tunneling coupling. Meanwhile, the switch regulatory effect, which changes from the anomalous dispersion regime to the normal dispersion regime, is likely to be achieved by changing the strength of the interdot tunneling coupling. For the nonlinear case, two coupled nonlinear Schrdinger equations, which govern the evolutions of left- and right-polarized components of the weak, -linear-polarized probe field under the applied longitudinal magnetic field, are derived. By studying the nonlinear properties, it is shown that a large nonlinear Faraday rotation angle can be obtained due to the quantum interference effect which is induced by the interdot tunneling coupling with a very low absorption of the weak, -linear-polarized probe field. In addition, it is also found that the nonlinear Faraday rotation direction is opposite to line Faraday rotation for the same magnetic field. What is more, the nonlinear Faraday rotation angle grows bigger than the linear Faraday rotation. These results mean that the Faraday rotation of the three semiconductor QDs with the electromagnetically induced transparency can be more effectively controlled by the nonlinear effect.

Ferromagnetic and underscreened Kondo behavior in quantum dot arrays

We analyze the low energy properties of a device with $N+1$ quantum dots in a star configuration. A central quantum dot is tunnel coupled to source and drain electrodes and to $N$ quantum dots. Extending previous results for the $N=2$ case we show that, in the appropriate parameter regime, the low energy Hamiltonian of the system is a ferromagnetic Kondo model for a $S=(N-1)/2$ impurity spin. For small enough interdot tunnel coupling, however, a two-stage Kondo effect takes place as the temperature is decreased. The spin $1/2$ in the central quantum dot is Kondo screened first and at lower temperatures the antiferromagnetic coupling to the side coupled quantum dots leads to an underscreened $S=N/2$ Kondo effect. We present numerical results for the thermodynamic and spectral properties of the system which show a singular behavior at low temperatures and allow to characterize the different strongly correlated regimes of the device.

Pauli Spin Blockade of Heavy Holes in a Silicon Double Quantum Dot.

In this work, we study hole transport in a planar silicon metal-oxide-semiconductor based double quantum dot. We demonstrate Pauli spin blockade in the few hole regime and map the spin relaxation induced leakage current as a function of interdot level spacing and magnetic field. With varied interdot tunnel coupling, we can identify different dominant spin relaxation mechanisms. Application of a strong out-of-plane magnetic field causes an avoided singlet-triplet level crossing, from which the heavy hole g-factor ~0.93 and the strength of spin-orbit interaction ~110 μeV can be obtained. The demonstrated strong spin-orbit interaction of heavy holes promises fast local spin manipulation using only electric fields, which is of great interest for quantum information processing.

Undoped accumulation-mode Si/SiGe quantum dots

We report on a quantum dot device design that combines the low disorder properties of undoped SiGe heterostructure materials with an overlapping gate stack in which each electrostatic gate has a dominant and unique function—control of individual quantum dot occupancies and of lateral tunneling into and between dots. Control of the tunneling rate between a dot and an electron bath is demonstrated over more than nine orders of magnitude and independently confirmed by direct measurement within the bandwidth of our amplifiers. The inter-dot tunnel coupling at the charge configuration anti-crossing is directly measured to quantify the control of a single inter-dot tunnel barrier gate. A simple exponential dependence is sufficient to describe each of these tunneling processes as a function of the controlling gate voltage.

Manipulation of tunneling induced transparency windows and optical switching features in fivefold quantum dot molecules

Transient and steady-state behavior of the probe absorption in a multiple quantum dot (QD) molecule composed of five quantum dots molecules (with a center dot and four satellite dots) is explored with application in all-optical switching. We find that the absorption spectra of the light pulse can be efficiently modified via the effect of inter-dot tunnel couplings of QDs and incoherent pumping field. Results show that depending on the values of system parameters, at least one and at most four tunneling induced transparency (TIT) windows can be established in the multiple QD medium. We then investigate the dynamical behavior of the probe absorption-amplification as well as the optical switching in pulsed regime. By adjusting the incoherent pumping rate, the required switching time for changing the gain to the absorption or vice versa is then estimated approximately to be 20.7 nanosecond (ns), that is an appropriate time for such a QDM-based switch.

Quantum phase transition and Coulomb blockade effect in triangular quantum dots with interdot capacitive and tunnel couplings**Project supported by the National Natural Science Foundation of China (Grant Nos. 10874132 and 11174228) and the Doctoral Scientific Research Foundation of HUAT (Grant No. BK201407). One of the authors (Huang Hai-Ming) supported by the Scientific Research Items Foundation of Educational Committee of Hubei

The quantum phase transition and the electronic transport in a triangular quantum dot system are investigated using the numerical renormalization group method. We concentrate on the interplay between the interdot capacitive coupling V and the interdot tunnel coupling t. For small t, three dots form a local spin doublet. As t increases, due to the competition between V and t, there exist two first-order transitions with phase sequence spin-doublet-magnetic frustration phase-orbital spin singlet. When t is absent, the evolutions of the total charge on the dots and the linear conductance are of the typical Coulomb-blockade features with increasing gate voltage. While for sufficient t, the antiferromagnetic spin correlation between dots is enhanced, and the conductance is strongly suppressed for the bonding state is almost doubly occupied.

Ultra-slow propagation of light located in ultra-narrow transparency windows through four quantum dot molecules

This letter investigates the dispersion and absorption properties of a weak probe field in a multiple quantum dot molecule composed of four quantum dots. It is found that, by manipulating the electric field, the inter-dot tunneling coupling and the laser detunings, the transparency window as well as the positive derivative in the refractive index can be efficiently qualified. It is shown that switching from positive to negative dispersion or vice versa can be achieved by changing the tunneling couplings. Moreover, we realize that the width and the number of transparency windows can be properly controlled by adjusting the system’s parameters. We show that this multiple QD medium can experience very narrow transparency windows accompanied by very steep positive dispersions. The effect of an incoherent pumping field on the absorption–dispersion properties of the QD molecule is then discussed. We note that tunneling is used in this QD system instead of coupling lasers.