Triple Quantum Dot System Research Articles

Fano and Dicke Effects in Parallel-Triple Quantum Dots Embedded Between Two Leads

This article explores electronic transport in a triple quantum dot system connected in parallel to metallic leads while subjected to an external magnetic flux. The Green-function formalism and the equation of motion approach were employed to derive a comprehensive formula for conductance. The study reveals the presence and modulation of Fano and Dicke effects in the conductance spectra of the Triple quantum dot system (TQD). These effects are controlled by adjusting the interdot coupling energy ( ), the coupling (Γ) of the three dots to the right and left leads, and manipulating the external magnetic flux.

Interference effects in coupled triple quantum dot systems

Electronic transport through a coupled triple quantum dot (TQD) system is theoretically studied using Equilibrium Green’s function approach. The TQD system is systematically investigated for T-shape configuration and triangular shape configuration. T-shape (triangular shape) configuration corresponds to the TQD structure in which two quantum dots (QD)s are connected to the left and right leads in series and third one is side coupled to the right one (both) the QDs. In the electronic transmission spectrum of T-shape configuration, it is found that an antiresonance peak occurs at the QDs energy level and width of the peak increases with the increase in the tunnel coupling of the side coupled QD. Further, an asymmetric Fano lineshape is also observed while investigating transition from the T-shape to the triangular shape configuration. Interestingly, this Fano peak is found to occur when side coupled QD is weakly coupled to both the serially coupled QDs and its appearance becomes more prominent when the side coupled QD is symmetrically coupled to both the QDs. Both these effects reveal quantum interference effects that take place between discrete states and the continuum in electron transport through multiple channels in T-shape and triangular shape geometries.

Controlled quantum dot array segmentation via highly tunable interdot tunnel coupling

Recent demonstrations using electron spins stored in quantum dot array as qubits are promising for developing a scalable quantum computing platform. An ongoing effort is, therefore, aiming at the precise control of the quantum dot parameters in larger and larger arrays which represents a complex challenge. Partitioning of the system with the help of the inter-dot tunnel barriers can lead to a simplification for tuning and offers a protection against unwanted charge displacement. In a triple quantum dot system, we demonstrate a nanosecond control of the inter-dot tunnel rate permitting to reach the two extreme regimes, large GHz tunnel coupling, and sub-Hz isolation between adjacent dots. We use this development to isolate a subpart of the array in a metastable configuration while performing charge displacement and readout in the rest of the system. The degree of control over tunnel coupling achieved in a unit cell should motivate future protocol development for tuning, manipulation, and readout including this capability.

Charge stability diagram of serial triple quantum dots

<sec>Serial triple quantum dot (STQD) systems have received extensive attention in the past decade, not only because quantum dot scaling up is an indispensable ingredient for integrations, but also due to the fact that specific charge states of STQD can be employed to achieve fast full-electrical manipulation of spin qubits. For the latter, a comprehensive understanding of the relationship between neighboring charge occupancy states of STQD is essential for three-electron exchange-only spin qubit-based quantum computations. Charge stability diagram is usually employed to map out the charge occupation states about the plunger gate voltages of STQDs and to study the degeneracy among charge occupation states. Experimentally, two- rather than three-dimensional charge stability diagram was obtained in a lot of early studies by keeping one of plunger gates unchanged to reduce complexity. The obtained two-dimensional diagram can only provide limited information and is subject to blurred boundary of charge occupation states due to the low tunneling current and the energy level broading effects. It is, therefore, challenge to searching for the working points where quantum manipulation can be performed promptly and accurately.</sec><sec>In principle, three-dimensional charge occupation stability diagram can be efficiently constructed by numerical simulations based on constant interaction (CI) model. In this study, we calculate the electrochemical potential of STQD about three plunger gate voltages by using the CI model-based capacitance network to reproduce any desired two-dimensional charge stability diagram. The simulated diagram not only well accords with the diagrams obtained from the early experimental data of STQD, but also provides high clarity of the charge state boundaries with tunable parameters. The systematical study of two-dimensional charge stability diagram reviews the energy degeneracy triple and quadruple points of STQD charge occupation states and concludes the energy degeneracy points in three types to compare with experimental data. For each of the energy degeneracy points, we discuss both the electron and hole transport by using the electrochemical potential alignment schematics. We reveal the common and unique triple points of STQD in comparison with those of double quantum dot. The quadruple points of STQD are also addressed in the manipulation of quantum cellular automata and quantum logical gate. The comprehensive understanding of these energy degeneracy points can efficiently guide experiments to build an optimal working point of the STQD system for quantum computations and simulations.</sec>

Interplay of dark states and superconducting correlations in charge transport through quantum dot trimers

Electronic transport through a hybrid triple quantum dot system is theoretically studied by means of the real-time diagrammatic technique in the lowest order of perturbation theory. The central part of the system is arranged in a triangular geometry, with two quantum dots weakly coupled to metallic electrodes, while the third dot is proximitized by an s-wave superconductor. The focus is put on the transport regimes, where one- and two-electron dark states are formed due to the destructive interference of the electronic wavefunctions. This effect greatly influences the properties of the system, leading to the coherent population trapping and consequently to current blockade, negative differential conductance and enhanced shot-noise. It is shown that the presence of the superconducting pairing correlations in the system can lift the dark state blockade and reduce the shot-noise. Moreover, the current oscillations due to the magnetic flux enclosed by the triangular structure and the effect of superconducting correlations are considered. When the dark state has eigenenergy near the chemical potential of superconducting electrode, the amplitude of oscillations is strongly reduced while the current blockade is lifted. However, when the eigenenergy of the dark state is shifted away from the chemical potential of superconducting lead, the current oscillations remain unaffected.

Dicke and Fano-Andreev reflections in a triple quantum-dot system

This article studies quantum interference effects and their influence on the electronic transport through a parallel triple quantum-dot system coupled to normal and superconducting leads in the linear response and non-equilibrium regime. We model the system by a triple impurity Anderson Hamiltonian including the Coulomb intra-dot correlations in all quantum-dots. Using the non-equilibrium Green’s function formalism, we calculate the Andreev conductance and the transmittance for energies within the superconductor gap. Our results show that the Andreev reflection spectra, both in the presence and absence of Coulomb interaction, reveal Fano and Dicke-like resonances in analogy to the Fano and Dicke effects in atomic physics. As one of the main results, we obtain that the charge shows abrupt changes due to the Dicke effect.

Realistic nonlocal refrigeration engine based on Coulomb-coupled systems.

We investigate, in detail, a triple quantum dot system that exploits Coulomb coupling to achieve nonlocal refrigeration. The system under investigation is a derivative of the nonlocal thermodynamic engine, originally proposed by Sánchez and Büttiker [Phys. Rev. B 83, 085428 (2011)PRBMDO1098-012110.1103/PhysRevB.83.085428], that employs quadruple quantum dots to attain efficient nonlocal heat harvesting. Investigating the cooling performance and operating regime using the quantum master equation approach, we point out some crucial aspects of the refrigeration engine. In particular, we demonstrate that the maximum cooling power for the setup is limited to about 70% of the optimal design. Proceeding further, we point out that to achieve a target reservoir temperature lower than the average temperature of the current path, the applied voltage must be greater than a given threshold voltage V_{TH} that increases with the decrease in the target reservoir temperature. In addition, we demonstrate that the maximum cooling power, as well as the coefficient of performance, deteriorates as one approaches a lower target reservoir temperature. The triple quantum dot system, investigated in this paper, combines fabrication simplicity along with descent cooling power and may pave the way towards the practical realization of efficient nonlocal cryogenic refrigeration systems.

Current cross-correlations and waiting time distributions in Andreev transport through Cooper pair splitters based on a triple quantum dot system

We study the spin-resolved subgap transport in a triple quantum-dot system coupled to one superconducting and two ferromagnetic leads. We examine the Andreev processes in the parallel and antiparallel alignments of ferromagnets magnetic moments in both the linear and nonlinear response regimes. The emphasis is put on the analysis of the current cross-correlations between the currents flowing through the left and right arms of the device and relevant electron waiting time distributions. We show that both quantities can give an important insight into the subgap transport processes and their analysis can help optimizing the system parameters for achieving the considerable Andreev current and efficient Cooper pair splitting. Strong positive values of cross-correlations are associated with the presence of tunneling processes enhancing the Cooper pair splitting efficiency, while short waiting times for electrons tunneling through distinct ferromagnetic contacts indicate fast splitting of emitted Cooper pairs. In particular, we study two detuning schemes and show that antisymmetric shift of side quantum dots energy levels is favorable for efficient Cooper pair splitting. The analysis of spin-resolved waiting time distributions supports the performance enhancement due to the presence of ferromagnetic contacts, which is in particular revealed for short times. Finally, we consider the effect of changing the inter-dot hopping amplitude and predict that strong inter-dot correlations lead to a reduction of Andreev transport properties in low-bias limit.

A generalised approach to calculate various transport observables for a linear array of series and parallel quantum dots

A systematic generalised approach to find transport observables for a linear array of different quantum dot (QD) systems has been discussed, using non-equilibrium Green function (NEGF) formalism, in the presence of on-dot Coulomb interaction and inter-dot tunnelling. The equation of motion (EOM) method has been used to derive expressions for Green functions (GFs) within the simplest mean-field approximation to tackle the Coulomb correlation term. Starting from the mathematical structures of GFs for single, double and triple quantum dot systems, the expressions for GFs and transport observables have been generalised for the quantum dot systems containing N number of quantum dots in series as well as parallel linear array of dots. Further, the formulae so obtained have been used for numerical calculations of transmission probability and the I–V characteristics of linear arrays of quantum dots in series as well as parallel configuration containing up to three dots. The results show that, with the increase in number of dots in the scattering region, transmission probability and electron current decrease in series case, while both quantities increase in parallel configuration of dots. The inter-dot tunnelling leads to the splitting of transmission peaks in double QD system in series case whereas, it induces Fano effect in triple QD system in parallel configuration.

Theory of valley-resolved spectroscopy of a Si triple quantum dot coupled to a microwave resonator

We theoretically study a silicon triple quantum dot (TQD) system coupled to a superconducting microwave resonator. The response signal of an injected probe signal can be used to extract information about the level structure by measuring the transmission and phase shift of the output field. This information can further be used to gain knowledge about the valley splittings and valley phases in the individual dots. Since relevant valley states are typically split by several , a finite temperature or an applied external bias voltage is required to populate energetically excited states. The theoretical methods in this paper include a capacitor model to fit experimental charging energies, an extended Hubbard model to describe the tunneling dynamics, a rate equation model to find the occupation probabilities, and an input–output model to determine the response signal of the resonator.

Sensing electrons during an adiabatic coherent transport passage

We study the detection of electrons undergoing coherent transfer via adiabatic passage (CTAP) in a triple quantum-dot system with a quantum point-contact sensing the change of the middle dot. In the ideal scenario, the protocol amounts to perfect change transfer between the external dots with vanishing occupation of the central dot at all times, rendering the measurement and its backaction moot. Nevertheless, even with minor corrections to the protocol, a small population builds up in the central dot. We study the measurement backaction by a Bayesian formalism simulation of an instantaneous detection at the time of maximal occupancy of the dot. We show that the interplay between the measurement backaction and the non-adiabatic dynamics induce a change of the success probability of the protocol, which quantitatively agrees with a continuous detection treatment. We introduce a correlated measurement signal to certify the non-occupancy of the central dot for a successful CTAP protocol, which, in the weak measurement limit, confirms a vanishing occupation of the central dot. Our proposed correlated-signal purports that proper experimental method by which to confirm CTAP.

Physically defined triple quantum dot systems in silicon on insulator

We report characterizations of two types of Si triple quantum dot (TQD) devices with charge sensors, with the aim of integrating spin qubits. The QDs of a single TQD device are connected in line to adjacent QD(s), while all QDs are tunnel-coupled to each other in the other device to form a triangle. Both TQD systems are physically defined on silicon-on-insulator substrates using electron beam lithography and dry etching. From electron transport measurements of each type of TQD system at 4.2 K, we demonstrate the formation of tunnel-coupled TQD systems and the tunability of their electric potentials.

Long-range overlapping of Kondo clouds in open triple quantum dots

We study the phenomena of overlapping of Kondo clouds in an open triple quantum dots (OTQDs) system by using the dissipaton equation of motion (DEOM) theory. Motivated by the long-rang interaction of the TQDs system demonstrated in Cheng et al (2017 Phys. Rev. B 95 155417), we present a comprehensive picture of the long-range overlapping behavior of Kondo clouds via investigation of the spectral functions, spin–spin correlation, dot occupancies and susceptibility. For the configuration , a conduction electron peak occurs in the spectral function of intermediate QD in the Kondo regime. This peak results from the overlapping of the two Kondo clouds forming from between the two peripheral QDs and leads, enhances with decreasing temperature and increasing dot-lead coupling. Both the spin–spin correlations between the two adjacent QDs and the two peripheral QDs own negative values. It also confirms the physical picture of the overlapping between left and right Kondo clouds via the intermediate QD. To understand the physical insight, we examine also the electron occupacies and the spectral functions, with their dependence on the temperature and dot-lead coupling. In addition, a distinct nonmonotonic behavior of the susceptibility associated with the Kondo clouds is characterized.

The Zeno effect and relaxation rates in a triple quantum dot system

We study the quantum Zeno effect (QZE) and relaxation rates in a three quantum dot system with a mesoscopic detector near one of the three dots. The evolution of three dot states is analyzed under different conditions. For small energy differences, we find that quantum anti-Zeno effect (QAZE) occurs because measurements cannot localize the electron in the initial dot state at arbitrary voltage or temperature, but accelerate quantum transition of the electron. For large energy gaps, dot states remain the initial values, namely, Zeno effect occurs. With increasing voltage or temperature, the relaxation rates which are related to quantum transition between eigenstates increase. Furthermore, it is demonstrated that they are not absolutely dependent on the eigen energy and the difference of eigen energy. The voltage and temperature play a similar role on the relaxation rates, but a different role on occupation probabilities. In addition, it is proved that the voltage induces relaxation at zero temperature. Moreover, we demonstrate that the change rates of occupation probabilities under eigenstate and dot state are related to the energy differences. In both dot-state and eigenstate representations, the first derivatives of occupation probabilities versus voltage change obviously when the voltage is matched with the difference of eigen energy (We use the unit system of e = kB = ℏ = 1), but the first derivatives of occupation probabilities versus temperature change obviously when the temperature is matched with the difference of dot-state energy. Especially, for large energy gaps, the first derivatives of occupation probabilities versus voltage change rapidly when the voltage is matched with the difference of dot-state energy. The temperatures, at which the first derivatives of occupation probabilities versus temperature change rapidly, are independent of the differences of both dot-state and eigen energy.

Tunable self-focusing and self-defocusing effects in a triple quantum dot via the tunnel-enhanced cross-Kerr nonlinearity.

Kerr-nonlinearity induced self-focusing or self-defocusing effect provides the opportunity for exploring fundamental phenomena related to the light-matter interactions. Here we show that the linear and nonlinear dispersion responses are significantly sensitive to both the detunings and the tunneling strengths of the indirect-excitonic (IX) states in an asymmetric triple quantum dot system. In particular, the nonlinear dispersion properties are dominated by the tunnel-enhanced cross-Kerr nonlinearity from one of the IX states. Meanwhile, by varying the detunings of other IX states, we reveal that the tunnel-enhanced cross-Kerr nonlinearity gives rise to the realization of the self-focusing and self-defocusing effects. Moreover, by taking into account the effect of the longitudinal-acoustic-phonon induced dephasing of the IX states, it is possible to modulate the height and position of the peak of the self-focusing or self-defocusing effect. Our results may have potential applications in nonlinear-optics and quantum-optics devices based on the tunnel-enhanced nonlinearities in this solid-state system.

Dephasing effects on ac-driven triple quantum dot systems

We analyze the effect of environmental dephasing on the electrical current in an ac-driven triple quantum dot system in a symmetric $\mathrm{\ensuremath{\Lambda}}$ configuration. The current is explored by solving the time evolution equation of the density matrix as a function of the frequency and amplitude of the driving field. Two characteristic spectra are observed depending on the field amplitude. At the resonance condition, when the frequency matches the interdot energy difference, one spectrum shows a distinctive Fano-type peak, while the other, occurring at larger values of the field amplitude, exhibits a strong current suppression due to dynamic localization. In the former case we observe that the current maximum is reduced due to dephasing, while in the latter it is shown that dephasing partially alleviates the localization. In both cases, away from resonance, we observe current oscillations which are dephasing-enhanced for a wide range of frequencies. These effects are also discussed using Floquet theory, and analytical expressions for the electrical current are obtained within the rotating wave approximation.

Influence of electron-phonon interaction on quantum phase transition in a triangular triple quantum dot

We investigate the quantum phase transition in triple quantum dot system with triangular geometry, in which one of the dots is connected to metallic leads and electrons in the dot interact with a local phonon mode. The influence of electron-phonon interaction on the quantum phase transition between local moment phase and Kondo screened strong coupling phase at the particle-hole symmetric point is studied based on the analytical arguments and the numerical renormalization group method. The results show that the critical value of tunnel-coupling between side dots decreases with the increase of electron-phonon coupling in “spin Kondo” regime. Furthermore, at a certain critical value of electron-phonon coupling, there appears only strong coupling phase, irrespective of tunnel-coupling between dots. The study of the influence of electron-phonon interaction on the quantum phase transition in triple quantum dot has the great importance for clarifying the mechanism of Kondo screening in the system.

A linear triple quantum dot system in isolated configuration

The scaling up of electron spin qubit based nanocircuits has remained challenging up till date and involves the development of efficient charge control strategies. Here, we report on the experimental realization of a linear triple quantum dot in a regime isolated from the reservoir. We show how this regime can be reached with a fixed number of electrons. Charge stability diagrams of the one, two, and three electron configurations where only electron exchange between the dots is allowed are observed. They are modeled with the established theory based on a capacitive model of the dot systems. The advantages of the isolated regime with respect to experimental realizations of quantum simulators and qubits are discussed. We envision that the results presented here will make more manipulation schemes for existing qubit implementations possible and will ultimately allow to increase the number of tunnel coupled quantum dots which can be simultaneously controlled.

Strongly Correlated Effects in a Triangular Dot System Induced by Inter-Dot Hopping and Coulomb Repulsion

We study the transport property and the phase transition for a triple quantum dot system in a triangular geometry with one centered dot and two side dots by adopting the Wilson’s numerical renormalization group method. When three dots are decoupled with no coupling, the Kondo peak turns to reach the unitary limit, and the spin-1/2 Kondo effect is found. When the hopping between the centered dot and two side dots increases, two side dots form a local spin triplet due to the Ruderman–Kittel–Kasuya–Yosida interaction mediated by the centered dot, and the Kondo peak is suppressed. As the hopping between two side dots increases, a first order quantum phase transition occurs. In this case, two side dots form a spin singlet and the Kondo peak is recovered. When the inter-dot Coulomb repulsion between two side dots is taken into account and the hopping between two side dots is small, the charge on each side dot drops to 0.5 through a first-order quantum phase transition. As a result, one of the side dots is singly occupied, while the other one is empty. The linear conductance is suppressed due to the strong coupling between the centered dot and the singly occupied side dot. When the hopping between two side dots is large enough, the charge on each side dot decreases to 0.5 continuously and a crossover is found, for in this case the symmetry of spin configurations within two side dots is broken.

Screened spin−1 and −1/2 Kondo effect in a triangular quantum dot system with interdot Coulomb repulsion

By means of the numerical renormalization group (NRG) technique, we study the low temperature transport property and the phase transition for a triangular triple quantum dot system, including two centered dots (dot 1 and 2) and one side dot (dot 3). We focus on the effect of interdot repulsion V between two centered dots in a wide range of the interdot hopping tij (i,j = 1,2,3). When the hoppings between the centered dot and the side dot are symmetric, i.e., t13 = t23, and that between two centered dots t12 is small, two centered dots form a spin triplet when V is absent, and a totally screened spin−1 Kondo effect is observed. In this case, one has a spin 1 that is partially screened by the leads as in the usual spin−1 Kondo model, and the remaining spin 1/2 degree of freedom forms a singlet with the side dot. As V is large enough, one of the centered dots is singly occupied, while the other one is empty. The spin−1/2 Kondo effect is found when t13 is small. For large t12, two centered dots form a spin singlet when V = 0, leading to zero conductance. As V is large enough, the spin−1/2 Kondo effect is recovered in the case of small t13. For asymmetric t13≠t23 and small t12, a crossover is found as V increases in comparison with a first order quantum phase transition for the symmetric case. In the regime of large V, the spin−1/2 Kondo effect could also be found when both t13 and t23 are small. We demonstrate the present model is similar to the side-coupled double dot system in some appropriate regimes, and it appears as a possible realization of side-controllable molecular electronics and spintronics devices.