Quadruple Quantum Dot Research Articles

Ray-Based Automatic Tuning of a Single Quantum Dot in a GaAs/AlGaAs Quadruple Dot Array

Abstract Semiconductor quantum dot arrays, a key platform for spin-based quantum computing, 
face scalability challenges due to the time-consuming manual tuning of potential 
landscapes. This paper proposes that combining minimal one-dimensional voltage sweeps 
with machine learning offers a practical method for automating the tuning of four separate 
single quantum dots, inspired by the Ray-based Classification framework. Our method 
successfully tunes single quantum dots in a GaAs quadruple quantum dot device, while 
reducing the complexity of data acquisition and simplifying the tuning process.

Electronic correlations in parallel-coupled double quantum dot system: An exact analytical approach

Exact eigenstates of the parallel coupled double quantum dots attached to the non-interacting leads taken in the zero-bandwidth limit (effectively quadruple quantum dots) are analytically obtained in each particle and spin subspace. The ground state of the half-filled system is determined within a four-dimensional subspace of the twenty-dimensional Hilbert space. The effects of tunable parameters, such as quantum dot energy levels, interdot tunneling, ondot and interdot Coulomb interactions, on spin-spin correlation and dot occupancies are analyzed. In the parameter space defined by interdot tunneling and ondot Coulomb interaction, the tunnel-coupled dots exhibit both ferromagnetic and antiferromagnetic correlations, suggesting suitability for singlet-triplet qubits in quantum computing. A critical dependency of interdot tunneling on ondot Coulomb interaction leads to a transition from ferromagnetic to antiferromagnetic correlation as interdot tunneling increases. These correlations persist even without interdot tunneling via indirect exchange through the leads, with the interdot Coulomb interaction significantly influencing this dependency.

Quantum Interference Effects on Josephson Current through Quadruple-Quantum-Dot Molecular Inserted between Superconductors.

We study theoretically the Josephson current through a junction composed of quadruple quantum dots (QDs), of which only one is coupled directly to the left and right superconductor leads (denoted by QD1). The other three QDs are side-coupled to QD1 and free from coupling to the leads. It is found that when the energy levels of all the four QDs are identical, the Josephson current varying with energy level of QD1 develops three peaks with two narrow and one wide, showing the typical Dicke lineshape. With increasing inter-dot coupling strength, the triple-peak configuration is well retained and accompanied by an obviously increased current amplitude. The critical current as a function of the energy level of QD1 shows a single resonance peak whose position and height depend on the energy levels of the side-coupled QDs and the inter-dot coupling strengths. We also find that the curve of the critical current versus energy levels of the side-coupled QDs shows a pair of Fano resonances and the same number Fano antiresonances (valleys). When the energy levels of the side-coupled QDs are different from each other, another Fano resonance and antiresonance are induced due to the quantum interference effect. The present results are compared with those in double and triple QDs systems, and may serve as unique means, such as the combination of quantum Dicke and Fano effects, to manipulate the Josehpson currents.

Single-Electron Occupation in Quantum Dot Arrays at Selectable Plunger Gate Voltage.

The small footprint of semiconductor qubits is favorable for scalable quantum computing. However, their size also makes them sensitive to their local environment and variations in the gate structure. Currently, each device requires tailored gate voltages to confine a single charge per quantum dot, clearly challenging scalability. Here, we tune these gate voltages and equalize them solely through the temporary application of stress voltages. In a double quantum dot, we reach a stable (1,1) charge state at identical and predetermined plunger gate voltage and for various interdot couplings. Applying our findings, we tune a 2 × 2 quadruple quantum dot such that the (1,1,1,1) charge state is reached when all plunger gates are set to 1 V. The ability to define required gate voltages may relax requirements on control electronics and operations for spin qubit devices, providing means to advance quantum hardware.

Circuit quantum electrodynamics with a quadruple quantum dot

In this theoretical work, we describe a mechanism for the coupling between a plane structure consisting of four quantum dots and a resonator. We systematically study the dependence of the quadruple coupling strength and the qubit decoherence rate and point out the optimized operating position of the hybrid system. According to the transmission given by the input–output theory, the signatures in the resonator spectrum are predicted. Furthermore, based on the parameters already achieved in previous works, we prove that the device described in this paper can achieve the strong coupling limit, i.e., this approach can be used for system extension under the existing technical conditions. Our results show an effective and promotable approach to couple quantum dot structures in plane with the resonator and propose a meaningful extension method.

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.

Frustration-controlled quantum phase transition between multiple singular two-stage Kondo behaviors in a tetrahedral quadruple quantum dot structure

Semiconductor quantum dots are considered to be promising candidates for the hardware of quantum information technology and optoelectronic devices. Herein, motivated by a tetrahedrally shaped colloidal quadruple quantum dot structure made from In-based III--V semiconductors, which has been synthesized very recently by Leemans et al. [J. Am. Chem. Soc., 143, 4290 (2021)], we provide timely insight into the electronic transport and the quantum phase transition (QPT) for such an architecture. When the interdot hopping between different side dots (${t}_{2}$) is absent, a singular two-stage Kondo effect is revealed for small central-side coupling ${t}_{1}$. The two screening processes are separated by an energy scale of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, and the fitting parameters deviate from the regular ones of the side-coupled double dot system. The RKKY interaction and temperature are well illustrated by functions of ${t}_{1}^{4}/(U{T}_{K1}^{2})$, where $U$ and ${T}_{K1}$ are the on-site electron-electron repulsion and the first Kondo temperature, respectively. When ${t}_{2}$ turns on, the ground state of the side dots transits from a spin quadruplet to a magnetic frustration phase, and then to a singlet, through two first-order QPTs. In the frustration phase, another new two-stage Kondo effect is demonstrated, which includes the process of screening the local spin on the central dot firstly, and then that on the neighborless side dot is screened at a lower temperature. Both the Kondo temperatures are found to be rather sensitive to ${t}_{2}$. When ${t}_{2}$ is large enough, the reappearance of the regular Kondo effect is found. With fixed ${t}_{2}=0$, charging the central dot triggers a transition from an antiferromagnetic correlation among the side dots to a ferromagnetic one, accompanied by a Kondo behavior in the central dot. We adopt the state-of-the-art numerical renormalization group method to implement the above behaviors, combined with analytical arguments.

Spin-polarized transport in quadruple quantum dots attached to ferromagnetic leads

Motivated by the experimental evidence of the Nagaoka ferromagnetism in quantum dot systems by Dehollain et al. (2020), we search for possible confirmation of such kind of ferromagnetism by analyzing the spin-resolved transport properties of a quadruple quantum dot system focusing on the linear response regime. In particular, we consider four quantum dots arranged in a two-by-two square lattice, coupled to external ferromagnetic source and drain electrodes. Turning on and off the specific conditions for the Nagaoka ferromagnetism to occur by changing the value of the intra-dot Coulomb interactions, we determine the transport coefficients, including the linear conductance, tunnel magnetoresistance and current spin polarization. We show that a sign change of the current spin polarization may be an indication of a ferromagnetic order of Nagaoka type which develops in the system.

A non-local cryogenic thermometer based on Coulomb-coupled systems

We investigate a quadruple quantum dot setup that can be employed to sense the temperature of an electrically isolated remote target reservoir. Such a setup was conceived earlier by Sánchez et al. [New J. Phys. 19, 113040 (2017)] as non-local thermodynamic engine and relies on the electrostatic interaction between Coulomb-coupled quantum dots. The conjugation of Coulomb-coupling and energy-filtering results in an overall change in conductance with remote reservoir temperature. The performance of the thermometer is then theoretically investigated using density matrix formulation, and it is demonstrated that the quadruple quantum dot design ensures a superior temperature sensitivity and noise robustness compared to a simple thermometer consisting of two Coulomb-coupled quantum dots. In the end, we investigate the regime of operation and comment on the ground state configuration for optimal performance of the thermometer. The setup investigated in this paper can be employed to construct highly efficient non-local cryogenic thermometers.

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.

Electron cascade for distant spin readout

The spin of a single electron in a semiconductor quantum dot provides a well-controlled and long-lived qubit implementation. The electron charge in turn allows control of the position of individual electrons in a quantum dot array, and enables charge sensors to probe the charge configuration. Here we show that the Coulomb repulsion allows an initial charge transition to induce subsequent charge transitions, inducing a cascade of electron hops, like toppling dominoes. A cascade can transmit information along a quantum dot array over a distance that extends by far the effect of the direct Coulomb repulsion. We demonstrate that a cascade of electrons can be combined with Pauli spin blockade to read out distant spins and show results with potential for high fidelity using a remote charge sensor in a quadruple quantum dot device. We implement and analyse several operating modes for cascades and analyse their scaling behaviour. We also discuss the application of cascade-based spin readout to densely-packed two-dimensional quantum dot arrays with charge sensors placed at the periphery. The high connectivity of such arrays greatly improves the capabilities of quantum dot systems for quantum computation and simulation.

A highly tunable quadruple quantum dot in a narrow bandgap semiconductor InAs nanowire.

Quantum dots (QDs) made from semiconductors are among the most promising platforms for the development of quantum computing and simulation chips, and they have the advantages of high density integration and compatibility with the standard semiconductor chip fabrication technology compared to other platforms. However, the development of a highly tunable semiconductor multiple QD system still remains a major challenge. Here, we demonstrate the realization of a highly tunable linear quadruple QD (QQD) in a narrow bandgap semiconductor InAs nanowire via a fine finger gate technique. The QQD is studied by electron transport measurements in the linear response regime. Characteristic two-dimensional charge stability diagrams containing four groups of resonant current lines of different slopes are obtained for the QQD. It is shown that these current lines arise from and can be individually assigned to resonant electron transport through the energy levels of different QDs. Benefitting from the excellent gate tunability, we also demonstrate the tuning of the QQD to regimes where the energy levels of two QDs, three QDs and all four QDs are energetically in resonance, respectively, with the Fermi level of the source and drain contacts. A capacitance network model is developed for the linear QQD and the simulated charge stability diagrams based on this model show good agreement with the experiments. Our work provides solid experimental evidence that narrow bandgap semiconductor nanowire multiple QDs could be used as a versatile platform to achieve integrated qubits for quantum computing and to perform quantum simulations of complex many-body systems.

Single-Electron Operation of a Silicon-CMOS 2 × 2 Quantum Dot Array with Integrated Charge Sensing.

The advanced nanoscale integration available in CMOS technology provides a key motivation for its use in spin-based quantum computing applications. Initial demonstrations of quantum dot formation and spin blockade in CMOS foundry-compatible devices are encouraging, but results are yet to match the control of individual electrons demonstrated in university-fabricated multigate designs. We show that quantum dots formed in a CMOS nanowire device can be measured with a remote single electron transistor (SET) formed in an adjacent nanowire, via floating coupling gates. By biasing the SET nanowire with respect to the nanowire hosting the quantum dots, we controllably form ancillary quantum dots under the floating gates, thus enabling control of all quantum dots in a 2 × 2 array, and charge sensing down to the last electron in each dot. We use effective mass theory to investigate the ideal geometrical parameters in order to achieve interdot tunnel rates required for spin-based quantum computation.

Coherent Multispin Exchange Coupling in a Quantum-Dot Spin Chain

Heisenberg exchange coupling between neighboring electron spins in semiconductor quantum dots provides a powerful tool for quantum information processing and simulation. Although so far unrealized, extended Heisenberg spin chains can enable long-distance quantum information transfer and the generation of non-equilibrium quantum states. In this work, we implement simultaneous, coherent exchange coupling between all nearest-neighbor pairs of spins in a quadruple quantum dot. The main challenge in implementing simultaneous exchange couplings is the nonlinear and nonlocal dependence of the exchange couplings on gate voltages. Through a combination of electrostatic simulation and theoretical modeling, we show that this challenge arises primarily due to lateral shifts of the quantum dots during gate pulses. Building on this insight, we develop two models, which can be used to predict the confinement gate voltages for a desired set of exchange couplings. Although the model parameters depend on the number of exchange couplings desired (suggesting that effects in addition to lateral wavefunction shifts are important), the models are sufficient to enable simultaneous and independent control of all three exchange couplings in a quadruple quantum dot. We demonstrate two-, three-, and four-spin exchange oscillations, and our data agree with simulations.

Charge Kondo effects in a quadruple quantum dot in spinless and spinful regimes

We theoretically study charge Kondo effects in a quadruple quantum dot. This system has been realized in a carbon nanotube [Nature (London) 535, 395 (2016)] by A. Hamo et al., while it can be also formed in a two-dimensional electron gas (2DEG). The system is in a particular situation where a quadruple dot has twofold degenerate ground states of $({n}_{\text{A}}=1,{n}_{\text{B}}=1,{n}_{\text{C}}=1,{n}_{\text{D}}=0)$ and (0,0,0,1) charge configurations, where ${n}_{\ensuremath{\lambda}}$ is the electron occupation number of the individual dot $\ensuremath{\lambda}=\text{A,B,C,D}$ of the quadruple dot. The two charge states behave as the pseudospin-1/2 states of a Kondo impurity. In the spinless regime, where the real spin of electrons is frozen, for example, by an external magnetic field, the quadruple dot can exhibit a single-channel charge Kondo effect in which coherent charge fluctuations massively occur between the two charge states with the help of electron tunneling between the quadruple dot and its electron reservoirs. The origin of the charge Kondo effect is similar to that of a negative-$U$ Anderson impurity. In the spinful regime, on the other hand, the real spin and charge degrees of freedom couple each other due to interdot electron tunneling between the dots A and B so that the spin singlet is formed in the charge state (1,1,1,0). In this regime, the low-energy Hamiltonian of the quadruple dot system can be mapped onto a two-channel Kondo Hamiltonian having channel anisotropy. In realistic situations of carbon nanotubes or GaAs 2DEGs, the channel anisotropy is so large that the quadruple dot shows a single-channel charge Kondo effect also in the spinful regime at experimentally available temperatures. We compute the temperature dependence of electron transport through the quadruple dot, which is useful for identifying the charge Kondo effects.

Efficient Orthogonal Control of Tunnel Couplings in a Quantum Dot Array

Electrostatically-defined semiconductor quantum dot arrays offer a promising platform for quantum computation and quantum simulation. However, crosstalk of gate voltages to dot potentials and inter-dot tunnel couplings complicates the tuning of the device parameters. To date, crosstalk to the dot potentials is routinely and efficiently compensated using so-called virtual gates, which are specific linear combinations of physical gate voltages. However, due to exponential dependence of tunnel couplings on gate voltages, crosstalk to the tunnel barriers is currently compensated through a slow iterative process. In this work, we show that the crosstalk on tunnel barriers can be efficiently characterized and compensated for, using the fact that the same exponential dependence applies to all gates. We demonstrate efficient calibration of crosstalk in a quadruple quantum dot array and define a set of virtual barrier gates, with which we show orthogonal control of all inter-dot tunnel couplings. Our method marks a key step forward in the scalability of the tuning process of large-scale quantum dot arrays.

Measurements of Capacitive Coupling Within a Quadruple-Quantum-Dot Array

We present measurements of the capacitive coupling energy and the inter-dot capacitances in a linear quadruple quantum dot array in undoped Si/SiGe. With the device tuned to a regime of strong ($>$1 GHz) intra-double dot tunnel coupling, as is typical for double dot qubits, we measure a capacitive coupling energy of $20.9 \pm 0.3$ GHz. In this regime, we demonstrate a fitting procedure to extract all the parameters in the 4D Hamiltonian for two capacitively coupled charge qubits from a 2D slice through the quadruple dot charge stability diagram. We also investigate the tunability of the capacitive coupling energy, using inter-dot barrier gate voltages to tune the inter- and intra-double dot capacitances, and change the capacitive coupling energy of the double dots over a range of 15-32 GHz. We provide a model for the capacitive coupling energy based on the electrostatics of a network of charge nodes joined by capacitors, which shows how the coupling energy should depend on inter-double dot and intra-double dot capacitances in the network, and find that the expected trends agree well with the measurements of coupling energy.

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.

Local magnetic moments and electronic transport in closed loop quantum dot systems: A case of quadruple quantum dot ring at and away from equilibrium

We apply the non-equilibrium functional renormalization group approach treating flow of the electronic self-energies, to describe local magnetic moments formation and electronic transport in a quadruple quantum dot (QQD) ring, coupled to leads, with moderate Coulomb interaction on the quantum dots. We find that at zero temperature depending on parameters of the QQD system the regimes with zero, one, or two almost local magnetic moments in the ring can be realized, and the results of the considered approach in equilibrium agree qualitatively with those of more sophisticated fRG approach treating also flow of the vertices. It is shown that the almost formed local magnetic moments, which exist in the equilibrium, remain stable in a wide range of bias voltages near equilibrium. The destruction of the local magnetic moments with increasing bias voltage is realized in one or two stages, depending on the parameters of the system; for two-stage process the intermediate phase possesses fractional magnetic moment. We present zero-temperature results for current-voltage dependences and differential conductances of the system, which exhibit sharp features at the transition points between different magnetic states. The occurrence of interaction induced negative differential conductance phenomenon is demonstrated and discussed. For one local moment in the ring and finite hopping between the opposite quantum dots, connected to the leads, we find suppression of the conductance for one of the spin projections in infinitesimally small magnetic field, which occurs due to destructive interference of different electron propagation paths and can be used in spintronic devices.

Charge Reconfiguration in Isolated Quantum Dot Arrays

AbstractA high level of tunability and control over arrays of quantum dots are key ingredients toward the goal of scalable‐based qubit architectures. Increasing array size simultaneously increases the parameter space and therefore the tuning complexity. The electron reconfiguration behavior of quantum dot arrays isolated from the electron reservoirs is studied experimentally. Isolating a quantum dot array from the reservoirs does not only enable a high degree of control over the tunnel couplings but at the same time drastically simplifies the stability diagrams for small numbers of electrons trapped in the array. Experimental results on double, triple, and quadruple quantum dot arrays are presented and complementary model calculations allow the identification of all transitions observed in the experiment. Highly tunable long‐range transitions are observed in isolated triple quantum dots and evidence of higher‐order cotunneling is found for the quadruple quantum dot array.