Multielectron Quantum Dot Research Articles

Simultaneous Operations in a Two-Dimensional Array of Singlet-Triplet Qubits

In many physical approaches to quantum computation, error-correction schemes assume the ability to form two-dimensional qubit arrays with nearest-neighbor couplings and parallel operations at multiple qubit sites. While semiconductor spin qubits exhibit long coherence times relative to their operation speed and single-qubit fidelities above error correction thresholds, multiqubit operations in two-dimensional arrays have been limited by fabrication, operation, and readout challenges. We present a two-by-two array of four singlet-triplet qubits in gallium arsenide and show simultaneous coherent operations and four-qubit measurements via exchange oscillations and frequency-multiplexed single-shot measurements. A larger multielectron quantum dot is fabricated in the center of the array as a tunable interqubit link, which we utilize to demonstrate coherent spin exchange with selected qubits. Our techniques are extensible to other materials, indicating a path towards quantum processors with gate-controlled spin qubits.

Fast spin exchange across a multielectron mediator

Scalable quantum processors require tunable two-qubit gates that are fast, coherent and long-range. The Heisenberg exchange interaction offers fast and coherent couplings for spin qubits, but is intrinsically short-ranged. Here, we demonstrate that its range can be increased by employing a multielectron quantum dot as a mediator, while preserving speed and coherence of the resulting spin-spin coupling. We do this by placing a large quantum dot with 50–100 electrons between a pair of two-electron double quantum dots that can be operated and measured simultaneously. Two-spin correlations identify coherent spin-exchange processes across the multielectron quantum dot. We further show that different physical regimes of the mediated exchange interaction allow a reduced susceptibility to charge noise at sweet spots, as well as positive and negative coupling strengths up to several gigahertz. These properties make multielectron dots attractive as scalable, voltage-controlled coherent coupling elements.

Electronic spectra and chemical potential of 2-D multi-electron quantum dots in magnetic field: exact multi-pole expansion of coulomb correlation

Two-dimensional superlattices, TMDCs and graphene family exhibit strong coulomb correlations among e–e, e–h, electron-phonon and etc. As the number of electron increases, confining gate voltage and transverse magnetic field are superseded by increasing coulomb interactions (N(N−1)/2 factors) that composes non-trivial Schrödinger equations. Representing such equations in Whittaker-M functions yields a modest alternate formalism, that accommodates integrals of coulomb (exchange) correlations in single-summed, finite and exact Lauricella functions via Chu-Vandermonde identity. For higher carrier density (N = 3, 4, 5, 6, ..), the multipole expansion is incurred as exact and finite-summed coulomb, coulomb-type and dipole-type integrals. Although, fermionic exchange symmetry of many electron systems could be included in terms of various two-electron integrals, for the sake of brevity we have aimed to reproduce experimental results without spin. Signature of interplay among gate voltage, magnetic field, dielectric constant, mass and density of carriers is examined in electronic spectra, magnetization, chemical potential for the systems spanning over wide range of materials (He, BN, GaAs and etc.). Interestingly, chemical potential and addition energy as a function of magnetic field and number of carriers monitor the statistics between strongly degenerate to weakly degenerate composite fermions, coulomb blockade and shell structure of 2-D superlattices. At the most, quadrapole and octapole suffice the convergence.

Singlet vs. triplet interelectronic repulsion in confined atoms

Hund’s multiplicity rule invariably holds for the ground configurations of few-electron atoms as well as those of multi-electron quantum dots. However, the ordering of the corresponding interelectronic repulsions exhibits a reversal in the former but not in the latter system, upon varying the system parameters. Here, we investigate the transition between these two types of behaviour by studying few-electron atoms confined in spherical cavities. “Counter-intuitive” ordering of the interelectronic repulsions is confirmed when the nuclear charge is low enough and the cavity radius is large enough.

Spin of a Multielectron Quantum Dot and Its Interaction with a Neighboring Electron

We investigate the spin of a multielectron GaAs quantum dot in a sequence of nine charge occupancies, by exchange coupling the multielectron dot to a neighboring two-electron double quantum dot. For all nine occupancies, we make use of a leakage spectroscopy technique to reconstruct the spectrum of spin states in the vicinity of the interdot charge transition between a single- and a multielectron quantum dot. In the same regime we also perform time-resolved measurements of coherent exchange oscillations between the single- and multielectron quantum dot. With these measurements, we identify distinct characteristics of the multielectron spin state, depending on whether the dot's occupancy is even or odd. For three out of four even occupancies we do not observe any exchange interaction with the single quantum dot, indicating a spin-0 ground state. For the one remaining even occupancy, we observe an exchange interaction that we associate with a spin-1 multielectron quantum dot ground state. For all five of the odd occupancies, we observe an exchange interaction associated with a spin-1/2 ground state. For three of these odd occupancies, we clearly demonstrate that the exchange interaction changes sign in the vicinity of the charge transition. For one of these, the exchange interaction is negative (i.e. triplet-preferring) beyond the interdot charge transition, consistent with the observed spin-1 for the next (even) occupancy. Our experimental results are interpreted through the use of a Hubbard model involving two orbitals of the multielectron quantum dot. Allowing for the spin correlation energy (i.e. including a term favoring Hund's rules) and different tunnel coupling to different orbitals, we qualitatively reproduce the measured exchange profiles for all occupancies.

Tunable Spin-Qubit Coupling Mediated by a Multielectron Quantum Dot.

We present an approach for entangling electron spin qubits localized on spatially separated impurity atoms or quantum dots via a multielectron, two-level quantum dot. The effective exchange interaction mediated by the dot can be understood as the simplest manifestation of Ruderman-Kittel-Kasuya-Yosida exchange, and can be manipulated through gate voltage control of level splittings and tunneling amplitudes within the system. This provides both a high degree of tunability and a means for realizing high-fidelity two-qubit gates between spatially separated spins, yielding an experimentally accessible method of coupling donor electron spins in silicon via a hybrid impurity-dot system.

Validity of the single-particle description and charge noise resilience for multielectron quantum dots

We construct an optimal set of single-particle states for few-electron quantum dots (QDs) using the method of natural orbitals (NOs). The NOs include also the effects of the Coulomb repulsion between electrons. We find that they agree well with the noniteracting orbitals for GaAs QDs of realistic parameters, while the Coulomb interactions only rescale the radius of the NOs compared to the noninteracting case. We use NOs to show that four-electron QDs are less susceptible to charge noise than their two-electron counterparts.

Coherent Operations and Screening in Multielectron Spin Qubits

Multielectron spin qubits are demonstrated, and performance examined by comparing coherent exchange oscillations in coupled single-electron and multielectron quantum dots, measured in the same device. Fast (>1 GHz) exchange oscillations with a quality factor Q∼15 are found for the multielectron case, compared to Q∼2 for the single-electron case, the latter consistent with experiments in the literature. A model of dephasing that includes voltage and hyperfine noise is developed that is in good agreement with both single- and multielectron data, though in both cases additional exchange-independent dephasing is needed to obtain quantitative agreement across a broad parameter range.

Generation of entangled channels for perfect teleportation using multielectron quantum dots

In this work we have proposed a scheme for generating $N$ qubit entangled states which can teleport an unknown state perfectly. By switching on the exchange interaction ($J$) between the qubits one can get the desired states periodically. A multi electron quantum dot can be a possible realization for generating such $N$ qubit states with high fidelity. In the limit of $N \to \infty$, there exists a unique time $t=\frac{1}{J}\cos^{-1}(-1/8)$ where the Hamiltonian dynamics gives the $N$ qubit state that can assist perfect teleportation. We have also discussed the effect of the nuclear spin environment on the fidelity of teleportation for a general $N$ qubit entangled channel.

Spin relaxation due to spin–orbit coupling in multi-electron quantum dots

We show that the number of electrons confined in a semiconductor quantum dot has a strong influence over the Rashba and Dresselhaus spin–orbit (SO) admixture. This can be exploited to improve the lifetime of spin excitations, as compared to the usual one- and two-electron devices. The physical mechanisms reducing SO admixture are discussed, and numerical results for realistic weakly confined GaAs/AlGaAs dots are reported.

Phase lapses in scattering through multielectron quantum dots: Mean-field and few-particle regimes

We show that the observed evolution of the transmission phase through multielectron quantum dots with more than approximately ten electrons, which shows a universal (i.e., independent of $N$) as yet unexplained behavior, is consistent with an electrostatic model, where electron-electron interaction is described by a mean-field approach. Moreover, we perform exact calculations for an open one-dimensional quantum dot and show that carrier correlations may give rise to a nonuniversal (i.e., $N$-dependent) behavior of the transmission phase, ensuing from Fano resonances, which is consistent with experiments with a few $(Nl10)$ carriers. Our results suggest that in the universal regime, the coherent transmission takes place through a single level, while in the few-particle regime, the correlated scattering state is determined by the number of bound particles.

Electronic Structure of Multi-Electron Quantum Dots

Quantum dots are artificially fabricated atoms, in which charge carriers are confined in all three dimensions just like electrons in real atoms. Consequently, they exhibit properties normally associated with real atoms such as quantised energy levels and shell structures. These properties are described by the electron wavefunctions whose evolution is governed by the Schrodinger equation and the Pauli exclusion principle.

Reduced Electron Relaxation Rate in Multielectron Quantum Dots

We use a configuration-interaction approach and the Fermi golden rule to investigate electron-phonon interaction in multielectron quantum dots. Lifetimes are computed in the low-density, highly correlated regime. We report numerical evidence that electron-electron interaction generally leads to reduced decay rates of excited electronic states in weakly confined quantum dots, where carrier relaxation is dominated by the interaction with longitudinal acoustic phonons.

Spin-based quantum computation in multielectron quantum dots

In a quantum computer the hardware and software are intrinsically connected because the quantum Hamiltonian (or more precisely its time development) is the code that runs the computer. We demonstrate this subtle and crucial relationship by considering the example of electron-spin-based solid state quantum computer in semiconductor quantum dots. We show that multielectron quantum dots with one valence electron in the outermost shell do not behave simply as an effective single spin system unless special conditions are satisfied. Our work compellingly demonstrates that a delicate synergy between theory and experiment (between software and hardware) is essential for constructing a quantum computer.

Model of Qubit in Multi-Electron Quantum Dot

Model of Qubit in Multi-Electron Quantum Dot

Kondo effect in multielectron quantum dots at high magnetic fields

We present a general description of low-temperature transport through a quantum dot with any number of electrons at filling factor $1<\ensuremath{\nu}<2$. We provide a general description of a Kondo effect that is turned on by application of an appropriate magnetic field. The spin-flip scattering of carriers by the quantum dot only involves two states of the scatterer that may have a large spin. This process is described by spin-flip Hubbard operators, which change the angular momentum, leading to a Kondo Hamiltonian. We obtain antiferromagnetic exchange couplings depending on tunneling amplitudes and correlation effects. Since Kondo temperature has an exponential dependence on exchange couplings, quantitative variations of the parameters in different regimes have important experimental consequences. In particular, we discuss the chessboard aspect of the experimental conductance when represented in a gray scale as a function of both the magnetic field and the gate potential affecting the quantum dot.