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arXiv:cond-mat/0407081 · Physical Review Letters

Tuning the Nonlocal Spin-Spin Interaction between Quantum Dots with a Magnetic Field

Gonzalo Usaj, Pablo Germán Lustemberg, C. A. Balseiro

Published Jan 27, 2005• 17 citations
arXivHTMLPDF

Abstract

We describe a device where the nonlocal spin-spin interaction between quantum dots (QDs) can be turned on and off with a small magnetic field. The setup consists of two QDs at the edge of two two-dimensional electron gases (2DEGs). The QDs' spins are coupled through a RKKY-like interaction mediated by the electrons in the 2DEGs. A magnetic field B(z) perpendicular to the plane of the 2DEG is used as a tuning parameter. When the cyclotron radius is commensurate with the interdot distance, the spin-spin interaction is amplified by a few orders of magnitude. The sign of the interaction is controlled by finely tuning B(z). Our setup allows for several dots to be coupled in a linear arrangement and it is not restricted to nearest-neighbor interaction.

DOI
10.1103/physrevlett.94.036803

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We describe a device where the nonlocal spin-spin interaction between quantum dots (QDs) can be turned on and off with a small magnetic field. The setup consists of two QDs at the edge of two two-dimensional electron gases (2DEGs). The QDs' spins are coupled through a RKKY-like interaction mediated by the electrons in the 2DEGs. A magnetic field B(z) perpendicular to the plane of the 2DEG is used as a tuning parameter. When the cyclotron radius is commensurate with the interdot distance, the spin-spin interaction is amplified by a few orders of magnitude. The sign of the interaction is controlled by finely tuning B(z). Our setup allows for several dots to be coupled in a linear arrangement and it is not restricted to nearest-neighbor interaction.
We study the spin-spin coupling between two single-electron quantum dots due to the Coulomb and spin-orbit interactions, in the absence of tunneling between the dots. We find an anisotropic XYXYXY spin-spin interaction that is proportional to the Zeeman splitting produced by the external magnetic field. This interaction is studied both in the limit of weak and strong Coulomb repulsion with respect to the level spacing of the dot. The interaction is found to be a nonmonotonic function of interdot distance a0{a}_{0}a0​ and external magnetic field and, moreover, vanishes for some special values of a0{a}_{0}a0​ and/or magnetic field orientation. This mechanism thus provides a new way to generate and tune spin interaction between quantum dots. We propose a scheme to measure this spin-spin interaction based on the spin-relaxation-measurement technique.
Finding efficient methods for controlling entanglement is an important issue in quantum information processing. Here, we inspect theoretically possible ways for tuning orbital and spin entanglement of two interacting particles confined to a double quantum dot with spin-orbit coupling (SOC) which renders possible the coupling of spin to an external electric field. The entanglement in the spin part is sensitive to a transverse electric field. We show that through the field-induced SOC the entanglement of the spin subsystem can be slightly increased; the effect of a longitudinal electric field is more subtle: For a small interdot distance, a longitudinal electric field enhances substantially the entanglement of spins, while for a large interdot distance it has no impact. An external longitudinal electric field has a minor effect on the entanglement in the orbital part irrespective of the interdot distance. We trace back this observed phenomenon to a combined effect of the applied external electric field and the overlap of wave functions which is enhanced for decreasing interdot distances. As a result, at large interdot separation, the concurrence of the two-electron states turns insensitive to the applied electric field.
We determine the spin-exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization at in-plane fields of a few T, and perpendicular fields of the order of 10 T for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken techniques, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states, and therefore for microscopic spin measurements. In the case where dots of different sizes are coupled, we present a simple method to switch the spin coupling on and off with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.
Recent experiments on semiconductor quantum dots have demonstrated the ability to utilize a large quantum dot to mediate superexchange interactions and generate entanglement between distant spins. This opens up a possible mechanism for selectively coupling pairs of remote spins in a larger network of quantum dots. Taking advantage of this opportunity requires a deeper understanding of how to control superexchange interactions in these systems. Here, we consider a triple-dot system arranged in linear and triangular geometries. We use configuration interaction calculations to investigate the interplay of superexchange and nearest-neighbor exchange interactions as the location, detuning, and electron number of the mediating dot are varied. We show that superexchange processes strongly enhance and increase the range of the net spin-spin exchange as the dots approach a linear configuration. Furthermore, we show that the strength of the exchange interaction depends sensitively on the number of electrons in the mediator. Our results can be used as a guide to assist further experimental efforts towards scaling up to larger, two-dimensional quantum dot arrays.
The Heisenberg exchange interaction between neighboring quantum dots allows precise voltage control over spin dynamics, due to the ability to precisely control the overlap of orbital wavefunctions by gate electrodes. This allows the study of fundamental electronic phenomena and finds applications in quantum information processing. Although spin-based quantum circuits based on short-range exchange interactions are possible, the development of scalable, longer-range coupling schemes constitutes a critical challenge within the spin-qubit community. Approaches based on capacitative coupling and cavity-mediated interactions effectively couple spin qubits to the charge degree of freedom, making them susceptible to electrically-induced decoherence. The alternative is to extend the range of the Heisenberg exchange interaction by means of a quantum mediator. Here, we show that a multielectron quantum dot with 50-100 electrons serves as an excellent mediator, preserving speed and coherence of the resulting spin-spin coupling while providing several functionalities that are of practical importance. These include speed (mediated two-qubit rates up to several gigahertz), distance (of order of a micrometer), voltage control, possibility of sweet spot operation (reducing susceptibility to charge noise), and reversal of the interaction sign (useful for dynamical decoupling from noise).