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arXiv:1209.0920 · Physical Review Letters

Optical Measurement and Modeling of Interactions between Two Hole Spins or Two Electron Spins in Coupled InAs Quantum Dots

A. Greilich, Ştefan C. Bǎdescu, D. Kim, A. S. Bracker, D. Gammon

Published Mar 12, 2013• 12 citations
arXivHTMLPDF

Abstract

Two electron spins in quantum dots coupled through coherent tunneling are generally acknowledged to approximately obey Heisenberg isotropic exchange. This has not been established for two holes. Here we measure the spectra of two holes and of two electrons in two vertically stacked self-assembled InAs quantum dots using optical spectroscopy as a function of electric and magnetic fields. We find that the exchange is approximately isotropic for both systems, but that significant asymmetric contributions, arising from spin-orbit and Zeeman interactions combined with spatial asymmetries, are required to explain large anticrossings and fine-structure energy splittings in the spectra. Asymmetric contributions to the isotropic Hamiltonian for electrons are of the order of a few percent while those for holes are an order of magnitude larger.

DOI
10.1103/physrevlett.110.117402

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Acta Physica Sinica•Jan 1, 2007•1 citation
Two electron spins in quantum dots coupled through coherent tunneling are generally acknowledged to approximately obey Heisenberg isotropic exchange. This has not been established for two holes. Here we measure the spectra of two holes and of two electrons in two vertically stacked self-assembled InAs quantum dots using optical spectroscopy as a function of electric and magnetic fields. We find that the exchange is approximately isotropic for both systems, but that significant asymmetric contributions, arising from spin-orbit and Zeeman interactions combined with spatial asymmetries, are required to explain large anticrossings and fine-structure energy splittings in the spectra. Asymmetric contributions to the isotropic Hamiltonian for electrons are of the order of a few percent while those for holes are an order of magnitude larger.
We obtain a microscopic description of the interaction between electron spins in bulk semiconductors and in pairs of semiconductor quantum dots. Treating the $\mathbf{k}\mathbf{∙}\stackrel{\mathbf{\ifmmode \hat{}\else \^{}\fi{}}}{\mathbf{p}}$ band mixing and the Coulomb interaction on the same footing, we obtain in the third order an asymmetric contribution to the exchange interaction arising from the coupling between the spin of one electron and the relative orbital motion of the other. This contribution does not depend on the inversion asymmetry of the crystal and does not conserve the total spin. We find that this contribution is $\ensuremath{\sim}{10}^{\ensuremath{-}3}$ of the isotropic exchange, and is of interest in quantum information. Detailed evaluations of the asymmetric exchange are given for several quantum dot systems.
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.
The states of two electrons in tunnel-coupled semiconductor quantum dots can be effectively described in terms of a two-spin Hamiltonian with an isotropic Heisenberg interaction. A similar description needs to be generalized in the case of holes due to their multiband character and spin-orbit coupling, which mixes orbital and spin degrees of freedom and splits j=3/2j=3/2j=3/2 and j=1/2j=1/2j=1/2 multiplets. Here we investigate two-hole states in prototypical coupled Si and Ge quantum dots via different theoretical approaches. Multiband $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ and configuration-interaction calculations are combined with entanglement measures in order to thoroughly characterize the two-hole states in terms of band mixing and justify the introduction of an effective spin representation, which we analytically derive a from generalized Hubbard model. We find that, in the weak interdot regime, the ground state and first excited multiplet of the two-hole system display---unlike their electronic counterparts---a high degree of JJJ mixing, even in the limit of purely heavy-hole states. The light-hole component additionally induces MMM mixing and a weak coupling between spinors characterized by different permutational symmetries.
In the last years, the electron spin in quantum dots has become a most promising candidate for the realization of qubits, the basic element for quantum computation. In quantum dot spin qubits the exchange interaction implements a fundamental two qubit gate, which originates in the Coulomb interaction and the Pauli principle. Compared to single qubit gates, the exchange based gates are much faster and easier to control locally, motivating the solely exchange energy based quantum computation. The control is based on the exponential sensitivity of the exchange energy on the interparticle distance. Manipulation then can proceed, for example, shifting the single particle states electrically or compressing them magnetically. The practical manipulation schemes require quantitative knowledge of the exchange energy. The spin-orbit interaction plays an important role in this nano-system. Indeed the usual exchange interaction changes its magnitude, while a new term, called anisotropic exchange, appears. In this thesis we propose an accurate effective spin Hamiltonian for modeling spin-orbit-induced spin dynamics in the presence of the magnetic field. We have also performed numerically exact calculations of the isotropic and anisotropic exchange coupling in realistic two-electron GaAs coupled quantum dots in the presence of both Dresselhaus and Bychkov-Rashba spin-orbit interactions. The numerics allow us to establish the goodness of our model and to see the limits of previous statements. Furthermore we find that in zero magnetic field the second-order spin-orbit effects are absent at all interdot couplings.
The spin states of electrons and holes confined in InAs quantum dot molecules have recently come to fore as a promising system for the storage or manipulation of quantum information. We describe here a feasible scheme for complete quantum optical control of two electron spin qubits in two vertically-stacked singly-charged InAs quantum dots coupled by coherent electron tunneling. With an applied magnetic field transverse to the growth direction, we construct a universal set of gates that corresponds to the possible Raman transitions between the spin states. We detail the procedure to decompose a given two-qubit unitary operation, so as to realize it with a successive application of up to 8 of these gates. We give the pulse shapes for the laser pulses used to implement this universal set of gates and demonstrate the realization of the two-qubit quantum Fourier transform with fidelity of 0.881 and duration of 414 ps. Our proposal therefore offers an accessible path to universal computation in quantum dot molecules and points to the advantages of using pulse shaping incoherent manipulation of optically active quantum dots to mitigate the negative effects of unintended dynamics and spontaneous emission.
The electronic structure of a two-electron quantum-dot molecular has studied using the effective mass approximation. The quantum-dot molecular consists of two vertically coupled self-assembled quantum disks in a magnetic field with varying orientation. Based on the calculation, a qubit modulated by the orientation of magnetic field is proposed with the total spin of the system. Electron correlations may lead to the switching of the total spin between S=0 and S=1 states. The switching is realized not by the changing strength but by the changing orientation of an external magnetic field. Our results provide a possibility to use the total spin of the system as a qubit modulated by varying the orientation of the magnetic field. Since high-quality vertically stacked quantum disks can be fabricated successfully, it is realistic to obtain qubits of this type.