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Applied Physics Letters

Si-based Coulomb blockade device for spin qubit logic gate

S. D. Lee, Seung‐Jun Shin, S. J. Choi, J. J. Lee, Jihun Choi, S. Park, Seunghoon Yang, S. J. Lee, Tae Hyoung Zyung

Published Jul 10, 2006• 12 citations
Publisher

Abstract

A lateral gate-controlled double dot structure in Si has been fabricated for studying coupled two qubits. Nonequilibrium single-electron tunneling measurements at 1.4K show that the second Coulomb peak, associated with a two-electron occupation, splits into two side peaks, and that their separation displays a strong magnetic-field dependence for various interdot coupling constants. Moreover, for some fixed magnetic fields, the separation of the side peaks decays exponentially as a function of the interdot coupling. We attribute this behavior to electron spin exchange and spin swapping between singlet and triplet states in the coupled double dot in the presence of a magnetic field.

DOI
10.1063/1.2221513

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A lateral gate-controlled double dot structure in Si has been fabricated for studying coupled two qubits. Nonequilibrium single-electron tunneling measurements at 1.4K show that the second Coulomb peak, associated with a two-electron occupation, splits into two side peaks, and that their separation displays a strong magnetic-field dependence for various interdot coupling constants. Moreover, for some fixed magnetic fields, the separation of the side peaks decays exponentially as a function of the interdot coupling. We attribute this behavior to electron spin exchange and spin swapping between singlet and triplet states in the coupled double dot in the presence of a magnetic field.
We report a successful measurement of the magnetic field-induced spin singlet-triplet transition in silicon-based coupled dot systems. Our specific experimental scheme incorporates a lateral gate-controlled Coulomb-blockaded structure in Si to meet the proposed scheme of Loss and DiVincenzo [1], and a non-equilibrium single-electron tunneling technique to probe the fine energy splitting between the spin singlet and triplet, which varies as a function of applying magnetic fields and interdot coupling constant. Our results, exhibiting the singlet-triplet crossing at a magnetic field for various interdot coupling constants, are in agreement with the theoretical predictions, and give the first experimental demonstration of the possible spin swapping occurring in the coupled double dot systems with magnetic field. *Electronic address: jungchoi@chungbuk.ac.kr [1] D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
We propose a set of universal gate operations for the singlet-triplet qubit realized by two-electron spins in a double quantum dot, in the presence of a fixed inhomogeneous magnetic field. All gate operations are achieved by switching the potential offset between the two dots with an electrical bias, and do not require time-dependent control of the tunnel coupling between the dots. We analyze the two-electron dynamics and calculate the effective qubit rotation angle as a function of the applied electric bias. We present explicit gate sequences for single-qubit rotations about two orthogonal axes, and a CNOT gate sequence, completing the universal gate set.
Charge separation from the (4,0)(4,0)(4,0) to the (3,1)(3,1)(3,1) state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the (3,1)(3,1)(3,1) singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of ggg-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.
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 qubit is the fundamental building block of a quantum computer. We fabricate a qubit in a silicon double-quantum dot with an integrated micromagnet in which the qubit basis states are the singlet state and the spin-zero triplet state of two electrons. Because of the micromagnet, the magnetic field difference ΔB between the two sides of the double dot is large enough to enable the achievement of coherent rotation of the qubit's Bloch vector around two different axes of the Bloch sphere. By measuring the decay of the quantum oscillations, the inhomogeneous spin coherence time T2* is determined. By measuring T2* at many different values of the exchange coupling J and at two different values of ΔB, we provide evidence that the micromagnet does not limit decoherence, with the dominant limits on T2* arising from charge noise and from coupling to nuclear spins.
We study the interplay between Kondo correlations and the singlet-triplet exchange splitting K between the two spins in a double quantum dot. We calculate the cotunneling current with elastic and inelastic contributions and its renormalization due to Kondo correlations, away and at the degeneracy point K = 0. We show that these Kondo correlations induce pronounced peaks in the conductance G as a function of magnetic field B , inter-dot coupling t H , and temperature. The long-range part of the Coulomb interaction becomes visible due to Kondo correlations resulting in an additional peak in G vs. t H with a strong B -field dependence. These conductance peaks thus provide direct experimental access to K , and thus to a crucial control parameter for spin-based qubits and entanglement.