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Journal of Applied Physics

Optimal spin-state transition in singly occupied quantum dots network

M. Yaghouti, Mohammad Javad Sharifi, A. Kazemi

Published Jan 11, 2013• 0 citations
Publisher

Abstract

We present a general model to study the spin-state transition in a network of singly occupied lateral quantum dots. The perturbative expansion of the extended Hubbard model is used to describe the dynamics of confined electrons as an effective spin Hamiltonian in the strong correlation regime. To optimize the transition, we apply the gradient ascent pulse engineering algorithm to control the exchange couplings constrained to the manifolds evaluated by Heitler-London approximation. The method is applicable to an arbitrary number of quantum dots in any arrangement. Results of the method applied to the case of triple quantum dot are presented for linear and triangular topologies.

DOI
10.1063/1.4775403

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We present a general model to study the spin-state transition in a network of singly occupied lateral quantum dots. The perturbative expansion of the extended Hubbard model is used to describe the dynamics of confined electrons as an effective spin Hamiltonian in the strong correlation regime. To optimize the transition, we apply the gradient ascent pulse engineering algorithm to control the exchange couplings constrained to the manifolds evaluated by Heitler-London approximation. The method is applicable to an arbitrary number of quantum dots in any arrangement. Results of the method applied to the case of triple quantum dot are presented for linear and triangular topologies.
The double-quantum-dot device benefits from the advantages of both the spin and charge qubits, while offering ways to mitigate their drawbacks. Careful gate voltage modulation can grant greater spinlike or chargelike dynamics to the device, yielding long coherence times with the former and high electrical susceptibility with the latter for electrically driven spin rotations or coherent interactions with microwave photons. As this architecture is a serious contender for the realization of a versatile physical qubit, improving its control is a critical step toward building a large-scale spin-based universal quantum computer. We show that optimal control pulses generated using the gradient ascent pulse engineering algorithm can yield higher fidelity operating regime transfers than can be achieved using linear methods.
We present a computational LCHO-CI approach allowing for the simulation of exchange interactions in gated lateral quantum dot networks. The approach is based on single-particle states calculated using a linear combination of harmonic orbitals (LCHO) of each of the dots, and a configuration interaction (CI) approach to the interacting electron problem. The LCHO-CI method is applied to a network of three quantum dots with one electron spin per dot, and a Heisenberg spin Hamiltonian is derived. The manipulation of spin states of a three-spin molecule by applying bias to one of the dots is demonstrated and related to the bias dependence of effective exchange interaction parameters.
We present a computational LCHO-CI approach allowing for the simulation of exchange interactions in gated lateral quantum dot networks. The approach is based on single-particle states calculated using a linear combination of harmonic orbitals (LCHOs) of each of the dots and a configuration interaction (CI) approach to the interacting electron problem. The LCHO-CI method is applied to a network of three quantum dots with one-electron spin per dot, and a Heisenberg spin Hamiltonian is derived. The manipulation of spin states of a three-spin molecule by applying bias to one of the dots is demonstrated and related to the bias dependence of effective exchange interaction parameters.
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.
In semiconductor spin qubits which typically interact through short-range exchange coupling, shuttling of spin is a practical way to generate quantum operations between distant qubits. Although the exchange is often tunable through voltages applied to gate electrodes, its minimal value can be significantly large, which hinders the applicability of existing shuttling protocols to such devices, requiring a different approach. In this work, we extend our previous results for double- and triple-dot systems, and describe a method for implementing spin state transfer in long chains of singly occupied quantum dots in a non-adiabatic manner. We make use of Cartan decomposition to break down the interacting problem into simpler problems in a systematic way, and use dynamical invariants to design smooth non-adiabatic pulses that can be implemented in devices with modest control bandwidth. Finally, we discuss the extensibility of our results to directed shuttling of spin states on two-dimensional lattices of quantum dots with fixed coupling. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.