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Bulletin of the American Physical Society

Electron shuttling in phosphorus donor qubit systems

N. Tobias Jacobson, John King Gamble, Erik Nielsen, Richard P. Muller, Wayne M. Witzel, Inès Montaño, Malcolm S. Carroll

Published Mar 4, 2014• 0 citations
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In this brief, we study robust pulse design for electron shuttling in solid-state devices. This is crucial for many practical applications of coherent quantum mechanical systems. Our objective is to design control pulses that can transport an electron along a chain of donors and that also make this process robust to parameter uncertainties. We formulate this problem here as a set of optimal control problems and derive explicit expressions for the gradients of the aggregate transfer fidelity. Numerical results for a donor chain of ionized phosphorus atoms in bulk silicon demonstrate the efficacy of our algorithm.
In this paper we apply an optimal control technique to derive control fields that transfer an electron between ends of a chain of donors or quantum dots. We formulate the transfer as an optimal steering problem, and then derive the dynamics of the optimal control. A numerical algorithm is developed to effectively generate control pulses. We apply this technique to transfer an electron between sites of a triple quantum dot and an ionized chain of phosphorus dopants in silicon. Using the optimal pulses for the spatial shuttling of phosphorus dopants, we then add hyperfine interactions to the Hamiltonian and show that a 500 G magnetic field will transfer the electron spatially as well as transferring the spin components of two of the four hyperfine states of the electron-nuclear spin pair.
Gate control of donor electrons near interfaces is a generic ingredient of donor-based quantum computing. Here, we address the question: how is the phonon-assisted qubit relaxation time T 1 affected as the electron is shuttled between the donor and the interface? We focus on the example of the 'flip-flop qubit' (Tosi et al arXiv:1509.08538v1), defined as a combination of the nuclear and electronic states of a phosphorus donor in silicon, promising fast electrical control and long dephasing times when the electron is halfway between the donor and the interface. We theoretically describe orbital relaxation, flip-flop relaxation, and electron spin relaxation. We estimate that the flip-flop qubit relaxation time can be of the order of 100 μs, 8 orders of magnitude shorter than the value for an on-donor electron in bulk silicon, and a few orders of magnitude shorter (longer) than the predicted inhomogeneous dephasing time (gate times). All three relaxation processes are boosted by (i) the nontrivial valley structure of the electron-phonon interaction, and (ii) the different valley compositions of the involved electronic states.