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arXiv:1308.3079 · Physical Review Letters

Steady-State Entanglement in the Nuclear Spin Dynamics of a Double Quantum Dot

Martin J. A. Schuetz, E. M. Kessler, Lieven M. K. Vandersypen, J. I. Cirac, G. Giedke

Published Dec 9, 2013• 27 citations
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Abstract

We propose a scheme for the deterministic generation of steady-state entanglement between the two nuclear spin ensembles in an electrically defined double quantum dot. Because of quantum interference in the collective coupling to the electronic degrees of freedom, the nuclear system is actively driven into a two-mode squeezedlike target state. The entanglement buildup is accompanied by a self-polarization of the nuclear spins towards large Overhauser field gradients. Moreover, the feedback between the electronic and nuclear dynamics leads to multistability and criticality in the steady-state solutions.

DOI
10.1103/physrevlett.111.246802

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We propose a scheme for the deterministic generation of steady-state entanglement between the two nuclear spin ensembles in an electrically defined double quantum dot. Because of quantum interference in the collective coupling to the electronic degrees of freedom, the nuclear system is actively driven into a two-mode squeezedlike target state. The entanglement buildup is accompanied by a self-polarization of the nuclear spins towards large Overhauser field gradients. Moreover, the feedback between the electronic and nuclear dynamics leads to multistability and criticality in the steady-state solutions.
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The hyperfine coupling of the electronic spins in quantum dots to nuclear spins in the semiconductor host material poses a major challenge, as it can lead to decoherence of the electron spins. In this work, the authors revert the typical approach in which the nuclear spins are considered as an environment for the electronic spin, but rather rather view the nuclear spins as the quantum system coupled to an electronic environment with an exceptional degree of tunability. They show that nuclear spin bath could be turned from the dominant source of decoherence into a useful resource for manipulating an electron spin qubit.
In this thesis we present protocols for the polarization of nuclear spins in a quantum dot via the hyperfine interaction with a conduction band electron and give a quantitative solution to the master equation we derive. The collective interference effects limiting the polarization are studied in detail, and ways of mitigating them are proposed. At high polarization levels the electron-nuclear interaction is approximated with simple and practical (quantum optical) models, suggesting the possibility of novel coherent manipulation schemes which actively make use of the nuclei. Finally we demonstrate that even completely mixed nuclear spin ensembles can be utilized for the important task of sequentially generating entanglement between electron spins.
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In double quantum dots, the exchange interaction between two electron spins renormalizes the excitation energy of pair flips in the nuclear spin bath, which in turn modifies the non-Markovian bath dynamics. As the energy renormalization varies with the static Overhauser field mismatch between the quantum dots, the electron singlet-triplet decoherence resulting from the bath dynamics depends on sampling of nuclear spin states from an ensemble, leading to the transition from superexponential decoherence in single-sample dynamics to power-law decay under ensemble averaging. In contrast, the decoherence of a single electron spin in one dot is essentially the same for different choices of the nuclear spin configuration.
We present a scheme for achieving coherent spin squeezing of nuclear spin states in semiconductor quantum dots. The nuclear polarization dependence of the electron spin resonance generates a unitary evolution that drives nuclear spins into a collective entangled state. The polarization dependence of the resonance generates an area-preserving, twisting dynamics that squeezes and stretches the nuclear spin Wigner distribution without the need for nuclear spin flips. Our estimates of squeezing times indicate that the entanglement threshold can be reached in current experiments.