Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2009-03-12
Phys. Rev. B 79, 245314 (2009)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
25 pages, 10 figures, new title, one new figure, section VB changed, accepted for publication in PRB
Scientific paper
10.1103/PhysRevB.79.245314
We investigate decoherence due to pure dephasing of a localized spin qubit interacting with a nuclear spin bath. Although in the limit of a very large magnetic field the only decoherence mechanism is spectral diffusion due to dipolar flip-flops of nuclear spins, with decreasing field the hyperfine-mediated interactions between the nuclear spins become important. We take advantage of their long-range nature, and resum the leading terms in an 1/N expansion of the decoherence time-evolution function (N, being the number of nuclear spins interacting appreciably with the electron spin, is large). For the case of the thermal uncorrelated bath we show that our theory is applicable down to low magnetic fields (~10 mT for a large dot with N=10^6) allowing for comparison with recent experiments in GaAs quantum dot spin qubits. Within this approach we calculate the free induction decay and spin echo decoherence in GaAs and InGaAs as a function of the number of the nuclei in the bath (i.e. the quantum dot size) and the magnetic field. Our theory for free induction decay in a narrowed nuclear bath is shown to agree with the exact solution for decoherence due to hyperfine-mediated interaction which can be obtained when all the nuclei-electron coupling constants are identical. For the spin echo evolution we show that the dominant decoherence process at low fields is due to interactions between nuclei having significantly different Zeeman energies (i.e. nuclei of As and two isotopes of Ga in GaAs), and we compare our results with recent measurements of spin echo signal of a single spin confined in a GaAs quantum dot. For the same set of parameters we perform calculations of decoherence under various dynamical decoupling pulse sequences, and predict the effect of these sequences in low B regime in GaAs.
Cywinski Lukasz
Sarma Sankar Das
Witzel Wayne M.
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