Electron Spin Decoherence in Quantum Dots due to Interaction with Nuclei

Abstract

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei. The decay is caused by the spatial variation of the electron wave function within the dot, leading to a nonuniform hyperfine coupling A. We evaluate the spin correlation function and find that the decay is not exponential but rather power (inverse logarithm) lawlike. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by (planck)N/A, where N is the number of nuclei inside the dot, and the amplitude of precession decays to a finite value. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.

Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization

“…Here we take advantage of the interaction of 1 the electrons with the nuclear magnetic field of the Ga and As sublattices of the host material in order to generate the required magnetic field gradient. While fluctuations of this hyperfine field are known to be a major source of decoherence [8][9][10][11][12] , in this letter we demonstrate the possibility of building up a gradient in the hyperfine field that significantly exceeds the fluctuations and can be sustained for times longer than 30 min. This is done by employing pumping schemes that transfer spin and thus magnetic moment from the electronic system to the nuclei.…”

Electron Spin as a Spectrometer of Nuclear-Spin Noise and Other Fluctuations

“…This approximation clearly does not hold at low magnetic fields, and the problem becomes considerably more complicated. The study of electron spin evolution subject to the full isotropic hyperfine interaction has attracted a great deal of attention lately [26,27,25,28], particularly because of a series of free induction decay experiments probing electron spin dynamics in quantum dots in the low magnetic field regime [29]. In the author's opinion the most successful theoretical approach so far in the description of these experiments is to treat the collective nuclear spin field classically by taking averages over its direction and magnitude [26].…”

Decoherence dynamics of a single spin versus spin ensemble

“…The FID line shape is given by the cosine transform of M x ͑t͒. Applying the central limit theorem to this situation, [25][26][27][28] one can find that the FID of a single S spin is approximately Gaussian, with the width given by b = ͱ ͚ k A k 2 -where the coupling parameters A k are determined by the positions of the spins I on a crystal lattice with respect to the given S spin. More generally, the moments of the FID line shape can be calculated directly from Eqs.…”