Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics

By W. Coish, Daniel Loss. 2004

344 citations recorded by the source corpus.

We have performed a systematic calculation for the non-Markovian dynamics of a localized electron spin interacting with an environment of nuclear spins via the Fermi contact hyperfine interaction. This work applies to an electron in the $s$-type orbital ground state of a quantum dot or bound to a donor impurity, and is valid for arbitrary polarization $p$ of the nuclear spin system, and arbitrary nuclear spin $I$ in high magnetic fields. In the limit of $p=1$ and $I=\frac{1}{2}$, the Born approximation of our perturbative theory recovers the exact electron spin dynamics. We have found the form of the generalized master equation (GME) for the longitudinal and transverse components of the electron spin to all orders in the electron spin-nuclear spin flip-flop terms. Our perturbative expansion is regular, unlike standard time-dependent perturbation theory, and can be carried out to higher orders. We show this explicitly with a fourth-order calculation of the longitudinal spin dynamics. In zero magnetic field, the fraction of the electron spin that decays is bounded by the smallness parameter $\ensuremath{\delta}=1∕{p}^{2}N$, where $N$ is the number of nuclear spins within the extent of the electron wave function. However, the form of the decay can only be determined in a high magnetic field, much larger than the maximum Overhauser field. In general the electron spin shows rich dynamics, described by a sum of contributions with nonexponential decay, exponential decay, and undamped oscillations. There is an abrupt crossover in the electron spin asymptotics at a critical dimensionality and shape of the electron envelope wave function. We propose a scheme that could be used to measure the non-Markovian dynamics using a standard spin-echo technique, even when the fraction that undergoes non-Markovian dynamics is small.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/e205d995515133afcae62e48f675be17da56e83a

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Citations in the corpus

Spins in few-electron quantum dots (2006, background): “…in the nuclear field are the internuclear magnetic dipole-dipole interaction (de Sousa and Das Sarma, 2003a,c; Witzel and Rogerio de Sousa, 2005; Yao et al., 2005) and the electron-nuclear hyperfine interaction (Coish and Loss, 2004; Khaetskii et al., 2002; Shenvi and Rogerio de Sousa, 2005).”
Ultrafast optical spin echo in a single quantum dot (2010, positive): “The spin-echo technique allows a qubit of information to be stored throughout the spin’s decoherence time T2, which is limited by dynamical processes such as nuclear spin diffusion and electron-nuclear spin feedback [22–25].”
Spin qubits in graphene quantum dots (2006, background): “The coherence time given by the hyperfine coupling can be estimated as [12] t ≈ √ N/cA−1, whereN is the number of atoms in the dot (for a typical graphene dot, N ≈ 104), cN is the number of atoms per dot with a nuclear spin, and A the coupling constant of the hyperfine interaction.”
Detecting crosstalk errors in quantum information processors (2019, neutral): “[12, 8, 59, 3, 32, 60].”
Dynamics of non-Markovian open quantum systems (2015, background): “An example of the central spin model is an electron in a quantum dot coupled due to a hyperfine interaction with the surrounding nuclear spins (Coish and Loss, 2004; Kessler et al., 2012; Khaetskii et al., 2002; Merkulov et al., 2002; Schliemann et al., 2003; Schuetz et al., 2012).”
A quantum spin transducer based on nanoelectromechanical resonator arrays (2009, background): “During this time spins interact with their local magnetic environment which leads to a loss of coherence ∼ e−(tg/T2) , whereα ≥ 1 depends on specific properties of the environment and the ga te sequence [42, 43, 44].”
Confluence of resonant laser excitation and bidirectional quantum-dot nuclear-spin polarization (2009, background): “Suppression of the long-timescale Overhauser field fluctuations by laser dragging may be used to ensure that the time/ensemble averaged spin coherence measurements yield a dephasing time that is limited only by the fundamental spin decoherence processes [24, 25, 26].”