Non-Markovian Dynamics of a Localized Electron Spin Due to the Hyperfine Interaction

Miguel Angel Rodriguez-Moreno, Lilia Meza-Montes, José Álvaro David Hernández de la Luz

W. A. Coish, Daniel Loss

We review our theoretical work on the dynamics of a localized electron spin interacting with an environment of nuclear spins. Our perturbative calculation is valid for arbitrary polarization p of the nuclear spin system and arbitrary nuclear spin I in a sufficiently large magnetic field. In general, the electron spin shows rich dynamics, described by a sum of contributions with exponential decay, nonexponential decay, and undamped oscillations. We have found an abrupt crossover in the long-time spin dynamics at a critical shape and dimensionality of the electron envelope wave function. We conclude with a discussion of our proposed scheme to measure the relevant dynamics using a standard spin-echo technique

Samuel E. Begg

Luca Chirolli, Guido Burkard

The interaction of solid-state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid-state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review, we discuss how decoherence affects two of the most successful realizations of solid-state qubits, namely, spin qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented by confining the electron spin in a semiconductor quantum dot. Superconducting devices show quantum behaviour at low temperatures, and the qubit is encoded in the two lowest energy levels of a superconducting circuit. The electron spin in a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted relaxation channel, due to the presence of a spin–orbit interaction, and a (non-Markovian) spin bath constituted by the spins of the nuclei in the quantum dot that interact with the electron spin via the hyperfine interaction. In a superconducting qubit, decoherence takes place as a result of fluctuations in the control parameters, such as bias currents, applied flux and bias voltages, and via losses in the dissipative circuit elements.

P. R. Crompton

Following the recent successful formation and manipulation of entangled $C^{13}$ atoms on the surface of Diamond we calculate the decoherence of the electron spin polarization in Diamond via a nonperturbative treatment of the time-dependent Greens function of the Central-Spin model, describing the phonon and Hyperfine couplings of the electron to a bath of $C^{13}$ atoms, for arbitrary initial polarizations, applied field strengths, and for up to eight entangled $C^{13}$ atoms. We compare these numerical results with the exact treatment available in the fully initially polarized limit of the non-Markovian dynamics regime, and comment on the role of dangerously irrelevant scaling in the meta-stability of $C^{13}$ flip-flop processes.