Dynamics of Quantum Information of the Central Spin Problem

Abstract

Environmental effects on the evolution of a spin system in the context of the central spin problem, have been studied for more than 60 years. With the growing complexity of quantum information processors there is a new need to better understand and control the interactions of qubits with their environment. Decoherence is an apparent loss of quantum coherence of the central spin, which is the result of the coherent evolution of the central spin and its spin environment. This evolution may be understood as the consequence of local field fluctuations induced by heteronuclear dipolar interaction between the central spin and the environment spins and homonuclear dipolar interaction of spins in the environment. A complete theoretical description for the evolution of the central spin does not exist and numerical solutions are restricted to small spin environments.

Another way of looking at the central spin problem is to study the correlations between the central spin and the environment spins. In this method the evolution of the central spin is described with the dynamics of multi-spin correlations resulting from interactions of the central spin and the environment spins. Using Multiple Quantum Nuclear Magnetic Resonance (MQ NMR) techniques, we have designed experiments for the direct detection of multi-spin correlations between the central spin and environment spins. These experiments are used to observe the progress in production of correlations between the central spin and the environment. They reveal the multi-spin dynamics that underlies the decoherence process.

The central spin is initially uncorrelated with the environment and quantum information resides exclusively on it. After the interaction with the environment spins quantum information is shared in the form of correlated operators between the central spin and the environment. Using our experiments this flow of quantum information from the central spin to the environment and the quantum information content of the environment, can be quantified. Further, these experiments are used to gauge the sensitivity of correlation to perturbation in the environment, by observing the mixing dynamics of the multi-spin correlations. The Out-of-Time Correlation metric is used for the sensitivity measurements. We find that the dynamics of correlations in our system is better explained by the extent of information flow to the environment rather than the evolution time.