A Lie-algebraic approach to decoherence in a quantum spin system

Quantum spin systems interacting with environment lose quantum coherence and information due to the debilitating effects of the noise. Quantitative description of decoherence even in the simplest spin-1/2 systems is technically complicated and the conventional approach (e.g., calculating $T_1$ and $T_2$) involves a number of strong approximations. In order to go beyond this approximation scheme and identify its regime of validity, we use the Lie-algebraic contraction, which reduces the su(2) algebra into the solvable oscillator algebra to connect the two dynamical systems. We take advantage of the general exact solution to the latter and build a regular expansion in the contraction parameter to describe dissipative quantum dynamics of the spin. This procedure allows for a controlled non-perturbative treatment of the non-Markovian effects. New interesting effects include deviations from pure diffusion due to bath spectrum and non-Markovian effects in both systems. Our approach could shed light on the spin decoherance problem and noise characterization in experiments relevant for quantum computing.