Spin relaxation and decoherence of two-level systems

We revisit the concepts of spin relaxation and spin decoherence of two-level spin-1 /2 systems. From two toy models, we clarify two issues related to the spin relaxation and decoherence: 1 For an ensemble of two-level particles each subjected to a different environmental field, there exists an ensemble relaxation time T1 , which is fundamentally different from T1. When the off-diagonal coupling of each particle is in a single mode with the same frequency but a random coupling strength, we show that T1 * is finite while the spinrelaxation time of a single-spin T1 and the usual ensemble decoherence time T2 * are infinite. 2 For a two-level particle under only a random diagonal coupling, its relaxation time T1 shall be infinite, but its decoherence time T2 is finite.