Spin relaxation and decoherence of two-level systems

TL;DR

This paper clarifies the distinctions between various spin relaxation and decoherence times in two-level systems, highlighting differences between ensemble and single-particle behaviors under different environmental couplings.

Contribution

It introduces toy models that differentiate ensemble relaxation time $T_1^*$ from single-spin $T_1$ and ensemble decoherence time $T_2^*$, providing new insights into spin dynamics.

Findings

Ensemble relaxation time $T_1^*$ is finite even when $T_1$ and $T_2^*$ are infinite.

Under diagonal coupling, $T_1$ is infinite but $T_2$ is finite.

Different environmental couplings lead to distinct relaxation and decoherence behaviors.

Abstract

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 $T_1^*$ which is fundamentally different from $T_1$. 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 $T_1^*$ is finite while the spin relaxation time of a single spin $T_1$ and the usual ensemble decoherence time $T_2^*$ are infinite. 2) For a two-level particle under only a random diagonal coupling, its relaxation time $T_1$ shall be infinite but its decoherence time $T_2$ is finite.