Decoherence dynamics of a single spin versus spin ensemble

We study decoherence of central spins by a spin bath, focusing on the difference between measurement of a single central spin and measurement of a large number of central spins (as found in typical spin-resonance experiments). For a dilute spin bath, the single spin demonstrates Gaussian free-induction decay, in contrast to exponential decay characteristic of spin ensembles. A strong difference between a single spin and a spin ensemble also exists for the Rabi oscillation decay: for a repeated Rabi oscillation experiment, suppression of decoherence happens for a single spin while acceleration takes place for a spin ensemble. The mathematical origin of such behavior is similar to quantum Zeno/anti-Zeno effects.

Figure 1

Schematic representation of a crystal containing an ensemble of $S$ spins, every such spin being decohered by a bath made of dilute $I$ spins. Each window (marked by dashed line) shows a part of the crystalline sample containing an $S$ spin (white circle with white arrow inside) and a number of $I$ spins located sufficiently close to a given $S$ spin to form its own spin bath. Arrangement of $I$ spins is different for each $S$ spins, although all arrangements are structurally similar.