π-pulse → echo

LITErwin Hahn discovered the spin echo in 1950. Nuclear spins precessing at slightly different rates fan out and the signal vanishes. A π pulse at time τ flips the fan, so the fast spins are now behind, and at 2τ they all realign: an echo. It is a genuine time reversal of the dephasing, the basis of MRI's T₂ measurements. The Loschmidt echo generalises the idea to chaotic systems.

COMPUTED200 spins with random frequency offsets. Net magnetisation |Σ e^(iφ)|/N is computed live. Press π at any time; the echo appears at exactly twice that time. MODELOptional T₂ decay (true irreversible loss) shrinks the echo.

π pulseT₂ decay: off

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