Animation of a Hahn echo. Examples of the Hahn echo include the spin echo and the photon echo. The red arrows can be thought of as spins. Applying the first pulse rotates the spins by 90 degrees, producing an equal superposition of spin up and spin down. The spins then "spread out" because each is in a slightly different environment. This spreading out looks like decoherence, but it can be refocused by a second pulse which rotates the spins by 180 degrees. Several simplifications are used in this animation: no decoherence is included and each spin experiences perfect pulses during which the environment provides no spreading. Animation made by Gavin W Morley with POV-Ray 3.6; some rights reserved. A higher resolution version is available here: <a href="//commons.wikimedia.org/wiki/File:GWM_HahnEcho.gif" title="File:GWM HahnEcho.gif">File:GWM_HahnEcho.gif</a> but neither one animates in Wikipedia if they are rescaled, due to a Wikipedia bug. For use with a projector, blue often does not show up on a black background so use <a class="external free" href="https://commons.wikimedia.org/wiki/File:GWM_HahnEcho_GreyBgd.gif">http://commons.wikimedia.org/wiki/File:GWM_HahnEcho_GreyBgd.gif</a> instead. An animation with spin dephasing is shown here: <a class="external free" href="https://commons.wikimedia.org/wiki/File:GWM_HahnEchoDecay.gif">http://commons.wikimedia.org/wiki/File:GWM_HahnEchoDecay.gif</a>
<a href="//commons.wikimedia.org/wiki/User:Niabot" title="User:Niabot">Niabot</a>
<span class="int-own-work" lang="en">Own work</span>