Echoes Made Simple

Echoes are common in many areas of physics, including NMR, plasma physics, nonlinear optics, cavity quantum electrodynamics, cold atoms physics, and dynamics of proton storage rings.  Recently, we theoretically found (probably) the simplest classical system featuring the echo phenomenon — a collection of randomly oriented free rotors with dispersed rotational velocities. The mechanism of this echo is based on the kick-induced filamentation of the rotational phase space, and I will present a simple toy model explaining this phenomenon at the high school level.  This prediction was confirmed in a dozen laser experiments on molecules and resulted in an efficient tool for studies on collisional relaxation in dense molecular gases. The described mechanism of the rotational echo formation is rather general. It has implications in other areas of physics ranging from high harmonics generation in free-electron lasers to the spectroscopy of gravitational quantum states of ultra-cold neutrons, atoms, and anti-atoms bouncing in the Earth’s gravitational field.