Nature Commun. 3, 2214 (2012)

Credit: © 2012 NPG

There is particular interest in systems whose dynamical behaviour can be driven from regular to chaotic by a small perturbation. A number of intriguing quantum-dynamical features have been unveiled so far, but there is still much to be learned about the transition to chaos when it occurs abruptly at critical values. Now, Gabriela Lemos and co-workers from Universidade Federal do Rio de Janeiro in Brazil have proposed a scheme for observing the transition by making a direct measurement of the optical Wigner distribution. The researchers fired the beam from a He–Ne laser into a quantum-kicked harmonic oscillator, where it reflected multiple times between a spatial light modulator and a mirror. The spatial light modulator produced an instantaneous kick perturbation and the harmonic evolution relevant to the effective Planck constant was implemented by sections of free propagation and a cylindrical lens. The displacement and tilting of a steering mirror at the entrance of a three-mirror Sagnac interferometer displaced the optical field by an amount Q and changed its direction of propagation by an amount P. The researchers obtained Wigner distributions corresponding to the Q–P map by an interferometric method. The results showed the transition from regular to chaotic dynamics, in which the parameters of the kick strength and effective Planck constant were tuned.