Observation of Fermi-Pasta-Ulam-Tsingou Recurrence and Its Exact Dynamics

One of the most controversial phenomena in nonlinear dynamics is the reappearance of initial conditions. Celebrated as the Fermi-Pasta-Ulam-Tsingou problem, the attempt to understand how these recurrences form during the complex evolution that leads to equilibrium has deeply influenced the entire development of nonlinear science. The enigma is rendered even more intriguing by the fact that integrable models predict recurrence as exact solutions, but the difficulties involved in upholding integrability for a sufficiently long dynamic has not allowed a quantitative experimental validation. In natural processes, coupling with the environment rapidly leads to thermalization, and finding nonlinear multimodal systems presenting multiple returns is a long-standing open challenge. Here, we report the observation of more than three Fermi-Pasta-Ulam-Tsingou recurrences for nonlinear optical spatial waves and demonstrate the control of the recurrent behavior through the phase and amplitude of the initial field. The recurrence period and phase shift are found to be in remarkable agreement with the exact recurrent solution of the nonlinear Schrödinger equation, while the recurrent behavior disappears as integrability is lost. These results identify the origin of the recurrence in the integrability of the underlying dynamics and allow us to achieve one of the basic aspirations of nonlinear dynamics: the reconstruction, after several return cycles, of the exact initial condition of the system, ultimately proving that the complex evolution can be accurately predicted in experimental conditions.

D. Pierangeli, M. Flammini, L. Zhang, G. Marcucci, A. J. Agranat,
P. G. Grinevich, P. M. Santini, C. Conti, and E. DelRe in PHYSICAL REVIEW X 8, 041017 (2018)

Spin-orbit algebra with graphene

Laser & photonic reviews published the paper by Ciattoni et al. on the spin orbit coupling in graphene (arXiv version). The coupling of 2D electrons with OAM and Spin allows to control the state of nano-scale light beams, and is potentially useful for multilevel quantum gates.

Nonlinear transmission matrix of random optical media

Random media with tailored optical properties are attracting burgeoning interest for applications in imaging, biophysics, energy, nanomedicine, spectroscopy, cryptography and telecommunications.
A key paradigm for devices based on this class of materials is the transmission matrix, the tensorial link between the input and the output signals, that describes in full their optical behavior. The transmission matrix has specific statistical properties, as the existence of lossless channels, that can be used to transmit information, and are determined by the disorder distribution. In nonlinear materials, these channels may be modulated and the transmission matrix tuned accordingly. Here we
report the direct measurement of the nonlinear transmission matrix of complex materials, exploiting the strong optothermal nonlinearity of scattering Silica Aerogel (SA). We show that the dephasing effects due to nonlinearity are both controllable and reversible, opening the road to applications based on the nonlinear response of random media.

A. Fleming, C. Conti, A. Di Falco, arXiv:1809.07077