Ultrafast Nonlinear Dynamics in Mesoscopic Oscillators

Abstract

Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to cryptography. Recently our team has examined two types of mesoscopic nonlinear oscillators—in optomechanics and frequency combs—that provide new platforms to uncover quintessential architectures of chaos generation and the underlying physics. In the first section, we will describe the measurements of deterministic chaos formation at 60 fJ intracavity energies, through coupled Drude electron-hole plasma and radiation pressure. Statistical and entropic characterization quantifies the complexity of the chaos, including a correlation dimension D2 approximately 1.67 for the chaotic attractor, reminiscent of Lorenz chaos, along with the Lyapunov exponents. The dynamical maps demonstrate the plethora of subharmonics and bifurcations, with distinct transitional routes into chaotic states. In the second section, we will describe the measurements of spontaneous Turing pattern formation in nonlinear oscillators from background noise. Transitional states of breathers, chaos, soliton molecules are involved, in addition to the Turing patterns. Our observed threshold-dependent stationary Turing pattern has a RF tone tunable between 1.14 to 1.57 THz. Local mode hybridizations in the nonlinear ring oscillator seeds the pattern formation and phase matching, with a record high conversion efficiency of 45% and strong asymmetry in the Turing roll pattern. By heterodyne beating against a 1-Hz stabilized frequency reference, we show a fractional frequency sideband non-uniformity measured at 6.6 × 10⁻¹⁶, potentially serving as a high-performance chip-scale frequency reference.