Observation of Fermi-Pasta-Ulam Recurrence Induced by Breather Solitons in an Optical Microresonator

We present, experimentally and numerically, the observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in a high-$Q$ SiN microresonator. Breather solitons can be excited by increasing the pump power at a relatively small pump phase detuning in microresonators. Out of phase power evolution is observed for groups of comb lines around the center of the spectrum compared to groups of lines in the spectral wings. The evolution of the power spectrum is not symmetric with respect to the spectrum center. Numerical simulations based on the generalized Lugiato-Lefever equation are in good agreement with the experimental results and unveil the role of stimulated Raman scattering in the symmetry breaking of the power spectrum evolution. Our results show that optical microresonators can be exploited as a powerful platform for the exploration of soliton dynamics.

Figure 1

(a) The experimental setup and operating regimes of Kerr frequency combs. Breather solitons are generated at relatively small detuning and high pump power, and we use three steps (illustrated by I, II, and III) to generate the breather soliton. MI, modulation instability; PD, photodiode; LNA, low noise amplifier; osc, oscillation. (b) The optical spectrum of the stable soliton (blue) and the simulated spectrum from the generalized LLE (the red line). (c) The rf spectrum of the soliton state. (d) The averaged spectrum of the breather soliton spectrum from the optical spectrum analyzer (blue) and from simulation (the red line). (e) The rf spectrum of the breather soliton. The pumped resonance has a linewidth of 100 MHz.

Figure 2

(a) The recorded fast evolution of the comb lines around the center and in the wings of the spectrum. (Inset) The rf spectrum of the power evolution measured over $4\mu \mathrm{s}$ for comb lines in the wings. A 20 MHz bandpass filter (BPF) is used to select the strongest rf tone. (b) Reconstructed comb line power evolution after numerical filtering. The blue (orange) shaded regions illustrate the time slots where the power flows toward the center (wing). Center (blue lines), comb lines within 1553–1569 nm; wing (orange lines), comb lines within 1530–1550 nm and 1569–1600 nm.

Figure 3

The recorded power evolution for different comb line groups when the pulse shaper is used to select spectral regions with finer resolution. The red dashed line illustrates the peak of different groups and shows different group experience modulations with different relative phases.

Figure 4

(a) The numerically filtered spectral evolution of the breather soliton in the simulation, with SRS included. The various spectral groups far away from the center have approximately the same phase, but their phase is clearly different from that of the group of comb lines around the center ($\sim 1560\mathrm{nm}$). (b) Simulation of the FPU recurrence for comb lines around the center (blue line, 1552–1567 nm) and comb lines in the wings (orange line, 1521–1550 nm and 1567–1592 nm, with the pump at 1551 nm excluded). The shaded regions illustrate the power exchange between the center and the wing. (c) The experimental traces at long (above 1600 nm) and short wavelengths (below 1530 nm), showing the same phase between them. (d) The numerically filtered spectral breathing in the simulation, without SRS. The phase for different slices is symmetric with respect to the center of the spectrum (1551 nm). The red dashed lines in (a),(d) illustrate the peak of different slices.