Quantum diffusion of pure-quartic solitons in a laser cavity

Ultrashort pulses experience random quantum motion as they propagate through a mode-locked laser cavity, a phenomenon that inevitably affects the recently introduced pure-quartic solitons. Investigating this process is essential, as quantum-limited noise establishes fundamental performance limits for their application. To date, studies on quantum diffusion and the resulting timing jitter of these solitons remain sparse. In this work, we examine the quantum motion of pure-quartic solitons by injecting amplified spontaneous emission noise into the gain medium, measuring their relative position, and performing analyses using Allan variance and timing jitter power spectral density. Our simulation findings reveal that long-range interactions due to pulse tailing can lead to high-frequency noise, which can be effectively filtered out. In the near-zero dispersion regime, we achieve quantum-limited noise levels significantly less than 1 fs. Good agreement is observed between the analytical model and the simulation results. This work provides insights into the noise levels and mechanisms of pure-quartic solitons and can be extended to more complex scenarios, such as pure-quartic Kerr solitons, and studies on the dynamics of higher-order dispersion solitons.