[Paper Review] Long-range Synchronization of Nanomechanical Oscillators with Light

Shreyas Y. Shah, Mian Zhang+2 more|arXiv (Cornell University)|Nov 27, 2015

Mechanical and Optical Resonators3 citations

TL;DR

This paper demonstrates long-range synchronization of two nanomechanical oscillators separated by 30 meters via optical fiber coupling, introducing a 139-ns delay due to the finite speed of light. Despite significant coupling delay, the system achieves multiple stable synchronized states with tunable frequencies by independently controlling directional coupling strengths, enabling reconfigurable RF networks and neuromorphic computing platforms.

ABSTRACT

We experimentally demonstrate mutual synchronization of two free-running nanomechanical oscillators separated by an effective distance of 30 meters and coupled through light. Due to the finite speed of light, the large separation introduces a significant coupling delay of 139 nanoseconds, approximately four and a half times the mechanical oscillation time period. We reveal multiple stable states of synchronized oscillations, enabled by delayed coupling, with distinct synchronization frequency in the coupled system. These states are accessed by tuning independently the directional coupling strengths. Our results demonstrate rich dynamics and could enable applications in reconfigurable radio-frequency networks and novel computing concepts.

Motivation & Objective

• To achieve mutual synchronization of nanomechanical oscillators over a 30-meter distance, far exceeding typical micrometer-scale coupling ranges.
• To overcome the challenge of long-distance coupling in nanomechanical systems by using low-loss optical fibers to transmit modulated light signals.
• To explore the impact of time-delayed coupling on synchronization dynamics in coupled nonlinear oscillators.
• To demonstrate independent control of directional coupling strengths to access multiple stable synchronization frequencies.
• To enable new applications in reconfigurable radio-frequency networks and neuromorphic computing through controllable synchronization states.

Proposed method

• Two optomechanical oscillators (OMOs) based on double microdisk structures are fabricated using electron-beam lithography and reactive ion etching on Si3N4/SiO2 membranes.
• Each OMO is driven into self-sustained oscillations via a continuous-wave laser, generating radio-frequency modulations in the transmitted optical power.
• Optical fibers are used to transmit the RF-modulated light between the two OMOs, introducing a 139-ns round-trip delay (approximately 4.5× the mechanical oscillation period).
• Directional coupling strengths (κ₁₂ and κ₂₁) are independently tuned via variable optical attenuators to control the strength of signal propagation from OMO1 to OMO2 and vice versa.
• Synchronization is observed by measuring the RF power spectrum of the transmitted light, revealing distinct locked frequencies depending on coupling ratios.
• The system is modeled using coupled nonlinear oscillator equations with time delay, and the synchronization frequency Ω_sn is normalized to the natural frequency difference (Ω₂ − Ω₁).

Experimental results

Research questions

• RQ1 Can nanomechanical oscillators be synchronized over distances of tens of meters using optical coupling?
• RQ2 How does a significant time delay (139 ns) affect the synchronization dynamics in coupled nanomechanical systems?
• RQ3 Can multiple stable synchronization states with distinct frequencies be accessed by tuning directional coupling strengths?
• RQ4 What role does asymmetric coupling (κ₁₂ ≠ κ₂₁) play in enabling new synchronization frequencies not accessible in symmetric systems?
• RQ5 Can such a system support reconfigurable, multi-state synchronization for applications in communication and computing?

Key findings

• Mutual synchronization of two nanomechanical oscillators is experimentally demonstrated over a 28.5-meter optical fiber link, with a 139-ns coupling delay.
• The system exhibits multiple stable synchronized states with distinct oscillation frequencies, accessible by tuning the ratio of directional coupling strengths (κ₁₂/κ₂₁).
• For a κ₁₂/κ₂₁ ratio of 6.3 dB, two synchronized states are observed at 32.93 MHz and 32.94 MHz, corresponding to Ω_sn = 0.65 and 0.85, respectively.
• At a κ₁₂/κ₂₁ ratio of 13.6 dB, a new synchronization frequency at Ω_sn = 0.4 is accessed, which is not reachable at the lower ratio.
• The synchronization frequency spans discrete values across the natural frequency range, forming four distinct clusters in the parameter space of κ₂₁ and κ₁₂/κ₂₁.
• Independent control of κ₁₂ and κ₂₁ enables access to non-trivial synchronization states, including master-slave locking (when κ₁₂/κ₂₁ is small) and symmetric locking (when coupling is balanced).