Signals can be amplified by an optimum amount of noise, but this stochastic resonance is a rather fragile phenomenon. Dutch researchers at AMOLF were the first to investigate the role of memory for this pheno­menon in an oil-filled optical micro­cavity. The effects of slow non-linearity on stochastic resonance were never considered before, but these experi­ments suggest that stochastic resonance becomes robust to variations in the signal frequency when systems have memory. This has impli­cations in many fields of physics and energy technology. In particular, the scientists numeri­cally show that introducing slow non-linearity in a mechanical oscillator harves­ting energy from noise can increase its effi­ciency by tenfold.

Whether it is some soft music, remote traffic noise or the hum of people chatting in the distance, for many people, an optimum amount of noise enables them to concentrate better. “This is the human equivalent of stochastic resonance”, says Said Rodriguez. “In our scientific labs stochas­tic resonance happens in non-linear systems that are bistable. This means that, for a given input, the output can switch between two possible values. When the input is a periodic signal, the response of a non-linear system can be amplified by an optimum amount of noise using the stochastic resonance condition.”

Stochastic resonance has been observed in many natural and techno­logical systems, but this wide-spread obser­vation poses a puzzle to scientists. Rodriguez: “Theory suggests that stochastic resonance can only occur at a very specific signal frequency. However, many noise-embracing systems live in environ­ments where signal frequencies fluctuate. For example, it has been shown that certain fish prey on plankton by detecting a signal they emit, and that an optimum amount of noise enhances the fish's ability to detect that signal through the pheno­menon of stochastic resonance. But how can this effect survive fluc­tuations in the signal frequency occurring in such complex environments?”

Rodriguez and his PhD student Kevin Peters were the first to demons­trate that memory effects must be taken into account to solve this puzzle. “The theory of stochastic resonance assumes that non-linear systems respond instan­taneously to an input signal. However, in reality most systems respond to their environment with a certain delay and their response depends on all that happened before”, he says. Such memory effects are difficult to describe theo­retically and to control experi­mentally, but the Inter­acting Photons group has now managed both. Rodriguez: “We have added a controlled amount of noise to a beam of laser light and have shined it on a tiny cavity filled with oil, which is a non-linear system. The light causes the temperature of the oil to rise, and its optical properties to change, but not imme­diately. It takes about ten microseconds, thus the system is non-instan­taneous as well. In our experiments, we have shown for the first time that stochastic resonance can occur over a broad range of signal frequencies when memory effects are present.”

Having thus shown that the widespread occur­rence of stochastic resonance may be due to yet un­noticed memory dynamics, the researchers hope that their results will inspire colleagues in several other fields of science to search for memory effects in in their own systems. To extend the impact of their findings, Rodriguez and his team have theoretically investigated the effects of non-instan­taneous response on mechanical systems for energy harvesting. “Small piezo-electric devices that harvest energy from vibrations are useful when battery replacement is difficult, for example in pacemakers or other biomedical devices”, he explains. “We have found a tenfold increase in the amount of energy that could be harvested from environ­mental vibrations, if memory effects would have been incor­porated.”

The obvious next step for the group is to expand their system with several connected oil-filled cavities and inves­tigate collective behavior emerging from noise. Rodriguez does not fear stepping outside his scientific comfort zone. He says: “It would be great if we could team up with researchers that have expertise in mechanical oscil­lators. If we can implement our memory effects in those systems, the impact on energy techno­logy will be enormous.” (Source: AMOLF)

Reference: K. J. H. Peters et al.: Extremely Broadband Stochastic Resonance of Light and Enhanced Energy Harvesting Enabled by Memory Effects in the Nonlinear Response, Phys. Rev. Lett. 126, 213901 (2021); DOI: 10.1103/PhysRevLett.126.213901

Link: Interacting Photons, Center for Nanophotonics, AMOLF, Amsterdam, Netherlands