Db Signal Boost Achieved by Mitigating Nonlinear Transduction Noise in Cavity Optomechanics

Precise displacement measurements are fundamental to numerous scientific fields, yet achieving accuracy at the standard quantum limit remains a significant challenge. Daniel Allepuz-Requena, Zohran Ali, and Dennis Høj, all from the Technical University of Denmark, alongside colleagues including Yingxuan Chen, Luiz Couto Correa Pinto Filho, and Alexander Huck, have demonstrated a novel technique to overcome limitations imposed by nonlinear transduction noise in cavity optomechanical systems. Their research addresses the issue of thermal intermodulation noise, which typically degrades measurement precision as optomechanical coupling strength increases. By applying a nonlinear transform to data from a high-cooperativity microcavity, the team successfully eliminated all orders of this noise, achieving a nearly 10 dB improvement in signal-to-noise ratio and paving the way for more sensitive and accurate measurements in future experiments. This advancement is particularly relevant for room-temperature systems where such noise is expected to be a dominant factor.

The team achieved this breakthrough by directly addressing and mitigating thermal intermodulation noise (TIN), a critical limitation in high-cooperativity optomechanical systems. This work centers on a membrane-in-the-middle microcavity system, engineered to exhibit high cooperativity, a measure exceeding the thermal occupation, and subjected to a novel nonlinear transform. Experiments show this transform effectively eliminates all orders of TIN, resulting in a nearly 10 dB improvement in the mechanical signal-to-noise ratio.

The study unveils a method for overcoming the challenges posed by nonlinear transduction, where strong optomechanical coupling drives the system into a regime where standard linearized analysis fails. Researchers identified that thermal intermodulation noise arises from the nonlinear mixing of thermomechanical motion, creating imprecision beyond the standard quantum limit. Previously, cancellation of this noise was limited to second-order nonlinearity through operation at a specific “magic detuning”, but this research establishes a technique to remove TIN across all orders. This was accomplished through detailed spectral analysis and correlation measurements, allowing the team to trace narrow features in the transmission spectrum to specific triple-mode mixing processes.

This breakthrough reveals the first experimental identification of third-order TIN within a cavity optomechanical system, a phenomenon expected to dominate noise in high-cooperativity, room-temperature setups. The team implemented a nonlinear position-reconstruction protocol that inverts the full cavity response, effectively removing all orders of TIN from the measurement record and restoring linear position readout. By applying this method to their microcavity system, they demonstrate a substantial improvement in signal-to-noise ratio and a clarified mechanical spectrum previously obscured by nonlinear mixing. The research establishes a pathway toward accessing the quantum backaction-dominated regime at room temperature, where ultimate performance limits are dictated by classical forces rather than thermal noise.

This capability is crucial for advancing room-temperature optomechanical platforms, offering potential for practical and scalable quantum technologies. The work opens possibilities for exploring quantum behavior in massive mechanical systems, including ground-state preparation and ponderomotive squeezing, without the limitations imposed by nonlinear transduction noise. This innovation promises to significantly enhance the sensitivity and precision of future optomechanical experiments.

Thermal Noise Cancellation in Optomechanical Systems

The study pioneered a method for significantly enhancing the precision of displacement measurements in cavity optomechanical systems by directly addressing thermal intermodulation noise (TIN). Researchers engineered a membrane-in-the-middle microcavity system, operating at room temperature, to achieve high cooperativity. This system facilitated the development of a nonlinear transform capable of eliminating all orders of TIN, ultimately improving the mechanical signal-to-noise ratio by nearly 10 dB. The work represents a substantial advancement in overcoming a key limitation in high-cooperativity room-temperature optomechanics.

Scientists developed a novel position-reconstruction protocol that inverts the full cavity response, effectively removing TIN from measurement records. This technique restores linear position readout, even with substantial detuning, and circumvents the dominant technical limitation previously hindering high-cooperativity systems. Experiments employed a direct-detection scheme, utilizing the reflected field from the microcavity to infer intracavity field fluctuations and, subsequently, mechanical displacement. The system delivers precise measurements by directly inverting equations relating cavity detuning to intracavity photon number and phase, bypassing the need for linear approximations that introduce noise.

The microcavity system itself consists of a stack comprising a silicon chipholder, a density phononic membrane, and a bottom mirror etched along specific crystalline planes, (100) and (101). A concave micromirror integrated into the top substrate further refines the optical path. Researchers harnessed the relationship between mechanical displacement and cavity detuning, expressed as ν(t) = ν0 − 2Gκx(t), where G represents the optomechanical coupling strength and κ is the cavity linewidth. By directly inverting the equations governing cavity response, the team achieved immunity to all orders of TIN, a breakthrough previously limited to second-order cancellation via “magic detuning”.

This innovative approach enables access to the quantum backaction-dominated regime at room temperature, where ultimate performance limits are dictated by higher-order classical forces rather than thermal noise. The technique reveals a clean mechanical spectrum previously obscured by nonlinear mixing, demonstrating a substantial improvement in signal clarity. By accurately reconstructing the true detuning from measurable quantities, the study overcomes a fundamental challenge in precision optomechanics and paves the way for future investigations into quantum phenomena.

Third-Order Noise Mitigation in Optomechanical Systems

Scientists achieved a significant breakthrough in cavity optomechanics by directly observing and mitigating third-order thermal intermodulation noise (TIN), a key limitation in high-cooperativity room-temperature systems. The research team employed a membrane-in-the-middle microcavity system, attaining high cooperativity, C nth, and successfully implemented a nonlinear transform to eliminate all orders of TIN. Experiments revealed an almost 10 dB improvement in the mechanical signal-to-noise ratio, restoring a clear mechanical spectrum previously obscured by nonlinear mixing processes. The study focused on the nonlinear transduction regime where thermomechanical motion modulates the cavity detuning, creating TIN and backaction.

Researchers recorded the output of the microcavity, identifying narrow features in the transmission spectrum that correspond to specific triple-mode mixing processes occurring among thermomechanical modes below the phononic bandgap. This constitutes the first experimental identification of third-order TIN within a cavity optomechanical system, confirming its dominance as an intrinsic noise source in high-cooperativity setups. Measurements confirm that conventional methods for canceling TIN, such as operating at “magic detuning”, are insufficient to address higher-order nonlinearities. The team developed a nonlinear position-reconstruction protocol that inverts the full cavity response, effectively removing all orders of TIN from the measurement record.

This reconstruction enables linear position readout even with substantial detuning excursions, overcoming a major technical hurdle in room-temperature optomechanics. Data shows the implemented protocol restores accurate position measurement by accounting for the complete cavity response, eliminating the impact of TIN. The breakthrough delivers a pathway towards accessing the quantum backaction-dominated regime at room temperature, where classical forces, rather than thermal noise, will ultimately limit performance. This advancement promises to unlock new possibilities for exploring quantum behavior in macroscopic mechanical systems and enhancing the practicality of optomechanical platforms.

Nonlinear Transform Mitigates Thermal Noise in Microcavity

This research details the successful mitigation of thermal intermodulation noise (TIN) in a membrane-in-the-middle microcavity operating at room temperature. By applying a nonlinear transform to the recorded output, the team achieved a significant improvement in the mechanical signal-to-noise ratio, approaching a 10 dB enhancement. This advancement addresses a key limitation in high-cooperativity cavity optomechanical systems, where third-order TIN previously obscured precise displacement measurements. The study demonstrates a pathway towards more efficient conditional cooling of mechanical motion and improved state preparation, benefiting from the simplicity of the implemented protocol. The digital implementation of the nonlinear transform, potentially within a field-programmable gate array, offers a versatile solution applicable beyond cavity optomechanics to systems exhibiting Lorentzian response functions, such as mechanically coupled nitrogen-vacancy centres and quantum dots. The authors acknowledge that extraneous noise, potentially originating from intrinsic cavity frequency fluctuations, currently limits access to the quantum backaction dominated regime, and future work will focus on addressing this issue.