Observing and utilizing quantum effects in macroscopic mechanical resonators is crucial for advancing fundamental physics and realizing quantum applications like quantum metrology and communication. However, thermal noise from the surrounding environment significantly hinders these efforts. While ground-state cooling has been achieved in sideband-resolved optomechanics, sideband-unresolved systems offer advantages in terms of ease of fabrication and suitability for low-frequency resonators, often required for macroscopic systems. This work focuses on overcoming the challenge of cooling macroscopic, low-frequency resonators operating at higher temperatures using feedback control schemes. The inherent limitation of measurement-based feedback cooling stems from the trade-off between measurement precision and back-action noise. The paper aims to demonstrate feedback cooling in a fully integrated, sideband-unresolved optomechanical device, achieving minimal phonon occupation even with moderate pre-cooling.

Previous demonstrations of ground-state cooling in mechanical resonators have primarily been achieved in the sideband-resolved regime, where the cavity linewidth is smaller than the mechanical frequency. These achievements have enabled the experimental observation of mechanical quantum behavior. However, the sideband-unresolved regime, where the cavity linewidth is larger than the mechanical frequency, is gaining traction, particularly for sensing applications. Operating in this regime relaxes stringent requirements on optical cavity properties, making it particularly attractive for low-frequency, macroscopic resonators. Recent experimental efforts have shown success in reaching phonon numbers below 1 in various systems, even starting from higher temperatures and lower frequencies. This paper builds upon these advancements, aiming to further improve the cooling efficiency and demonstrate its viability for practical applications.

The researchers utilized a fully integrated optomechanical device fabricated using a pick-and-place method. The device comprises a soft-clamped mechanical resonator with a fractal structure and a photonic crystal cavity, both made from silicon nitride. The mechanical resonator's fundamental mode oscillates at 1.1 MHz with an effective mass of 16 pg. The device operates in the deep sideband-unresolved regime (κ/(2π) = 8.8 GHz, κex/(2π) = 6.9 GHz). A homodyne measurement scheme continuously monitors the mechanical resonator's displacement. This information is fed to a controller which then actively reduces the motional energy via feedback control by modulating the optical input power. An out-of-loop heterodyne measurement, independent of the feedback loop, is used to measure sideband asymmetry, a hallmark of quantum behavior. The device's large optomechanical coupling (g0/(2π) = 224 kHz) and high mechanical quality factor (Qm ≈ 5.1 × 107 at 18 K) are crucial for efficient feedback cooling. The experiment involved two main stages: 1. Simultaneous homodyne and heterodyne measurements with liquid helium cooling and 2. Homodyne measurements only with improved detection efficiency, again with liquid helium cooling. Finally a set of measurements with liquid nitrogen cooling was performed to demonstrate higher temperature cooling. Data analysis involved fitting the measured spectra to extract phonon occupancy and comparing results from homodyne and heterodyne measurements to validate the calibration. A semi-classical model was used to describe the system's behavior, incorporating thermal noise, measurement imprecision, and feedback control.

The integrated optomechanical device exhibited a large optomechanical coupling and a high mechanical quality factor, placing it firmly in the sideband-unresolved regime. Feedback cooling with liquid helium pre-cooling resulted in a minimum average phonon occupation of 1.06 ± 0.06 using both homodyne and heterodyne measurements, confirming the validity of the calibration. By improving the detection efficiency (removing the heterodyne setup), the researchers achieved a minimum phonon number of 0.76 ± 0.16. Furthermore, successful feedback cooling was demonstrated even with liquid nitrogen pre-cooling (77 K), reaching a minimum phonon number of 3.45 ± 0.15. In both cases, significant sideband asymmetry was observed in the heterodyne measurements, providing further evidence for quantum mechanical behavior. The discrepancy between the measured effective bath temperature and the thermometer reading highlights the challenges in achieving perfect thermalization of the mechanical structure.

The results demonstrate the successful implementation of active feedback cooling in a fully integrated optomechanical system operating in the sideband-unresolved regime. The achievement of near ground-state cooling with liquid helium pre-cooling and observing clear quantum effects (sideband asymmetry) at 77 K are significant milestones. The success validates the effectiveness of the employed feedback control strategy, particularly highlighting its robustness in a relatively high-temperature environment. The agreement between the phonon numbers extracted from the homodyne and heterodyne measurements strengthens the confidence in the calibration procedure. The discrepancy between the effective bath temperature and the measured temperature suggests that further improvements in thermalization could potentially lead to even lower phonon occupation numbers. The ease of integration and the suitability for higher-temperature operation makes this approach highly promising for real-world applications.

This study demonstrates efficient feedback cooling of an integrated optomechanical resonator to near its motional ground state, even at elevated temperatures (77K). The use of a fully integrated device in the sideband-unresolved regime simplifies the experimental setup and opens up possibilities for diverse applications in quantum sensing and other quantum technologies. Future work may focus on further improvements in the mechanical quality factor and thermalization to reach the ground state from room temperature, enabling even more practical applications.

While the study successfully demonstrates feedback cooling, limitations exist. The effective bath temperature is higher than the measured temperature, possibly due to imperfect thermalization of the chip. The presence of higher-order mechanical modes might introduce some challenges in control. Further improvements in the detection efficiency and control algorithm could potentially lead to even lower phonon numbers. The relatively high initial phonon number at 77 K limits the minimum achievable phonon occupation in that condition.