The field of force sensing in hybrid optomechanical systems is pivotal for developing quantum technologies. Achieving sensitivity that surpasses the standard quantum limit (SQL) is a central goal, but this is often hindered by practical limitations such as operating power and thermal noise. In this theoretical work, we investigate how qubit-oscillator coupling and Kerr nonlinearity can be harnessed to overcome these challenges. We demonstrate that while each nonlinearity can independently enable surpass-SQL sensitivity, their joint effect significantly enhances performance, widening the detection bandwidth and substantially increasing robustness to thermal fluctuations. Our detailed analysis reveals that these two nonlinear mechanisms act as distinct tools for quantum noise reduction. Qubit-oscillator coupling is effective at suppressing both back-action and shot noise, whereas Kerr nonlinearity provides a powerful, yet frequency-localized suppression of these noise components. Our findings establish this hybrid system as a promising platform for developing highly sensitive and robust quantum sensors capable of operating under less-than-ideal conditions.

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• Quantum optics
• Weak values & weak measurements