Probing sideband asymmetry in mechanical oscillators in the presence of thermal effects*

Sideband asymmtery is a hallmark of the quantum nature of mechanical oscillators, and has recently been observed in several types of systems. Asymmetry measurements may provide the absolute temperature of the oscillator, without need of calibration. We implement sideband asymmetry measurement in the well-resolved sideband regime by probing simultaneously with red- and blue-detuned probes. We show however that such measurement may be plagued by 'fake' asymmetry generated due to the presence of additional tones close to the optical resonance, such as another red-detuned strong cooling tone. The slow-oscillating intracavity field undergoes frequency conversion in the presence of nonlinear cavity effects, such as photothermal and Kerr effects, causing exchange of energy between red-detuned probes as well as generating new frequencies. We model these effects and elucidate the means to circumvent them. This phenomenon has wide-ranging implications for any scheme utilizing several probing/pumping tones, such as backaction evasion measurements, dissipative optical squeezing and mechanical squeezing schemes.