Suppression of quantum-radiation-pressure noise in an optical spring

Recent advances in micro- and nanofabrication techniques have led to corresponding improvement in the performance of optomechanical systems, which provide a promising avenue towards quantum-limited metrology and the study of quantum behavior in macroscopic mechanical objects. One major impediment to reaching the quantum regime is thermal excitation, which can be overcome for a sufficiently high mechanical quality factor $Q$. Here, we propose a method for increasing the effective $Q$ of a mechanical resonator by stiffening it via the optical spring effect exhibited by linear optomechanical systems and show how the associated quantum-radiation-pressure noise can be evaded by sensing and feedback control. In a parameter regime that is attainable with current technology, this method allows for realistic quantum cavity optomechanics in a frequency band well below that which has been realized thus far.

Figure 1

Simplified experimental layout, with the canonical optomechanical system shown within the dashed box. Input vacuum fluctuations drive the cavity mode, which in turn exerts radiation pressure forces on the mechanical resonator forming the cavity boundary. The output mode of the cavity is sensed with a photodetector, and—in the relevant parameter regime—the measured power contains the radiation pressure fluctuations that drive the resonator with minimal sensitivity to the resonator position. This signal can therefore be used as an error signal for feeding back to the laser amplitude to suppress the radiation pressure noise on the resonator.

Figure 2

Graphical representation of the feedback model described in the text. The effects of the optical spring and the active external feedback are shown explicitly, while the (static) resonance of the classical field $\overline{a}$ is not. Using the input-output relations, the input fields at the left are split into the prompt reflections and the portions that enter the cavity. Then the leakage fields are summed with the prompt reflections to give the output. The feedback kernel is $H\equiv -K_c(\delta \widehat{P}/\sqrt{2}{\overline{a}}_{\mathrm{in}})$. Note that double-headed arrows correspond to the setting of a parameter block, while single-headed arrows denote signal transmission as usual.

Figure 3

Proposed experimental setup. A laser beam is split and one path is upshifted in frequency, allowing for independent control of the detuning of each field. Each beam's intensity can also be controlled by feeding back to the laser or the modulator, and these channels are used for radiation pressure (RP) noise feedback. A Pound-Drever-Hall (PDH) locking scheme is used to set the operating point before strengthening the stable optical spring.