Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK

We report on the use of a radiation pressure induced restoring force, the optical spring effect, to optically dilute the mechanical damping of a 1 g suspended mirror, which is then cooled by active feedback (cold damping). Optical dilution relaxes the limit on cooling imposed by mechanical losses, allowing the oscillator mode to reach a minimum temperature of 6.9 mK, a factor of $\sim 40000$ below the environmental temperature. A further advantage of the optical spring effect is that it can increase the number of oscillations before decoherence by several orders of magnitude. In the present experiment we infer an increase in the dynamical lifetime of the state by a factor of $\sim 200$.

Figure 1

Simplified schematic of the experiment. About 100 mW of ${\lambda }_0=1064\mathrm{nm}$ Nd:YAG laser light passes through a Faraday isolator (FI) and a half-waveplate (HWP) and polarizing beam splitter (PBS) combination that allows control of the laser power, before being injected into the cavity, which is mounted on a seismic isolation platform in a vacuum chamber (denoted by the shaded box). A Pound-Drever-Hall (PDH) error signal derived from the light reflected from the cavity is used to lock it, with feedback to both the cavity length (actuated via magnets affixed to each suspended mirror), as well as the laser frequency.

Figure 2

The transfer function of an applied force to mirror motion, for increasing levels of damping [curves (a) to (d)]. The force is applied via the magnet or coil actuators, and the response is measured by the PDH error signal. The points are measured data, and the lines are fitted Lorentzians from which the resonant frequency and damping constant are derived for each configuration. Statistical errors in the fit parameters are on the order of 1%.

Figure 3

The measured noise spectral density of the mirror displacement. The curves (a) to (d) correspond to increasing gain in the damping feedback loop; for each, the parameters of the resonance are measured and depicted in Fig. 2. The spectra are integrated from 850 to 1100 Hz, the frequency range where the mirror motion is the dominant signal, to obtain the rms motion of the mirror and its effective temperature. The broad limiting noise source is frequency noise of the laser. Narrow spectral features in addition to the main optical spring resonance are due to coupling of acoustically driven phase noise.