Active cooling of an audio-frequency electrical resonator to microkelvin temperatures

We have cooled a macroscopic LC electrical resonator using feedback-cooling combined with an ultrasensitive dc Superconducting Quantum Interference Device (SQUID) current amplifier. The resonator, with resonance frequency of 11.5 kHz and bath temperature of 135 mK, is operated in the high coupling limit so that the SQUID back-action noise overcomes the intrinsic resonator thermal noise. The effect of correlations between the amplifier noise sources clearly show up in the experimental data, as well as the interplay of the amplifier noise with the resonator thermal noise. The lowest temperature achieved by feedback is 14 μK, corresponding to 26 resonator photons, and approaches the limit imposed by the noise energy of the SQUID amplifier.