Cooling a nanomechanical resonator with quantum back-action

Abstract

Surprisingly, when biasing near a transport resonance, we observe cooling of the nanomechanical mode from 550 mK to 300 mK. These measurements have implications for nanomechanical readout of quantum information devices and the limits of ultra-sensitive force microscopy, e.g. single nuclear spin magnetic resonance force microscopy. Furthermore, we anticipate the use of these backaction effects to prepare ultra-cold and quantum states of mechanical structures, which would not be accessible with existing technology.In practice, these back-action impulses arise from the quantized and stochastic nature of the fundamental particles utilized in the measuring device. For example, in high precision optical interferometers such as the LIGO gravitational wave detector 4 or in the single-spin force microscope 5 , the position of a test mass is monitored by reflecting laser-light off of the measured object and interfering this light with a reference beam at a detector. The measured signal is the arrival rate of photons, and one might say that the optical "conductance" of the interferometer is modulated by the position of the measured object. Back-action forces which stochastically drive the measured object result from the random impact and momentum transfer of the discrete photons. This mechanical effect of light is thought to provide the ultimate limit to the position and force sensitivity of an optical interferometer. Although this photon "ponderomotive" noise has not yet been detected during the measurement of a macroscopic object 6 , these back-action effects are clearly observed and carefully utilized in the cooling of dilute atomic vapors to nanoKelvin temperatures.In the experiments reported here, we study an SSET which is capacitively coupled to a voltage-biased (V NR ), doubly-clamped nanomechanical resonator (Fig. 1). Like the interferometer, the conductance of the SSET is a very sensitive probe of the resonator's position, whereas the particles transported in this case are a mixture of single andCooper-paired electrons. We have recently shown the SSET to be nearly a quantumlimited position detector 7 , however reaching the best sensitivity will ultimately be limited by the back-action of the charged particles 3 , which could not be observed in previous experiments because of insufficient SSET-resonator coupling.The back-action force of the SSET results in three measurable effects on the resonator: a frequency shift, a damping rate, and position fluctuations. The frequency shift and damping rate are caused by the in-phase and small out-of phase response in the average electrostatic force between the SSET and resonator, as the resonator oscillates. .MHz is clearly visible, and accurately fits a simple harmonic oscillator response function, on top of a white power spectrum due to an ultra-low noise microwave preamplifier used to read out the SSET with microwave reflectometry 8 .For low SSET-nanoresonator coupling strengths, and the SSET biased close to the Josephson Quasiparticle Peak (JQP) 9 , T NR simply follows T ...

Optomechanics

“…We explain the classical effects of retarded radiation forces. Similar physics was investigated in a variety of other system, like driven LC-circuits coupled to cantilevers (Brown et al, 2007) or single-electron transistors and microwave cavities coupled to nanobeams (Naik et al, 2006;D A Rodrigues and Armour, 2007;Regal et al, 2008). Light-induced forces can not only cool the cantilever, but can also enhance the mechanical motion leading to an instability.…”

Advances in mechanical detection of magnetic resonance

“…195 Nevertheless, achieving subattonewton sensitivity may require moving beyond single-crystal silicon oscillators. While Si 3 N 4 was initially abandoned as a material for ultrasensitive cantilevers in favor of single crystal silicon, 38 recent work has shown that large increases in Si 3 N 4 's mechanical quality factor can be realized by working at millikelvin temperature 179 or by applying strains. 196 Novel materials such as metallic glasses 197 may potentially exhibit ultralow mechanical dissipation.…”

“…Achieving thermally limited force detection of rf cantilever motion at cryogenic temperatures is extremely challenging, but has been achieved, for example, by coupling a rf single-electron transistor to a metal-coated Si 3 N 4 cantilever 179 and by harnessing the piezoresistivity of a thin metal film coating a SiC cantilever. 180 Displacement detectors based on tunnel sensors are under development for use with rf cantilevers, 181 and one can also imagine using on-chip ring resonators to achieve exquisitely sensitive displacement sensing.…”

Quantum Limits on Measurement and Control of a Mechanical Oscillator

“…2. 45 Due to the nature of the problem, it seems reasonable to imagine that for a narrow longitudinal (along the beam) constriction with a transverse opening, squeeze-films get evacuated much more quickly than diffusion would suggest. In fact molecules in a squeeze film execute Lévy walks [247], lending plausibility to their absence after even a short pumping time.…”

“…nano-mechanical oscillators, featuring very high mechanical quality, brought the dream of witnessing the vacuum fluctuations of a macroscopic object ever closer. Integrating such oscillators with sensitive radio-frequency amplifiers, like single-electron transistors [43][44][45], quantum-point contacts [46,47], or SQUIDs [48], proved to be fruitful in terms of approaching the sensitivity required to see vacuum fluctuations (i.e. the standard quantum limit (SQL)).…”