By coupling a single-electron transistor to a high–quality factor, 19.7-megahertz nanomechanical resonator, we demonstrate position detection approaching that set by the Heisenberg uncertainty principle limit. At millikelvin temperatures, position resolution a factor of 4.3 above the quantum limit is achieved and demonstrates the near-ideal performance of the single-electron transistor as a linear amplifier. We have observed the resonator's thermal motion at temperatures as low as 56 millikelvin, with quantum occupation factors of N TH = 58. The implications of this experiment reach from the ultimate limits of force microscopy to qubit readout for quantum information devices.

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 ...

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