Comment on "Evidence for quantized displacement in macroscopic nanomechanical oscillators".

In a recent Letter, Gaidarzhy et al. [1] claim to have observed evidence for ''quantized displacements'' of a high-order mode of a nanomechanical oscillator. We contend that the methods employed by the authors are unsuitable in principle to observe such states for any harmonic mode. (1) According to standard quantum mechanics, continuous measurement of the energy quanta in any resonator mode requires a probe whose interaction Hamiltonian commutes with the oscillator Hamiltonian, i.e., one requires a quantum nondemolition (QND) measurement scheme. However, with continuous linear measurement of position or velocity, the best energy sensitivity one can, in principle, achieve is E @!  N p , where N is the average number of quanta, the so-called standard quantum limit [2]. The authors employ continuous magnetomotive detection [3]. This is a continuous linear measurement scheme and is not a QND measurement of the energy. In magneto-motive detection, the sample is immersed in a large magnetic field, and driven with an oscillating current through the mechanical element. The magnetic field transforms the applied oscillating currents into forces on the resonator, and transduces the resulting mechanical motion into measurable voltages. Such a detection scheme does not measure the absolute value of position, as the authors claim. The authors drive the resonator many orders of magnitude above the ground and first excited state during the measurement shown in Fig. 4c. Given the reported parameters (F 45 pN, k eff ˆ 188 N=m, and Q ˆ 150), the average number of energy quanta in the resonator during the measurement is N ˆ 120000 1, which corresponds to an effective resonator temperature of 8800 K. Furthermore, the authors use a room temperature semiconducting amplifier with a noise temperature of T N ˆ 440 K to detect the magnetically transduced voltages [4]. Thus, in addition to the magnetic drive, the backaction current noise of such an amplifier will act as a thermal bath, driving the resonator far above the temperature of 100 mK quoted by the authors. One does not expect to observe any evidence of the lowest quantized energy states of the resonator using this method. (2) For Q 100 and ! ˆ 10 10 s ÿ1 , the average lifetime of an energy quantum is 10 nsec. Even if the authors could measure the oscillator energy with single quantum accuracy, the observed jumps due to decay would certainly not be as long as tens of …