We study theoretically the measurement of a mechanical oscillator using a
single two level system as a detector. In a recent experiment, we used a single
electronic spin associated with a nitrogen vacancy center in diamond to probe
the thermal motion of a magnetized cantilever at room temperature {Kolkowitz et
al., Science 335, 1603 (2012)}. Here, we present a detailed analysis of the
sensitivity limits of this technique, as well as the possibility to measure the
zero point motion of the oscillator. Further, we discuss the issue of
measurement backaction in sequential measurements and find that although
backaction heating can occur, it does not prohibit the detection of zero point
motion. Throughout the paper we focus on the experimental implementation of a
nitrogen vacancy center coupled to a magnetic cantilever; however, our results
are applicable to a wide class of spin-oscillator systems. Implications for
preparation of nonclassical states of a mechanical oscillator are also
discussed.Comment: 17 pages, 6 figure
