Measuring mechanical motion with a single spin

TL;DR

This paper analyzes the theoretical limits and practical considerations of using a single spin, such as a nitrogen vacancy center, to measure mechanical motion, including zero point fluctuations, and discusses implications for quantum state preparation.

Contribution

It provides a detailed theoretical analysis of the sensitivity, backaction effects, and measurement limits of spin-based mechanical motion detection techniques.

Findings

Sensitivity limits for detecting zero point motion are established.

Backaction heating does not prevent zero point motion detection.

Results are applicable to a broad class of spin-oscillator systems.

Abstract

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.