Feedback cooling of cantilever motion using a quantum point contact transducer

Abstract

We use a quantum point contact (QPC) as a displacement transducer to measure and control the low-temperature thermal motion of a nearby micromechanical cantilever. The QPC is included in an active feedback loop designed to cool the cantilever's fundamental mechanical mode, achieving a squashing of the QPC noise at high gain. The minimum achieved effective mode temperature of 0.2 K and the displacement resolution of 10 −11 m/ √ Hz are limited by the performance of the QPC as a one-dimensional conductor and by the cantilever-QPC capacitive coupling. [5]. The displacement imprecision of some of these measurements approaches the standard quantum limit on position detection [6], i.e. the limit set by quantum mechanics to the precision of continuously measuring position. Such exquisite resolution has enabled recent experiments measuring quantum states of mechanical motion in a resonator [7][8][9].It naturally follows that with such fine measurement resolution comes equally fine control of the mechanical motion, enabling both tuning of a resonator's linear dynamic range [10] and manipulation of its time response [11]. In fact, such conditions allow for the application of active feedback cooling [11] as a method for preparing a mechanical oscillator near its quantum ground state. Unlike side-band cooling, which has recently been used to cool high-frequency resonators into their ground state [8,9], feedback cooling is particularly well-suited to the ultra-soft low-frequency cantilevers typically used in sensitive force measurements. The minimum phonon occupation number achieved by this method depends only on the detector's displacement imprecision and the resonator's thermal noise [11]. As a result, a widely applicable transduction scheme with low displacement imprecision has the potential to prepare resonators in quantum states of mechanical motion.Here we investigate one such technique: the use of a quantum point contact (QPC) as a sensitive detector of cantilever displacement [12]. The QPC transducer works by virtue of the strong dependence of its conductance on disturbances of the nearby electric field by an object's motion. In particular, a QPC is advantageous due to its versatility as an off-board detector, its applicability to nanoscale oscillators, and its potential to achieve quantum-limited detection [13,14]. Most other displace- Figure 1: Schematic diagram of the experimental setup. In the red loop, the motion of the cantilever is transduced by a quantum point contact and amplified by an optimal controller, before being sent to a piezoelectric element mechanically coupled to the cantilever. The motion is also independently detected by an out-of-loop fiber interferometer, shown in blue. ment detection schemes require the functionalization of mechanical resonators with electrodes, magnets, or mirrors [5]. These requirements tend to compete with the small resonator mass and high quality factor necessary to achieve low thermal noise and high coupling strength to the detector. Since all resonators disturb the near...

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