Measuring nanomechanical motion with a microwave cavity interferometer

Abstract

In recent years microfabricated microwave cavities have been extremely successful in a wide variety of detector applications. In this article we focus this technology on the challenge of quantum-limited displacement detection of a macroscopic object. We measure the displacement of a nanomechanical beam by capacitively coupling its position to the resonant frequency of a superconducting transmission-line microwave cavity. With our device we realize near state-of-the-art mechanical force sensitivity (3 aN/ √ Hz) and thus add to only a handful of techniques able to measure thermomechanical motion at 10's of milliKelvin temperatures. Our measurement imprecision reaches a promising 30 times the expected imprecision at the standard quantum limit, and we quantify our ability to extract measurement backaction from our results as well as elucidate the important steps that will be required to progress towards the full quantum limit with this new detector.The advent of micro and nanomechanical resonators has brought the long-standing goal of exploring quantum effects such as superposition and entanglement of macroscopic objects closer to reality. With this ability one could experimentally study decoherence of superposition states thus elucidating questions about the interface between the quantum and classical worlds. Micro and nanomechanical resonators have hastened progress towards macroscopic quantum limits by providing high-frequency, small-dissipation, yet lowmass resonators. Still it remains a challenge to freeze out the thermomechanical motion of these objects to leave only zeropoint fluctuations δx zp and, equally importantly, to detect motion at this level. The problem of detection at the quantum limit is in itself intriguing. As the imprecision of any detector is decreased, measurement backaction emerges to enforce the Heisenberg constraint, which for continuous displacement detection is S im x S ba F ≥ 2 . Here S im x and S ba F are respectively the displacement imprecision and backaction force spectral densities. In fact, at the minimum allowed total position uncertainty, referred to as the standard quantum limit (SQL), the measurement imprecision and backaction must together contribute an uncertainty equal to the zero-point fluctuations.A widely used displacement detector that, in principle, is capable of reaching the SQL is an optical cavity interferometer with a moving mirror [1]. Physically, at the SQL ones knowledge of the mirror position is limited equally by shot noise in the output signal and by motion of the mirror due to quantum fluctuations in the intracavity radiation pressure. This limit has long been of interest in quantum optics and in the gravitational wave detection community. Optical cavities generally outperform all other displacement detectors with regard to measurement imprecision; they can achieve shot-noise limited position sensitivity as low as ∼ 10. Still reaching the SQL has historically been a challenge due to the inaccessibility of quantum backaction effects [3,4]. Recent experimental...

Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit

“…Over the past decade, it has been widely perceived that the most promising approach to address these two challenges are electro nanomechanical systems [2,6,7,8,9,10], which can be cooled with milli-Kelvin scale dilution refrigerators, and feature large ∆x ∼ 10 −14 m resolvable with electronic transducers such as a superconducting single-electron transistor [7,8,11], a microwave stripline cavity [9] or a quantum interference device [12]. In this manner, thermal occupation as low as 25 quanta [7,10] has been measured.…”

“…Here we approach for the first time the quantum regime with a mechanical oscillator of mesoscopic dimensions-discernible to the bare eye-and 1000-times more massive than the heaviest nano-mechanical oscillators used to date. Imperative to these advances are two key principles of cavity optomechanics [13]: Optical interferometric measurement of mechanical displacement at the attometer level [14,15], and the ability to use measurement induced dynamic back-action [16,17,18,19] to achieve resolved sideband laser cooling [9,20] of the mechanical degree of freedom. Using only modest cryogenic pre-cooling to 1.65 K, preparation of a mechanical oscillator close to its quantum ground state (63 ± 20 phonons) is demonstrated.…”

Cooling-by-measurement and mechanical state tomography via pulsed optomechanics

“…A versatile approach to manipulate mechanical states of motion is provided by the interaction with electromagnetic radiation, typically confined to microwave or optical cavities. Such cavity-optomechanics experiments [4][5][6][7][8] have thus far largely concentrated on high sensitivity continuous monitoring of the mechanical position [9][10][11][12][13][14]. Because of the back-action imparted by the probe onto the measured object, the precision of such a measurement is fundamentally constrained by the standard quantum limit (SQL) [15,16], and therefore only allows for classical phase-space reconstruction [9,17,18].…”

Ultrasensitive detection of force and displacement using trapped ions

“…Current force-detection sensitivity limits have surpassed 1 aN/ √ Hz [6,7] (atto = 10 −18 ) through coupling of nanomechanical resonators to a variety of physical readout systems [1,[7][8][9][10]]. Here we demonstrate that crystals of trapped atomic ions [11,12] behave as nanoscale mechanical oscillators and may form the core of exquisitely sensitive force and displacement detectors.…”