Cavity Quantum Optomechanics: Coupling Light And Micromechanical Oscillators

Cavity optomechanics(1) is a new research field that has seen spectacular advances in recent years. Optomechanics combines advances in nano-and electromechanical systems with radiation pressure enabled control. The radiation pressure backaction enables to readout mechanical motion of micro-and nanoscale mechanical oscillators with an imprecision at the standard quantum limit, enables to amplify(2) mechanical motion - enabling coherent mechanical oscillators. Likewise the cooling(3,4) of mechanical oscillators has enabled to access the quantum regime of optomechanical systems. Likewise mechanical degrees of freedom provide new ways to control the propagation of light via the phenomenon of optomechanically induced transparency(5), which can e. g. enable switching, slowing or advancing of electromagnetic pulses(6). Cavity optomechanical systems also have reached the quantum regime of mechanical oscillators, which has been long anticipated. As one example of the possible range of optomechanical phenomena, we review an optomechanical microresonator in which optical and mechanical degrees of freedom exchange energy at a rate exceeding the relevant decoherence rates in the system, enabling quantum control of a mechanical oscillator with light. Such quantum coherent coupling provided a quantum coherent link(7) between engineered microscale oscillators and the light field.

Quantum limits on measurement and control of a mechanical oscillator

Vivishek Sudhir

The precision measurement of position has a long-standing tradition in physics. Cavendish's verification of the universal law of gravitation using a torsion pendulum, Perrin's confirmation of the atomic hypothesis via the precise measurement of the Brownian motion, and, the verification of the mechanical effect of electromagnetic radiation, all belong to this classical heritage. Quantum mechanics posits that the measurement of position results in an uncertain momentum; an idea developed to full maturity within the context of interferometric searches for gravity waves. Over the past decade, standing at the confluence of quantum optics and nanomechanics, cavity optomechanics has emerged as a powerful platform to study the quantum limits of position measurements. The subject of this thesis is the precision measurement of the position of a nano-mechanical oscillator, the fundamental limits of such measurements, and its relevance to measurement-based feedback control. The nano-mechanical oscillator is coupled to light confined in an optical micro-cavity via radiation pressure. The fluctuations in the position of the oscillator are transduced onto the phase of the light, while quantum fluctuations in the amplitude of the light leads to a disturbance in the momentum of the oscillator. We perform an interferometric position measurement with a sensitivity that is 10^5 times below what is required to resolve the zero-point motion of the oscillator, constituting the most precise measurement of thermal motion yet. The resulting disturbance -- measurement back-action -- is observed to be commensurate with the uncertainty principle, leading to a 10% contribution to the total motion of the oscillator. The continuous record of the measurement (performed in a 4 K cryogenic environment) furnishes the ability to resolve the zero-point motion of the oscillator within its decoherence rate - the necessary condition for measurement-based feedback control of the state of the oscillator. Using the measurement record as error signal, the oscillator is cooled towards its ground state, resulting in a factor 10^4 suppression of its total (thermal and back-action) motion, to a final occupation of 5 phonons on average. Measurements generally proceed by establishing correlations between the system being measured and the measuring device. For the class of quantum measurements employed here - continuous linear measurements - these correlations arise due to measurement back-action. These back-action-induced correlations appear as correlations between the degrees of freedom of the measuring device. For interferometric position measurements, quantum correlations are established between the phase and amplitude of the light. In a homodyne measurement, they lead to optical squeezing, while in a heterodyne measurement, they appear as an asymmetry in the sidebands carrying information about the oscillator position. Feedback is used to enhance sideband asymmetry, a first proof-of-principle demonstration of the ability to control quantum correlations using feedback. In the regime where amplified vacuum noise dominates the feedback signal, the disappearance of sideband asymmetry visualises a fundamental limit of linear feedback control. Using a homodyne detector, we also characterise these quantum correlations manifested as optical squeezing at the 1% level.

EPFL2016

Near-field cavity optomechanics with nanomechanical oscillators

Tobias Kippenberg, Albert Schliesser

Cavity-enhanced radiation-pressure coupling between optical and mechanical degrees of freedom allows quantum-limited position measurements and gives rise to dynamical backaction, enabling amplification and cooling of mechanical motion. Here, we demonstrate purely dispersive coupling of high-Q nanomechanical oscillators to an ultrahigh-finesse optical microresonator via its evanescent field, extending cavity optomechanics to nanomechanical oscillators. Dynamical backaction mediated by the optical dipole force is observed, leading to laser-like coherent nanomechanical oscillations solely due to radiation pressure. Moreover, sub-fm Hz(-1/2) displacement sensitivity is achieved, with a measurement imprecision equal to the standard quantum limit (SQL), which coincides with the nanomechanical oscillator's zero-point fluctuations. The achievement of an imprecision at the SQL and radiation-pressure dynamical backaction for nanomechanical oscillators may have implications not only for detecting quantum phenomena in mechanical systems, but also for a variety of other precision experiments. Owing to the flexibility of the near-field coupling platform, it can be readily extended to a diverse set of nanomechanical oscillators. In addition, the approach provides a route to experiments where radiation-pressure quantum backaction dominates at room temperature, enabling ponderomotive squeezing or quantum non-demolition measurements.

2009

Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators

Tobias Kippenberg, Albert Schliesser

Parametric coupling of optical and mechanical degrees of freedom forms the basis of many ultra-sensitive measurements of both force and mechanical displacement. An optical cavity with a mechanically compliant boundary enhances the optomechanical interaction, which gives rise to qualitatively new behavior which can modify the dynamics of the mechanical motion. As early as 1967, in a pioneering work, V. Braginsky analyzed theoretically the role of radiation pressure in the interferometric measurement process, but it has remained experimentally unexplored for many decades. Here, we use whispering-gallery mode optical microresonators to study these radiation pressure phenomena. Optical microresonators simultaneously host optical and mechanical modes, which are systematically analyzed and optimized to feature ultra-low mechanical dissipation, photon storage times exceeding the mechanical oscillation period (i.e. the "resolved-sideband regime") and large optomechanical coupling. In this manner, it is demonstrated for the first time that dynamical backaction can be employed to cool mechanical modes, i.e., to reduce their thermally excited random motion. Utilizing this novel technique together with cryogenic pre-cooling of the mechanical oscillator, the phonon occupation of mechanical radial-breathing modes could be reduced to (n) = 63 +/- 20 excitation quanta. The corresponding displacement fluctuations are monitored interferometrically with a sensitivity at the level of 1.10(-18) m/root Hz, which is below the standard quantum limit (SQL). This implies that the readout is already in principle sufficient to measure the quantum mechanical zero-point position fluctuations of the mechanical mode. Moreover, it is shown that optical measurement techniques employed here are operating in a near-ideal manner according to the principles of quantum measurement, displaying a backaction-imprecision product close to the quantum limit.

2010

Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators

Tobias Kippenberg, Albert Schliesser

2010

Quantum limits on measurement and control of a mechanical oscillator

Vivishek Sudhir

EPFL2016