<i>Measurement of Weak Forces in Physics Experiments</i>

Braginsky, V. B.; Manukin, A. B.; Hamilton, W. O.

doi:10.1063/1.2994920

Cited by 200 publications

(295 citation statements)

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“…Furthermore, we have shown how the spectrum of the optical cavity output could be used to measure the final temperatures achieved. Our results could apply to other systems exhibiting dynamical back-action such as an LC circuit with its capacitance modulated by a mechanical oscillator [24].…”

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confidence: 87%

Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction

et al. 2007

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A quantum theory of cooling of a mechanical oscillator by radiation pressure-induced dynamical back-action is developed, which is analogous to sideband cooling of trapped ions. We find that final occupancies well below unity can be attained when the mechanical oscillation frequency is larger than the cavity linewidth. It is shown that the final average occupancy can be retrieved directly from the optical output spectrum.PACS numbers: 42.65. Sf ,42.65.Ky, 42.79.Gn Mesoscopic mechanical oscillators are currently attracting interest due to their potential to enhance the sensitivity of displacement measurements [1] and to probe the quantum to classical transition of a macroscopic degree of freedom [2,3]. A prerequisite for these applications is the capability of initializing an oscillator with a long phonon lifetime in its quantum ground state. So far this has not been demonstrated because the combination of sufficiently high mechanical frequencies (ω m /2π) and quality factors in the relevant regime ω m ≫ k B T has not been reached [3]. In contrast, in atomic physics laser cooling has enabled the preparation of motional ground states [4,5]. This has prompted researchers to study means of cooling a single mechanical resonator mode directly using laser radiation. Early work demonstrated cooling of a mechanical degree of freedom of a Fabry-Pérot mirror using a radiation pressure force controlled by an electronic feedback scheme [6,7], in analogy to stochastic cooling. In contrast, the radiation pressure induced coupling of an optical cavity mode to a mechanical oscillator [cf. Fig. 1(a)] can give rise to self-cooling via dynamical back-action [8]. In essence, the cavity delay induces correlations between the radiation pressure force and the thermal Brownian motion that lead to cooling or amplification, depending on the laser detuning. In a series of recent experiments, these effects have been used to cool a single mechanical mode [9,10,11]. While classical and semiclassical analysis of dynamical back-action have been developed [13,14], the question as to whether ground state cooling is possible has not been addressed.Here a quantum theory of cooling via dynamical backaction is presented. We find that final occupancies below unity can indeed be attained when the optical cavity's lifetime is comparable to or exceeds the mechanical oscillation period. Along these lines, an analogy between this mechanism and the sideband cooling of trapped ions in the Lamb-Dicke regime is elucidated [5]. In our setting the optical cavity mode plays the role of the ion's pseudospin mediating the frequency up-conversion underlying the cooling cycle. Finally, we discuss how the average phonon occupancy can be retrieved from the spectrum of the optical cavity output. We note that these results can be applied to a wide range of experimental realizations of cavity self-cooling [9,11,12].We treat the laser driven optical cavity mode coupled to the mechanical resonator mode as an open quantum system and adopt a rotating frame at the laser freq...

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confidence: 87%

Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction

et al. 2007

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“…In 2.40 Although widely credited to the investigations of Braginsky's group in Moscow in the 1970's [64,194], it appears that dynamical back-action was observed and described in the 1930's by a group led by Hartley at Bell Labs [197]. It is however unclear whether the effect was solely due to radiation pressure.…”

Section: Dynamical Back-actionmentioning

confidence: 99%

“…The former effectively leads to a renormalisation of the susceptibilities -an effect called dynamical back-action [51,194,195]; the latter leads to stochastic back-action [51,64,65,67,96,196] 2.40 . When the fluctuations due to the environment are limited to the level allowed by quantum mechanics -for the optical cavity, this means that δâ 0 , δâ in are in their vacuum state, and for the mechanical oscillator, δb in is in the vacuum state -quantum (stochastic) back-action exclusively drives the motion of the optical cavity and the mechanical oscillator.…”

Section: Dynamical Back-actionmentioning

confidence: 99%

Quantum Limits on Measurement and Control of a Mechanical Oscillator

Sudhir

2018

Springer Theses

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PAR Vivishek SUDHIR JOSEPH CONRAD, Heart of DarknessExperimental physics demands a certain degree of manual dexterity, the patience to tolerate the mundane, and an inexhaustible supply of optimism. Tobias hired me to work on an immensely sophisticated experiment despite any proof of my possessing these qualities; I am indebted to him for the belief he has placed in me. I would also like to acknowledge his dedication to fostering an environment where the pursuit of science is unencumbered by other worldly concerns. Stefan, Ewold and Samuel bore the brunt of a theorist trying to perform delicate experiments; the stern, yet encouraging, stewardship of this trio ensured that I enjoyed the culture shock. Dal Wilson was more than a colleague and a post-doc; his pragmatic approach to physics provided the ideal counter-point in our attempts to forge a deeper understanding of things ranging from vibration isolation to the subtleties of quantum mechanics. Without the patient efforts of Amir, Ryan and Hendrik in designing, fabricating, and testing of devices, none of the results reported here would have been possible. I hope I have been able to bequeath a better vision of the future of our experiment to Sergey. Conversations with Alexey, Daniel and Nathan have enabled me to vicariously learn how to measure microwave "photons". John Jost once taught me how to decorate a Christmas tree; since then he has imparted some wisdom on frequency metrology, and some on atomic physics. Together with Dal, Victor and Caroline have probably spent the most time with me outside the lab; it was fun to exercise an air of social normalcy with this bunch. Christophe has been an amazing sparring partner on every subject capable of being brought under scientific scrutiny.The personal space required for the pursuit of science comes through the sacrifice of many people. My family back home in India -parents, sister, grand-parents -have had to patiently wait for the brief interludes when I go home. No words can do justice to this and the very many other pleasures they have surrendered over the years for my sake. Before physics attracted me, I was charmed by someone else; I am lucky to have married her. Long time friends, mentorsAjith and Subeesh -have played pivotal roles in my being able to engage in physics; I hope to repay this enormous debt, some day.It was a privilege to have learnt from a few great teachers during my formative years. Their vision of an indelible unity in nature continues to motivate my study of physics. vii AbstractThe 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 ...

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“…At device level, fundamental approaches involve manipulating flexural vibrations of mechanical structures (for example, tuning forks) and acoustic waves in crystals (for example, quartz), harnessing the sharply frequency-selecting functions offered by the high-quality (Q) resonances in these vibrations and waves [1][2][3][4][5][6][7] . Advances in surface micro/nanomachining technologies 8,9 have spurred unceasing miniaturization of vibrating mechanical devices, with rapid developments in resonant micro/nanoelectromechanical systems (MEMS/NEMS) and with the promise of monolithic integration on chip [10][11][12] .…”

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confidence: 99%

“…T he concept of exploiting resonance modes in mechanical systems for generating and processing high-frequency (HF) signals has profoundly facilitated scientific studies [1][2][3][4] and accrued successful enterprises in radio engineering, communication and sensing technologies 3,[5][6][7] . At device level, fundamental approaches involve manipulating flexural vibrations of mechanical structures (for example, tuning forks) and acoustic waves in crystals (for example, quartz), harnessing the sharply frequency-selecting functions offered by the high-quality (Q) resonances in these vibrations and waves [1][2][3][4][5][6][7] .…”

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confidence: 99%

Spatial mapping of multimode Brownian motions in high-frequency silicon carbide microdisk resonators

2014

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High-order and multiple modes in high-frequency micro/nanomechanical resonators are attractive for empowering signal processing and sensing with multi-modalities, yet many challenges remain in identifying and manipulating these modes, and in developing constitutive materials and structures that efficiently support high-order modes. Here we demonstrate high-frequency multimode silicon carbide microdisk resonators and spatial mapping of the intrinsic Brownian thermomechanical vibrations, up to the ninth flexural mode, with displacement sensitivities of B7 À 14 fm Hz À 1/2 . The microdisks are made in a 500-nm-carbide on 500-nm-oxide thin-film technology that facilitates ultrasensitive motion detection via scanning laser interferometry with high spectral and spatial resolutions. Mapping of these thermomechanical vibrations vividly visualizes the shapes and textures of high-order Brownian motions in the microdisks. Measurements on devices with varying dimensions provide deterministic information for precisely identifying the mode sequence and characteristics, and for examining mode degeneracy, spatial asymmetry and other effects, which can be exploited for encoding information with increasing complexity.

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Measurement of Weak Forces in Physics Experiments

Cited by 200 publications

References 0 publications

Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction

Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction

Quantum Limits on Measurement and Control of a Mechanical Oscillator

Spatial mapping of multimode Brownian motions in high-frequency silicon carbide microdisk resonators

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