A phonon laser

Vahala, Kerry J.; Herrmann, M. G.; Knünz, Sebastian; Batteiger, Valentin; Saathoff, G.; Hänsch, Theodor W.; Udem, Thomas

doi:10.1038/nphys1367

Cited by 219 publications

(214 citation statements)

References 29 publications

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“…The presented concepts find general relevance to other nonlinear systems in both quantum and classical domains. Besides the fundamental advance reported here, phononic frequency combs also find applications to accurate MEMS/NEMS resonant sensors adapted for stable long duration measurements [19][20], engineering phase-coherent phonon lasers [21], phonon computing [22][23], pulse train mediated ultrasonic imaging and fundamental investigations of nonlinear phononics [24]. Further, the combination of both optical and phononic frequency combs can also enable the extension of metrology link between optical frequencies to sub-Hz frequencies.…”

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confidence: 72%

Phononic Frequency Comb via Intrinsic Three-Wave Mixing

2017

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A frequency comb consists of a series of equally spaced discrete frequencies. In recent years, optical frequency combs [1][2][3][4][5][6][7][8] have emerged as a potential toolset spanning diverse applications ranging from frequency metrology [1-4] to molecular fingerprinting [8]. Specifically the ability to precisely define the frequency spacing between frequency markers and align these measurements with microwave sources through the comb generation process has led to a number of physical measurements [4] requiring very high accuracy including the observation of gravitational waves [9].Optical frequency combs have been generated by using the comb-like mode structure of modelocked lasers and more recently through the interaction of continuous-waver lasers with high Q toroidal optical microresonators mediated via the Kerr non-linearity [10].Despite the analogies between phonons and photons, a direct analogue for an optical comb in the phononic domain has not been observed and comb generation process is thought to be largely limited by the nonlinear dispersion relations of phonons. However, theoretical work [11] has recently demonstrated the possibility for generation of frequency combs in a phononic system represented by Fermi-Pasta-Ulam α (FPU-α) chains [15] where the dispersion relationship does not play a role. In this letter, we report the first experimental confirmation of a phononic frequency comb in a microfabricated structure bearing similar traits predicted by numerical simulations performed on a FPU-α chain [11]. Additionally, our resonator also captures the onset of Duffing nonlinear mechanism [12][13][14] and its interference with the nominal phononic comb.The non-linear three wave mixing mechanism resulting in the generation of frequency combs is theoretically facilitated through the excitation of non-linear resonances of various orders.Specifically, in Direct Nonlinear Resonance (DNR) as termed in [11], the interaction between the eigenmode and driven phonon mode in a non-linear lattice results in the formation of equi-spaced spectral lines at a characteristic frequency ∆ set by the drive frequency and the intrinsic phonon mode frequencies. Mathematically, the DNR phenomenon can be modelled through the coupled dynamics. Figure 1A) upon the drive level crossing a specific threshold value. Here, the displacement profile corresponding to the sub-harmonic mode can be conceived as a pre-stressed framework for the level of coupling between drive frequency and intrinsic resonance mode ( Figure 1B). That being said, the propensity for comb generation is higher at the antinodes of sub-harmonic mode. Additionally, figure 1b1 provides an evidence for the phase coherency of equidistant comb lines. In this letter, we systematically report the experimental results carried out in the extensional resonator based test bed to understand the frequency comb generation and discuss the opportunities for active tuning of comb structure.The drive amplitude dependence on the phononic comb for an off-resonant drive frequenc...

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confidence: 72%

Phononic Frequency Comb via Intrinsic Three-Wave Mixing

2017

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“…The forces due to the laser beams saturate as periodic Doppler shifts are induced by the ion motion. Recently, we could show that the amplification is due to the stimulated generation of vibrational quanta (phonons) and that the system represents a mechanical analogue of an optical laser, a phonon laser [6].We study the action of a weak, harmonic rf signal tuned close to the motional resonance on the dynamics of this oscillator using two different techniques, which both rely on the good spatial and temporal resolution of our imaging system. With the first method, a spatially selective Fourier transform technique, we obtain the motional spectrum of the oscillator.…”

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Injection Locking of a Trapped-Ion Phonon Laser

et al. 2010

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We report on injection locking of optically excited mechanical oscillations of a single, trapped ion. The injection locking dynamics are studied by analyzing the oscillator spectrum with a spatially selective Fourier transform technique and the oscillator phase with stroboscopic imaging. In both cases we find excellent agreement with theory inside and outside the locking range. We attain injection locking with forces as low as 5ð1Þ Â 10 À24 N so this system appears promising for the detection of ultraweak oscillating forces. [5]. In this Letter we report injection locking of an almost ultimately simple and well-controlled system, the motion of a single, harmonically bound ion.A Mg þ ion, held in a linear rf trap, is addressed by two laser beams tuned below (red detuned) and above (blue detuned) an atomic resonance, respectively. While the reddetuned laser damps the motion of the ion, the bluedetuned laser provides gain by amplifying an existing motion. For appropriate settings of laser detunings and intensities, regenerative oscillations with a stable amplitude start from noise. The forces due to the laser beams saturate as periodic Doppler shifts are induced by the ion motion. Recently, we could show that the amplification is due to the stimulated generation of vibrational quanta (phonons) and that the system represents a mechanical analogue of an optical laser, a phonon laser [6].We study the action of a weak, harmonic rf signal tuned close to the motional resonance on the dynamics of this oscillator using two different techniques, which both rely on the good spatial and temporal resolution of our imaging system. With the first method, a spatially selective Fourier transform technique, we obtain the motional spectrum of the oscillator. The second method, stroboscopic imaging, allows us to retrieve the phase of the ion relative to the drive. All our observations agree very well with theory, further substantiate the analogy to an optical laser, and extend its applicability. Our analysis reveals that we attain injection locking with minute forces as small as 5(1) yN (yocto 10 À24 ). This great sensitivity might allow the detection of nuclear spin flips of single atomic or molecular ions.Injection locking is a well-understood phenomenon [7,8]. Let us review some basic features for later reference: consider an oscillator of free-running frequency ! 0 , mass m, and linewidth . A weak oscillation induced by an injected auxiliary rf signal of frequency ! i and voltage U i is amplified by the blue-detuned laser. The gain of this auxiliary frequency component is proportional to [7] jgð Þj 2 % 2 2( 1) for sufficiently large detunings ¼ ! i À ! 0 . As the detuning decreases, the injected signal takes up more of the limited gain available from the blue-detuned laser. The gain at the free oscillation reduces accordingly; once it drops below threshold only the oscillation at ! i prevailsthe oscillator is injection locked to the external source [7]. Assuming the injected signal is weak, the total oscillation amplitude of the...

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“…The various traces show the effect of the sideband resolution, 2Ω m κ , which dictates the efficiency of the autonomous feedback enforced by the cavity that leads to dynamic back-action. Such dynamic backaction on the mechanical oscillator leading to optical spring [198,199], linewidth narrowing (amplification) [200][201][202] or damping (cooling) [203][204][205][206][207] have been observed. In the resolvedsideband regime, characterised by κ Ω m , it becomes possible to cool the mechanical oscillator to a level where its energy is comparable to the energy in its ground state [208][209][210][211].…”

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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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A phonon laser

Cited by 219 publications

References 29 publications

Phononic Frequency Comb via Intrinsic Three-Wave Mixing

Phononic Frequency Comb via Intrinsic Three-Wave Mixing

Injection Locking of a Trapped-Ion Phonon Laser

Quantum Limits on Measurement and Control of a Mechanical Oscillator

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