Optomechanically Induced TransparencyThis copy is for your personal, non-commercial use only.clicking here. colleagues, clients, or customers by , you can order high-quality copies for your If you wish to distribute this article to others here. following the guidelines can be obtained by Permission to republish or repurpose articles or portions of articles ): October 8, 2012 www.sciencemag.org (this information is current as ofThe following resources related to this article are available online at

Optical frequency combs allow for the precise measurement of optical frequencies and are used in a growing number of applications. The new class of Kerr-frequency comb sources, based on parametric frequency conversion in optical microresonators, can complement conventional systems in applications requiring high repetition rates such as direct comb spectroscopy, spectrometer calibration, arbitrary optical waveform generation and advanced telecommunications. However, a severe limitation in experiments working towards practical systems is phase noise, observed in the form of linewidth broadening, multiple repetition-rate beat notes and loss of temporal coherence. These phenomena are not explained by the current theory of Kerr comb formation, yet understanding this is crucial to the maturation of Kerr comb technology. Here, based on observations in crystalline MgF 2 and planar Si 3 N 4 microresonators, we reveal the universal, platformindependent dynamics of Kerr comb formation, allowing the explanation of a wide range of phenomena not previously understood, as well as identifying the condition for, and transition to, low-phase-noise performance.O ptical frequency combs [1][2][3][4] have revolutionized the field of frequency metrology and spectroscopy and are enabling components in a range of applications 5 . Recently, a novel class of frequency comb generators has been discovered 6 by coupling a continuous-wave (c.w.) laser to a high-finesse fused silica microcavity, where the Kerr nonlinearity enables (cascaded) fourwave-mixing (FWM), resulting in an optical frequency comb. These Kerr combs could complement conventional frequency combs in applications where high power per comb line (typically .100 mW) and high repetition rate (.10 GHz spacing between the comb lines) are desirable 7 , such as in astronomical spectrometer calibration [8][9][10] , direct comb spectroscopy 11 , arbitrary optical waveform generation 12,13 and advanced telecommunications. The creation of Kerr combs using microresonators has been demonstrated in crystalline CaF 2 (refs 14,15) and MgF 2 (refs 16-18) resonators, fused-silica microspheres 19 , planar high-index silica 20 and Si 3 N 4 ring resonators 21,22 , and compact fibre cavities 23 . Over recent years, a significant advance in Kerr comb technology has been achieved by demonstrating a single and well-defined radiofrequency (RF) beat note between adjacent comb lines (corresponding to the equidistant comb spacing and required for stabilizing the comb) 6,14,24 , a fully phase-stabilized Kerr comb 24 , the generation of octave-spanning spectra (required for self-referencing the comb using the f-2f scheme) 25,26 , the detection and shaping of pulses 13 , and extension of spectral coverage towards the visible 27 and midinfrared spectral regimes 18 . In addition to these experimental advances, theoretical work 28,29 has also enabled an explanation of the power distribution of Kerr combs, particularly the first comb modes appearing not necessarily adjacent to the pump. Despite these advances,...

Nanomechanical oscillators have been employed as transducers to measure force, mass and charge with high sensitivity. They are also used in opto-or electromechanical experiments with the goal of quantum control and phenomena of mechanical systems. Here, we report the realization and operation of a hybrid monolithically integrated transducer system consisting of a high-Q nanomechanical oscillator with modes in the MHz regime coupled to the near-field of a high-Q optical whispering-gallery-mode microresonator. The transducer system enables a sensitive resolution of the nanomechanical beam's thermal motion with a signal-to-noise of five orders of magnitude and has a force sensitivity of 74 aN Hz −1/2 at room temperature. We show, both theoretically and experimentally, that the sensitivity of continuous incoherent force detection improves only with the fourth root of the averaging time. Using dissipative feedback based on radiation pressure enabled control, we explicitly demonstrate by detecting a weak incoherent force that this constraint can be significantly relaxed. We achieve a more than 30-fold reduction in averaging time with our hybrid transducer and are able to detect an incoherent force having a force spectral density as small as 15 aN Hz −1/2 within 35 s of averaging. This corresponds to a signal which is 25 times smaller than the thermal noise and would otherwise remain out of reach. The reported monolithic platform is an enabling step towards hybrid nanomechanical transducers relying on the light-mechanics interface. Nanomechanical oscillators [1] serve as ultrasensitive detectors of force [2], mass [3] and charge [4]. Recently, increasing efforts have been devoted to sensitively detect the nanomechanical motion of these oscillators [5][6][7][8] with recent systems exhibiting a sensitivity below that at the standard quantum limit (SQL) [9,10]. For sensitive force detection the requirements on displacement sensitivity are less stringent, though, because of the thermal limit. Recent work has demonstrated that trapped ions have also the potential to be employed as sensitive transducers for ultrasmall forces [11,12], with the force sensitivity reaching levels of only 5 yN Hz −1/2 [12]. While being a promising approach to detect specific small forces, it presently suffers from challenging technology required for ion trap experiments, stable interaction times being only in the millisecond range [11] and a lack of field-deployable sensors. In contrast, cantilever-based sensing is a well-established technique that allowed remarkable achievements such as the detection of single spins [13] and the reconstruction of the structure of a virus [14], and it is increasingly used in the emerging field of biosensing [15]. A particularly promising approach is to parametrically couple a nanomechanical oscillator to a microwave [9,16] or optical [17] microcavity, thus enhancing the displacement sensitivity and allowing to efficiently resolve the motion of cantilevers with dimensions below the diffraction limit. Previous real...

Optical frequency combs [1,2,3] have revolutionized the field of frequency metrology within the last decade and have become enabling tools for atomic clocks [4], gas sensing [5,6] and astrophysical spectrometer calibration [7,8]. The rapidly increasing number of applications has heightened interest in more compact comb generators. Optical microresonator based comb generators bear promise in this regard. allow deriving an optical frequency comb directly from a continuous wave laser source and have been demonstrated in a number of optical microresonator geometries [9,10,11,12,13,14,15]. Critical to their future use as 'frequency markers', is however the absolute frequency stabilization of the optical comb spectrum [16]. A powerful technique for this stabilization is self-referencing [16,17], which requires a spectrum that spans a full octave, i.e. a factor of two in frequency. In the case of mode locked lasers, overcoming the limited bandwidth has become possible only with the advent of photonic crystal fibres for supercontinuum generation [18,19]. Here, we report for the first time the generation of an octave-spanning frequency comb directly from a toroidal microresonator on a silicon chip. The comb spectrum covers the wavelength range from 990 nm to 2170 nm and is retrieved from a continuous wave laser interacting with the modes of an ultra high Q microresonator, without relying on external broadening. Full tunability of the generated frequency comb over a bandwidth exceeding an entire free spectral range is demonstrated. This allows positioning of a frequency comb mode to any desired frequency within the comb bandwidth. The ability to derive octave spanning spectra from microresonator comb generators represents a key step towards achieving a radio-frequency to optical link on a chip, which could unify the fields of metrology with micro-and nano-photonics and enable entirely new devices that bring frequency metrology into a chip scale setting for compact applications such as space based optical clocks.In addition to the advantage of compact integration, microresonator based frequency combs have high power per comb line, which is a result of the smaller resonator size and the correspondingly higher repetition rate. This high power per comb line enables direct comb spectroscopy [20] and is advantageous for many applications, and critical for high capacity telecommunication. On the other hand, the high repetition rate of micro-combs results in a smaller peak power of the optical pulses that are underlying the generated frequency comb. This renders spectral broadening using nonlinear fibres [1,18] inefficient. Spectral broadening is a method which allowed for the first broadening of mode locked lasers to octave spanning combs ten years ago [19], leading to a breakthrough of the optical frequency comb technology.Here we show that the high power enhancement in a microresonator itself is sufficient for direct octave spanning frequency comb synthesis without the need for any additional spectral broadening. Optical freq...

We demonstrate a transducer of nanomechanical motion based on cavity enhanced optical nearfields capable of achieving a shot-noise limited imprecision more than 10 dB below the standard quantum limit (SQL). Residual background due to fundamental thermodynamical frequency fluctuations allows a total imprecision 3 dB below the SQL at room temperature (corresponding to (600 am/ √ Hz) 2 in absolute units) and is known to reduce to negligible values for moderate cryogenic temperatures. The transducer operates deeply in the quantum backaction dominated regime, prerequisite for exploring quantum backaction, measurement-induced squeezing and accessing sub-SQL sensitivity using backaction evading techniques.