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Optical frequency combs [1,2,3] provide equidistant frequency markers in the infrared, visible and ultra-violet [4,5] and can link an unknown optical frequency to a radio or microwave frequency reference [6,7]. Since their inception frequency combs have triggered major advances in optical frequency metrology and precision measurements [6,7] and in applications such as broadband laser-based gas sensing [8] and molecular fingerprinting [9]. Early work generated frequency combs by intra-cavity phase modulation [10,11], while to date frequency combs are generated utilizing the comb-like mode structure of mode-locked lasers, whose repetition rate and carrier envelope phase can be stabilized [12]. Here, we report an entirely novel approach in which equally spaced frequency markers are generated from a continuous wave (CW) pump laser of a known frequency interacting with the modes of a monolithic high-Q microresonator [13] via the Kerr nonlinearity [14,15]. The intrinsically broadband nature of parametric gain enables the generation of discrete comb modes over a 500 nm wide span (≈ 70 THz) around 1550 nm without relying on any external spectral broadening. Optical-heterodyne-based measurements reveal that cascaded parametric interactions give rise to an optical frequency comb, overcoming passive cavity dispersion. The uniformity of the mode spacing has been verified to within a relative experimental precision of 7.3×10 −18 . In contrast to femtosecond mode-locked lasers[16] the present work represents an enabling step towards a monolithic optical frequency comb generator allowing significant reduction in size, cost and power consumption. Moreover, the present approach can operate at previously unattainable repetition rates [17] exceeding 100 GHz which are useful in applications where the access to individual comb modes is required, such as optical waveform synthesis [18], high capacity telecommunications or astrophysical spectrometer calibration [19].Optical microcavities [20] are owing to their long temporal and small spatial light confinement ideally suited for nonlinear frequency conversion, which has led to a dramatic improvement in the threshold of nonlinear optical light conversion [21]. In contrast to stimulated gain, parametric frequency conversion [22] does not involve coupling to a dissipative reservoir, is broadband as it does not rely on atomic or molecular resonances and constitutes a phase sensitive amplification process, making it uniquely suited for tunable frequency conversion. In the case of a material with inversion symmetry -such as silica -the non linear optical effects are dominated by the third order non linearity. The process is based on four-wave mixing among two pump photons (frequency ν P ) with a signal (ν S ) and idler photon (ν I ) and results in the emergence of (phase coherent) signal and idler sidebands from the vacuum fluctuations at the expense of the pump field (cf. Fig.1). The observation of parametric interactions requires two conditions to be satisfied. First momentum conservation...

PACS numbers:Recent experimental progress in table-top experiments [1,2] or gravitational-wave interferometers [3] has enlightened the unique displacement sensitivity offered by optical interferometry. As the mirrors move in response to radiation pressure, higher power operation, though crucial for further sensitivity enhancement, will however increase quantum effects of radiation pressure, or even jeopardize the stable operation of the detuned cavities proposed for next-generation interferometers [4,5,6]. The appearance of such optomechanical instabilities [7,8] is the result of the nonlinear interplay between the motion of the mirrors and the optical field dynamics. In a detuned cavity indeed, the displacements of the mirror are coupled to intensity fluctuations, which modifies the effective dynamics of the mirror. Such "optical spring" effects have already been demonstrated on the mechanical damping of an electromagnetic waveguide with a moving wall [9], on the resonance frequency of a specially designed flexure oscillator [10], and through the optomechanical instability of a silica micro-toroidal resonator [11]. We present here an experiment where a micro-mechanical resonator is used as a mirror in a very high-finesse optical cavity and its displacements monitored with an unprecedented sensitivity. By detuning the cavity, we have observed a drastic cooling of the microresonator by intracavity radiation pressure, down to an effective temperature of 10 K. We have also obtained an efficient heating for an opposite detuning, up to the observation of a radiation-pressure induced instability of the resonator. Further experimental progress and cryogenic operation may lead to the experimental observation of the quantum ground state of a mechanical resonator [12,13,14], either by passive [15] or active cooling techniques [16,17,18].The resonator is placed at the end of a linear cavity, along with a conventional coupling mirror (Fig. 1a). As we are only interested in the motion at frequencies Ω close to a resonance frequency Ω m of the resonator, the mirror dynamics can be approximated as the one of a single harmonic oscillator, with resonance frequency Ω m , mass M , damping Γ m and mechanical susceptibility:The resonator is submitted to a radiation pressure force F rad induced by the intracavity field. Depending on the detuning Ψ ≡ 4πL/λ [2π], where L is the cavity length and λ the laser wavelength, any small displacement x of the resonator induces a variation of the intracavity power P and of the radiation pressure (see Fig. 1b). As a consequence, the spring constant k = M Ω 2 m of the resonator is balanced by the radiation pressure force: for a positive detuning, the displacement creates a negative linear force and thereby an additional binding force, increasing the effective spring constant, whereas for a negative detuning, the force corresponds to a softening of the oscillator. Effects are null at resonance, maximum at half-width of the optical resonance, and proportional to the incident power. These effects hav...

Micro-and nanoscale opto-mechanical systems-based on cantilevers [1,2], micro-cavities [3,4] or macroscopic mirrors [5,6]-provide radiation pressure coupling [7] of optical and mechanical degree of freedom and are actively pursued for their ability to explore quantum mechanical phenomena of macroscopic objects [8,9]. Many of these investigations require preparation of the mechanical system in or close to its quantum ground state. In the past decades, remarkable progress in ground state cooling has been achieved for trapped ions [10,11] and atoms confined in optical lattices [12,13], enabling the preparation of non-classical states of motion [14] and Schrödinger cat states [15]. Imperative to this progress has been the technique of resolved sideband cooling [16,17,18], which allows overcoming the inherent temperature limit of Doppler cooling [19] and necessitates a harmonic trapping frequency which exceeds the atomic species' transition rate. The recent advent of cavity back-action cooling [20] of mechanical oscillators by radiation pressure has followed a similar path with Doppler-type cooling being demonstrated [1,2,4,5,21], but lacking inherently the ability to attain ground state cooling as recently predicted [22,23]. Here we demonstrate for the first time resolved sideband cooling of a mechanical oscillator. By pumping the first lower sideband of an optical microcavity [24], whose decay rate is more than twenty times smaller than the eigen-frequency of the associated mechanical oscillator, cooling rates above 1.5 MHz are attained, exceeding the achievable rates in atomic species [10]. Direct spectroscopy of the motional sidebands reveals 40-fold suppression of motional increasing processes, which could enable attaining final phonon occupancies well below unity (< 0.03). Elemental demonstration of resolved sideband cooling as reported here, should find widespread use in opto-mechanical cooling experiments and represents a key step to attain ground state cooling of macroscopic mechanical oscillators [8]. Equally important, this regime allows realization of motion measurement with an accuracy exceeding the standard quantum limit by two mode pumping [25] and could thereby allow preparation of non-classical states of motion.In atomic laser cooling, the lowest temperature which can be attained for a trapped ion (or atom) whose harmonic trapping frequency Ω m is smaller than its decay rate γ is given by T D ∼ = γ/4k B , the Doppler limit [19]. In this "weak binding" regime [19] (cf . Fig 1a), the minimum average occupation number in the harmonic trapping potential is n min ≈ γ/4Ω m ≫ 1, which implies that the atoms' harmonic motion cannot be cooled to the quantum ground state. On the other hand, much lower occupation can be attained in the resolved sideband limit. Resolved sideband cooling [16,17] is possible when a harmonically bound dipole such as an atom or ion exhibits a trapping frequency Ω m ≫ γ, thereby satisfying the so called "strong binding condition" [19]. The physics behind resolved sideband cooling can...