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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...

Laser frequency combs are coherent light sources that emit a broad spectrum consisting of discrete, evenly spaced narrow lines, each having an absolute frequency measurable within the accuracy of an atomic clock. Their development, a decade ago, in the near-infrared and visible domains has revolutionized frequency metrology with numerous windfalls into other fields such as astronomy or attosecond science. Extension of frequency comb techniques to the mid-infrared spectral region is now under exploration. Versatile mid-infrared frequency comb generators, based on novel laser gain media, nonlinear frequency conversion or microresonators, promise to significantly expand the tree of applications of frequency combs. In particular, novel approaches to molecular spectroscopy in the fingerprint region, with dramatically improved precision, sensitivity, recording time and/or spectral bandwidth may spark off new discoveries in the various fields relevant to molecular sciences

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...

Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.

Cooling of a 58 MHz micromechanical resonator from room temperature to 11 K is demonstrated using cavity enhanced radiation pressure. Detuned pumping of an optical resonance allows enhancement of the blueshifted motional sideband (caused by the oscillator's Brownian motion) with respect to the redshifted sideband leading to cooling of the mechanical oscillator mode. The reported cooling mechanism is a manifestation of the effect of radiation pressure induced dynamical backaction. These results constitute an important step towards achieving ground state cooling of a mechanical oscillator.

Low-loss transmission and sensitive recovery of weak radio-frequency and microwave signals is a ubiquitous challenge, crucial in radio astronomy, medical imaging, navigation, and classical and quantum communication. Efficient up-conversion of radio-frequency signals to an optical carrier would enable their transmission through optical fibres instead of through copper wires, drastically reducing losses, and would give access to the set of established quantum optical techniques that are routinely used in quantum-limited signal detection. Research in cavity optomechanics has shown that nanomechanical oscillators can couple strongly to either microwave or optical fields. Here we demonstrate a room-temperature optoelectromechanical transducer with both these functionalities, following a recent proposal using a high-quality nanomembrane. A voltage bias of less than 10 V is sufficient to induce strong coupling between the voltage fluctuations in a radio-frequency resonance circuit and the membrane's displacement, which is simultaneously coupled to light reflected off its surface. The radio-frequency signals are detected as an optical phase shift with quantum-limited sensitivity. The corresponding half-wave voltage is in the microvolt range, orders of magnitude less than that of standard optical modulators. The noise of the transducer--beyond the measured 800 pV Hz-1/2 Johnson noise of the resonant circuit--consists of the quantum noise of light and thermal fluctuations of the membrane, dominating the noise floor in potential applications in radio astronomy and nuclear magnetic imaging. Each of these contributions is inferred to be 60 pV Hz-1/2 when balanced by choosing an electromechanical cooperativity of ~150 with an optical power of 1 mW. The noise temperature of the membrane is divided by the cooperativity. For the highest observed cooperativity of 6,800, this leads to a projected noise temperature of 40 mK and a sensitivity limit of 5 pV Hz-1/2. Our approach to all-optical, ultralow-noise detection of classical electronic signals sets the stage for coherent up-conversion of low-frequency quantum signals to the optical domain.

The small mass and high coherence of nanomechanical resonators render them the ultimate force probe, with applications ranging from biosensing and magnetic resonance force microscopy, to quantum optomechanics. A notorious challenge in these experiments is thermomechanical noise related to dissipation through internal or external loss channels. Here, we introduce a novel approach to defining nanomechanical modes, which simultaneously provides strong spatial confinement, full isolation from the substrate, and dilution of the resonator material's intrinsic dissipation by five orders of magnitude. It is based on a phononic bandgap structure that localises the mode, without imposing the boundary conditions of a rigid clamp. The reduced curvature in the highly tensioned silicon nitride resonator enables mechanical Q > 10 8 at 1 MHz, yielding the highest mechanical Qf -products (> 10 14 Hz) yet reported at room temperature. The corresponding coherence times approach those of optically trapped dielectric particles. Extrapolation to 4.2 Kelvin predicts ∼quanta/ms heating rates, similar to trapped ions.