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 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.

† These authors contributed equally to this work.Quantum control of engineered mechanical oscillators can be achieved by coupling the oscillator to an auxiliary degree of freedom, provided that the coherent rate of energy exchange exceeds the decoherence rate of each of the two sub-systems. We achieve such quantumcoherent coupling between the mechanical and optical modes of a micro-optomechanical system. Simultaneously, the mechanical oscillator is cooled to an average occupancy of n=1.7±0.1 motional quanta. Pulsed optical excitation 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. These results provide a route towards the realization of efficient quantum interfaces between mechanical oscillators and optical fields.Mechanical oscillators are at the heart of many precision experiments, such as single spin detection [1] or atomic force microscopy and can exhibit exceptionally low dissipation. The possibility to control the quantum states of such engineered micro-or nanomechanical oscillators, similar to the control achieved over the motion of trapped ions [2], has been a subject of longstanding interest [3, 4], with prospects of quantum state transfer [5][6][7][8], entanglement of mechanical oscillators [9] and testing of quantum theory in macroscopic systems [10, 11]. However, such experiments require coupling the mechanical oscillator to an auxiliary system-whose quantum state can be controlled and measured-with a coherent coupling rate that exceeds the decoherence rate of each of the subsystems. Equivalent control of atoms has been achieved in the context of cavity Quantum Electrodynamics (cQED [12]) and has over the past decades been extended to various other systems such as superconducting circuits [13], solid state emitters [14] or the light field itself [15].Recently, elementary quantum control at the single-phonon level has been demonstrated for the first time, by coupling a piezo-electrical dilatation oscillator to a superconducting qubit [16]. An alternative and highly versatile route is to use the radiation-pressure-induced coupling of optical and mechanical degrees of freedom, inherent to opti- * Electronic address: tobias.kippenberg@epfl.ch cal microresonators [17], which can be engineered in numerous forms at the micro-or nanoscale [18][19][20]. This coupling can be described by the interaction Hamiltonian H = g 0â †â (b † +b), whereâ (b) is the photon (phonon) annihilation operator, is the reduced Planck constant and g 0 is the vacuum optomechanical coupling rate. In the resolved sideband regime (where the mechanical resonance frequency Ω m exceeds the cavity energy decay rate κ), with an intense laser tuned close to the lower optomechanical sideband, one obtains in the rotating wave approximation the effective Hamiltonianfor the operatorsâ andb now displaced by their steady state values. We have introduced here the field-enhanced coupling rate [21, 22] g = √n c g 0 , wheren c de...