Final Report Summary - OMENT (Optomechanical entanglement and teleportation) The EU Marie-Curie Intra-European fellowship project OMENT has dealt with experimental work in a new and fast growing field in physics: cavity quantum optomechanics. In a cavity-optomechanical system, light inside an optical or microwave cavity is coupled to the motion of a mechanical oscillator. The resulting radiation pressure interaction provides a new way of controlling solid state mechanical devices using the toolbox of quantum optics. This opens up an hitherto unachieved parameter regime for quantum control of a physical system in terms of size and mass. Apart from fundamental tests involving macroscopic mechanical quantum systems cavity-optomechanical systems also enable new hybrid architectures for future quantum information processing (QIP) platforms.The challenging goal of OMENT has been to advance quantum optical control of a mechanical oscillator. To this end, the experimental demonstration of optomechanical entanglement, a major resource in QIP and a fundamentally interesting property of quantum states, and teleportation, a decisive protocol in QIP, were set as goals to manifest the ability to control a mechanical oscillator in the quantum regime. As a precursor for realizing non-classical optomechanical states, the initialization of the mechanical oscillator in a low-entropy state was set. Paramount for realizing these challenging goals is the design and fabrication of high quality mechanical oscillators and an optomechanical system, which operate in a cryogenic environment. Both requirements reduce the thermal decoherence of the mechanical oscillator, which is detrimental for any QIP protocol.Within the OMENT project different tasks were reached to implement the set goals. This included;(i) Proposals of theoretical protocols for demonstrating optomechanical entanglement, teleportation and ultrafast cooling.(ii) The design and fabrication of high-Q mechanical oscillators.(iii) The design and implementation of a low-noise, highly stable optical setup together with a rigid optomechanical low-temperature cavity design.All these results are described below. Novel optomechanical protocols include suggestions on how to implement optomechanical entanglement and teleportation as well as ultrafast optical cooling schemes in the pulsed optical regime. Both protocols have been published in peer-reviewed journals (PRA and PRL respectively). For the teleportation protocol, a blue-detuned optical pulse gets entangled with the mechanical oscillator and, after the optomechanical interaction, is interferometrically overlapped with another optical pulse, whose quantum mechanical state shall be teleported onto the mechanical oscillator. This can be achieved by a dual rail homodyne measurement and subsequent classical displacement of the oscillator. The success of this state teleportation can be verified by sending another optical pulse, which is red-detuned, to the optomechanical cavity system that essentially transfers the mechanical state back to the light field and can, therefore, be verified via homodyne detection. The entangling part of this protocol has only recently been successfully implemented by the Lehnert group at JILA using a microwave cavity optomechanical system (Palomaki et al., Science 342, 710 (2013)). In collaboration with Prof. K. Hammerer from Leibniz University Hannover, a continuous wave-protocol for reaching optomechanical entanglement has been obtained and is currently implemented. Another protocol allowing the reconstruction of the full optomechanical state from measurements of the light field alone and using Kalman filtering has been worked out with Prof. Hammerer. A publication is currently in preparation.A decisive step in OMENT has been the utilization of high-Q mechanical oscillators, composed of SiN membranes, which offer quality factors as high as 10^7 at low temperatures. More recently, a novel material system based on InGaP for membrane mechanical resonators, which can allow easy and monolithic integration of stacked membranes that promise a high single-photon coupling strength, has been investigated experimentally. The results have been published in a peer-reviewed journal (Applied Physics Letters).During the course of OMENT it was realized that stability of the cavity-optomechanical system at low temperatures is critical and a major effort was put into achieving this. An operating cavity-optomechanical system at temperatures below 1K with a cavity finesse of 20,000 was realized in a dilution refrigerator. Furthermore, a highly stable cavity-optomechanical system based on a monolithic cavity design was realized at 4K in a Helium flow cryostat. These developments have been paramount in realizing a set of experimental parameters that should allow to eventually observe optomechanical quantum entanglement between a laser field and a micromechanical oscillator. Although a result is expected in the near future, unfortunately for OMENT this will be some months after the completion of the project. In a bigger context, controlling the motion of massive mechanical devices in the quantum regime offers a wealth of opportunities for fundamental and applied research activities. These include hybrid systems for QIP mediating the coupling between disparate information carriers, quantum memories for storing quantum information or fundamental investigations of the interplay between gravity and quantum physics.