Hybrid cavity quantum optomechanics in an optical cavity

The central aim of this proposal is to introduce a quantum hybrid system which combines the advantages of physically different systems, each with a unique set of properties and capabilities, in a compatible experimental setup. With the combination of a strongly coupled paradigmical optomechanical system (cavity embedded massive mechanical resonator), on one hand, with cavity QED with many ions, on the other hand, a hybrid system emerges that can be a testbed for experiments on coherent dynamics between microscopic/mesoscopic (single ion or a few ions in the crystal or ensemble of atoms) and macroscopic (micromechanical oscillator) systems. Given the already well-developed toolbox for the manipulation of atomic states such an interface can be used for indirect preparation and manipulation of quantum states of macroscopic mechanical oscillators. On the path to achieving strong coupling between the two constituents (by strong coupling one means that the coherent interaction dominates the incoherent, environmental induced dynamics), the individual subsystems should naturally be strongly coupled to the mediating optical field. This is the case in the atom-optics system but not for typical optomechanical systems involving massive resonators inside cavities (such as vibrating end-mirrors or dielectric membranes, levitated plastic beads), where the momentum kick of a single photon is tiny on a scale defined by the largeness of the resonator`s mass. To address the smallness of the photon-phonon coupling, I propose an alternative route to the typical reflective optomechanics by describing a model of collective transmissive optomechanics, where an array of N scatterers each of polarizability is spaced such that light passes through unattenuated. Preliminary calculations suggest that a particular motional mode of this ensemble can couple to a cavity field with a strength that is, in principle, not bound by the same limitations as current models. Favourable scaling with the number of scatterers N 3/2, combined with a sort of photon-recycling cavity effect that leads to a 2 enhancement, can show a 3 orders of magnitude coupling increase, and thus render the system more compatible with hybrid atomsolid-state systems. Moreover, a natural long-ranged interaction develops between scatterers on opposite ends of the array, leading to possible investigation in many-body physics, where non-local interactions lead to exotic dynamics. On the atomic side, I propose to use an ion crystal system in a Paul trap that can be enclosed by a cm-sized optical cavity. The system is highly tunable in particle number that can range from 1 to thousands, well-controlled by lasers on the internal transitions and very stable with trapping times of hours or more. An immediate integration in the hybrid setup is based on its internal structure strong addressability by light that I have recently employed to show improved resolved-sideband cooling of a mirror. A more challenging and novel approach is to couple the motion of the crystal to light and indirectly to the mechanical oscillator. In order to achieve this, the complete feasibility of the crystal as a resonator in an optomechanics setup has to be elucidated. In other words, one has to identify and describe the vibrational modes that can couple strongly to a matched cavity field, the mechanical Q-factors of these modes and the influence of the environment as a decoherence factor. These are tasks that I plan to tackle following two hopefully converging theoretical approaches: i) a cold-fluid model (based on plasma physics) - successful in treating surface oscillation modes of the crystal, and ii) a discrete model that extends the single ionlight field interaction as for example used to treat sideband cooling of trapped ions.

The main concepts of Hybrid quantum optomechanics in an optical cavity are quantum optomechanics and collective dynamics of quantum emitters. At the macro-scale, relatively large objects (micro-and nano-mirrors, membranes etc) can be manipulated by light via the radiation pressure effect: a photon kick results in a momentum transfer and thus induces or modifies vibrations. The control over the quantum state of vibrating macroscopic objects via light quanta, i.e. photons, makes the object of investigations in the field of quantum optomechanics. At the micro-scale, tiny objects (atoms, molecules etc) modelled as two quantum level systems can be manipulated by photons tailored in energy to the match the resonance (energy difference between the two levels). These systems can absorb or emit light (and are therefore denoted as quantum emitters) in both a coherent (reversible) as well as an incoherent way (irreversible, lossy). While quantum optics has made great progress in controlling single quantum emitters with single photons, interesting physics occurs when ensemble of these emitters are collectively addressed. The interfacing of the macro- with the micro-scale objects via the radiation pressure effect of photons on matter results in the field of hybrid optomechanics.This project has shown progress in the engineering of multielement optomechanical platforms where stacks of vibrating membranes are inserted in optical cavities. In such cavities photons are recycled via continuous reflections off the two side mirrors: this enables a single photon to exert many more momentum kicks to an embedded vibrating membrane. For N -stacked membranes we have shown that the single photon-phonon coupling exceed an expected trivial N 1/2 scaling instead showing a superlinear N 3/2 scaling. This opens avenues towards cooling of the membranes vibrations to the quantum ground state or towards an efficient coupling of vibrations to internal states of quantum emitters. Moreover, the light induces non-trivial, long-range interactions between distant membranes which allows the study of exotic quantum walks and diffusion of phonons on reconfigurable platforms.On the quantum emitter side, we have investigated i) collective sub/superradiant states and their application in quantum metrology (accurate frequency measurements) or quantum memories and ii) transport of energy and charge in interacting quantum emitter systems. As each quantum emitter is unavoidably coupled to the quantum electromagnetic vacuum, loss of its excitation occurs spontaneously. For an ensembles of emitters, each emitter now has a modified vacuum (by the presence of its neighbors). A shared excitation among all emitters (for example produced by the absorption of an incoming photon with a large spatial extent that does not distinguish between different emitters) can then show either a strong coupling to the vacuum and a very quick loss (super- radiance) or an almost complete decoupling leading to a very long lifetime (subradiance). By proper geometrical design, selective energy driving etc, we have shown that one can exploit subradiance for more precise frequency measurements or towards the preparation of long-lived quantum memories.Neighboring quantum emitters can reversibly exchange photons (in cycles of emission-absorption) which leads to a so-called hopping model for exciton transport. Emitters embedded in cavities also show strong collective coupling to the highly-recycled cavity photons. We have shown that, by a combination of these two effects a different kind of transport, faster, can occur via delocalized light-matter hybrid states.