• levitated optomechanics
• nanoparticles
• Paul trap

Light can transfer momentum to a mechanical oscillator via the radiation pressure force. Conversely, the mechanical oscillator can act back on the reflected light field, modifying its frequency and amplitude. This dynamical back-action can be enhanced by the use of an optical cavity, where the optical interaction is enhanced by every round-trip performed by the photons inside the cavity. This light-matter interaction is at the heart of the field of cavity optomechanics.
Cavity optomechanics has been implemented in a large variety of physical systems, including interferometer's suspended mirrors for gravitational wave detection, micromechanical membrane in a superconducting microwave circuit, photonic crystal nano beam and cold atoms coupled to an optical cavity.
From this plethora of systems, several interesting applications arise, among which quantum control of mesoscopic systems is of particular interest, as well as quantum control of optical fields via mechanics.
To achieve this quantum control, it is necessary to bring the mechanical oscillator to the quantum regime. Then, one must be able to engineer the required quantum interaction. Finally, one must ensure that the mechanical oscillator does not decohere too fast, such that the environment erases the quantum features of the system.
Among the various optomechanical systems that aim at maximizing the decoupling from the thermal environment (decoherence), levitated systems provide superior performance due to the complete suppression of clamping losses. They are therefore ideal candidates to engineer long-lived quantum states.

In this thesis research, I took part in setting up from scratch the first levitated optomechanics experiment at the University of Innsbruck, which has the ambitious long-term goal to prepare the center-of-mass position of a nanosphere in a non-classical state of motion.
The system will be formed by a high-finesse optical cavity dispersively coupled to a glass nanosphere trapped in an electrodynamic Paul trap. Moreover, the cavity light field will couple as well to a single calcium ion, whose role will be to engineer non-linear interactions with the motion of the nanosphere. This bold assumption, however, relies on the feasibility of confining both the nanoparticle and the ion within the same trap.
Paul traps are based on the ponderomotive mean force felt by a charged particle in a quadrupolar time-oscillating electric potential, whose strength is weighted by the charge-to-mass ratio of the trapped particle. As a result, a good trap for an ion will not provide good confinement for a nanosphere, which has a typical charge-to-mass ratio 10^7 times larger than that of an ion.

My work has consisted of investigating a novel proposal to use a Paul trap driven by two frequencies in order to confine two species with a very large charge-to-mass difference.
To assess the viability of this approach, we have re-scaled the system, as the relevant quantity is only on the charge-to-mass ratios. We thus used nanometer- and micrometer-size silica spheres instead of ions and nanospheres.
First, a test Paul trap for working in air was designed and built, together with an optical detection system based on interferometric detection of particle motion. Afterwards, the single-particle behavior of both a nano-and a microsphere has been individually characterized, in order to determine the best trap parameters for each particle. Finally, both micro- and nanospheres were successfully trapped with a two-frequencies field.
From a careful analysis of the trap parameters space, however, it resulted that air damping reduced the two frequencies trapping efficiency. In the next future, the same investigations have thus to be carried in a vacuum environment.