Hybrid optomechanical states in the quantum motion of a levitated nanosphere

Trapping and levitation of micrometric objects in strongly focused light beams (optical tweezers) was introduced in the pioneering works by Arthur Ashkin in the early 1970s, and the major impact of such techniques in a multidisciplinary environment earned him the Nobel Prize in Physics 2018. In most applications, optical trapping occurs in a strongly damping background. The idea of operating in a high vacuum, thus reducing the interaction with the environment, and bringing levitating and oscillating nano-particles into the quantum regime was boosted about 10 years ago and has since developed into a fruitful research topic. Optically levitating nanoparticles in high vacuum offer a quite natural platform for the study of quantum mechanical features in all three spatial dimensions and the achievement of quantum coherent control of their motion, with applications ranging from quantum foundations and information processing to directional quantum sensing. In this thesis we have demonstrated the experimental realization of a quantum platform based on a levitating silica nanoparticle coupled to a mode of a high finesse optical cavity in a room temperature environment. The optical potential experienced by the nano-particle is proportional to the light intensity. As a consequence, its oscillatory motion is characterized by a lower frequency along the tweezer propagation axis, where the characteristic length is the Rayleigh range, with respect to the transverse plane, where the characteristic length is the beam waist. The two-dimensional motion on the plane orthogonal to the tweezer axis and the optical cavity mode define an optomechanical system with three degrees of freedom. With the protocol developed at the early stage of the doctoral work, based on the transfer of a levitated particle between two optical tweezers, we have been able to systematically levitate the particle in high vacuum on the axis of a high Finesse optical cavity and observe strong non classical signatures in the motional spectrum. Thanks to the coherent scattering setup, the oscillatory motion was strongly coupled to the cavity field thus leading to the observation of the hybrid optomechanical states, whose signature is a double avoided crossing between the eigenfrequencies of the three-body system. In high vacuum, where the mechanical oscillator is weakly coupled to the environment, the energy flows coherently between the optomechanical components and the collective excitations are described in terms of polaritonic modes. Here we have explored the two dimensional motion of the nanoparticle close to its minimum uncertainty state, characterised by peculiar non classical features. We have reached the mean phononic occupation number along the coldest motional direction below unity, thus achieving the 1D ground state cooling. Rotating the polarization of the trapping beam with respect to the cavity optical axis, we have strongly cooled the 2D motion achieving an effective occupancy below 1.5 along any motional direc tion. Moreover, the strongly broadened mechanical transfer function has allowed the observation of the quantum asymmetry on a bandwidth larger than the cavity linewidth, thus resolving the cavity mediated quantum back action noise, showing a distinctive modification due to the cavity mediated interference between the two mechanical oscillators.