The effective quantum field theory description of gravity, despite its non-renormalizability, allows for predictions beyond classical general relativity. As we enter the age of gravitational wave astronomy, an important and timely question is whether measurable quantum predictions that depart from classical gravity, analogous to quantum optics effects which cannot be explained by classical electrodynamics, can be found. In this work, we investigate quantum signatures in gravitational waves using tools from quantum optics. Squeezed-coherent gravitational waves, which can exhibit sub-Poissonian graviton statistics, can enhance or suppress the signal measured by an interferometer, a characteristic effect of quantum squeezing. Moreover, we show that Gaussian gravitational wave quantum states can be reconstructed from measurements over an ensemble of optical fields interacting with a single copy of the gravitational wave, thus opening the possibility of detecting quantum features of gravity beyond classical general relativity.

The superposition of a Gaussian mode and a Laguerre-Gauss mode with $\ell =0,p\ne 0$ generates the so-called bottle beam: a dark focus surrounded by a bright region. In this paper, we theoretically explore the use of bottle beams as an optical trap for dielectric spheres with a refractive index smaller than that of their surrounding medium. The forces acting on a small particle are derived within the dipole approximation and used to simulate the Brownian motion of the particle in the trap. The intermediate regime of particle size is studied numerically and it is found that stable trapping of larger dielectric particles is also possible. Based on the results of the intermediate-regime analysis, an experiment aimed at trapping living organisms in the dark focus of a bottle beam is proposed.

We discuss the quantum mechanical description of a gravitational wave interacting with a cavity electromagnetic field. Quantum fluctuations of the gravitational vacuum induce squeezing in the optical field. Moreover, this squeezing experiences revivals, a purely quantum effect. Measuring these gravitationally induced revivals, although out of reach from experiments, would provide evidence on the quantum nature of gravity. We also discuss the quantum mechanical treatment of the interaction between coherent and squeezed gravitational wave states and a gravity wave detector. In the case of a coherent gravitational wave, we reproduce the result from the classical theory with a quantum mechanical calculation. The case of a squeezed gravity wave is not calculable within the classical theory, and could provide evidence on the quantum nature of gravity.

We explore entanglement generation between multiple optically levitated nanospheres interacting with a common optical cavity via the coherent scattering optomechanical interaction. We derive the many-particle Hamiltonian governing the unitary evolution of the system and show that it gives rise to quantum correlations among the various partitions of the setup, following a non-Markovian dynamics of entanglement birth, death and revivals. We also consider the effects of coupling the system to external environments and show that under reasonable experimental conditions entanglement between the mechanical modes can survive even at room temperature. Its dependence upon the number of nanoparticles, their initial temperature and coupling strength is studied. A numerical toolbox to simulate the closed and open dynamics of Gaussian optomechanical states and their informational measures is developed.

A theoretical framework for the quantization of gravity has been an elusive Holy Grail since the birth of quantum theory and general relativity. While generations of scientists have attempted to find solutions to this deep riddle, an alternative path built upon the idea that experimental evidence could determine whether gravity is quantized has been decades in the making. The possibility of an experimental answer to the question of the quantization of gravity is of renewed interest in the era of gravitational wave detectors. We review and investigate an important subset of phenomenological quantum gravity, detecting quantum signatures of weak gravitational fields in table-top experiments and interferometers.

We implement an all-electrical controller for 3D feedback cooling of an optically levitated nanoparticle capable of reaching subkelvin temperatures for the center-of-mass motion. The controller is based on an optimal policy in which state estimation is made by delayed position measurements. The method offers a simplified path for precooling and decoupling the transverse degrees of freedom of the nanoparticle. Numerical simulations show that in an improved setup with quantum limited detection, all three axes can be cooled down to a few-phonon regime.