Quantum mechanics governs the motion of microscopic particles, such as electrons and photons, and potentially the behaviour of objects orders of magnitude bigger than the atomic scale. As technologies advance, it becomes realistic to fabricate and manipulate mechanical objects, which are large enough to contain a macroscopic number of atoms, and at the same time small enough for quantum mechanical effects to be observed. Observing such quantum mechanical effects is important for both fundamental research such as exploring the boundary between classical and quantum mechanics, and applications such as sensing beyond classical limits. In Chapter 1 of the thesis, we will briefly review two types of mechanical motion, harmonic oscillation and rigid body rotation. One widely used approach to detect the quantum nature of a mechanical object is to couple an optical field to the object, which is approximated as a harmonic oscillator. This forms the regime of optomechanics. By measuring properties of the optical field, which can be done with high precision, the quantum features of the mechanical oscillator may be deduced. In Chapter 2 of the thesis, we will show that, in a cavity optomechanical system, the measurement of the quadrature variance of the optical field is not viable to be used for deducing the quantum nature of the mechanical oscillator. We examine different models where the mechanical oscillator is dealt with as a classical degree of freedom, and find that squeezing in the optical field can be reproduced, thus ruling out optical squeezing as a witness of the quantum nature of the mechanical oscillator. Revival of optical squeezing, however, cannot be reproduced by models where the mechanical oscillator follows classical mechanics. But this is not a good witness of mechanical nonclassicality as the long interaction time required for the revival is not practical to be achieved experimentally.
The nonclassicality of mechanical oscillators have been reported in several experiments. However, for motion beyond harmonic oscillations such as rigid body rotation, demonstrating nonclassicality can take a different and novel path, due to the nonlinearity in the dynamical equations. In Chapter 3 of the thesis, we will show that, even without any coupling to a microscopic degree of freedom, a nanorotor can exhibit strong quantum mechanical effects. One important property of the mid-axis rotation of an asymmetric rotor is that, its mid-axis which is the main rotation axis, flips its orientation in space periodically. In a thermal ensemble where the initial rotations are slightly different, classical mechanics predicts that the flipping rapidly averages to zero, as each initial rotation corresponds to a vastly different flipping frequency. We will show that, according to quantum mechanics, the average flipping persists much longer. This is a result of the quantum tunnelling between pairwise equivalent trajectories. The tunneling effect modifies the flipping frequency of the mid-axis orientation, greatly reducing the frequency width corresponding to the thermal distribution of the initial rotation. The averaged mid-axis flipping thus persists for a long time. Coupling rigid body rotation to additional microscopic degrees of freedom can enrich the dynamics and provide extra handles for controlling the rotation. The coupling of rotation with a spin angular momentum is natural due to their common angular momentum origin. In Chapter 4 of the thesis, we will show that the spin-rotational coupling is especially strong for a near-symmetric rotor containing an embedded spin angular momentum along the mid-axis of the rotor. Although much smaller than the mechanical angular momentum, the spin angular momentum can strongly modify the rotation of the rotor, in the sense that the periodic flipping of the mid-axis of the rotor can be suppressed, resulting in the stabilisation of the rotation without the need for any external field. This effect should be observable in nanodiamond rotors containing nitrogen-vacancy centers. For this system, the quantum regime without classical correspondence can be straightforwardly reached by rotating the nanodiamond at a frequency on resonance with the NV zero-field-splitting. Stabilisation of a near-prolate rotor does not work in the on resonance regime, as the rotation induces state transitions of the NV centers. On the contrary, stabilisation of a near-oblate rotor still works in the on resonance regime, as the rotation suppresses the NV state transitions.
The richness of the dynamics of mechanical objects at the quantum level is far from being exhaustively explored. The interplay of the intrinsic nonlinearity in the mechanical motion and the coupling to microscopic degrees of freedom such as photons and spins, may lead to novel quantum mechanical phenomena in both the mechanical motion and the microscopic modes, improving our understanding of quantum mechanics. In Chapter 5 of the thesis, we will briefly discuss some possible directions to work on in the future.