ABSTRACT
Wave-particle duality refers to the peculiar property in quantum mechanics where electrons and photons can exhibit both wave and particle nature. For example, in the classic double-slit experiment, electrons or photons can be captured on a screen in the far-field one by one as particles; at the same time, interference patterns also arise from the interference between the two paths taken to reach the screen, demonstrating their wave nature. Interference and wavefunction collapse are thus two important aspects in quantum mechanics and can be further exploited in quantum optical devices.
Instead of considering wave-function collapse during measurement as an instantaneous process, recent theoretical approaches have begun to explore the possibility of modelling it as a continuous process. One approach is to include the measurement device within the theory as environmental coupling, and another is to extend the Schrödinger equation to a stochastic differential equation phenomenologically to model the Born rule as a continuous process. Currently, wave-function collapse in a two-state system can be easily formulated in the latter approach by adding white noise in the evolution of the two-state density matrix.
Regarding interference effects, instead of interference between two spatially separate paths as in the double-slit experiment, interference can also take place between two different quantum processes. A prominent example is the Hong-Ou-Mandel (HOM) effect, in which two photons incident on a 50-50 beam splitter—a two-port device—can result in three different two-port outputs: ∣2,0⟩, ∣1,1⟩, and ∣0,2⟩, but the ∣1,1⟩ state output is suppressed due to destructive interference.
In this thesis, I will study the collapse process which leads to these three output (two-port) states in the Fock space. I will extend the stochastic differential equation approach from the preexisting two-state theory by incorporating more noise terms with restrictions added to conserve probability in any trajectory and to conserve the ensemble-averaged diagonal elements of the density matrix. This allows the Born rule to be valid over instantaneous periods, i.e. interpretable as a continuous collapse process. In order to further such an understanding, I will adopt the use of metasurfaces to control quantum interference between the three output states ∣2,0⟩, ∣1,1⟩, and ∣0,2⟩ to investigate the polarisation-HOM effect, exploring both constructive and destructive quantum interference with added reconfigurability through rotating optical elements in front of the metasurface.
As a metasurface consists of thousands of nanostructures on a single interface, it provides many degrees of freedom with which to control the three output states. I will demonstrate these capabilities through both numerical and experimental approaches using polarisation-entangled quantum sources, metasurface samples, and single-photon detectors. Through these investigations, I have demonstrated that metasurfaces can serve as a versatile platform to manipulate two-photon interference and is potentially useful to study more fundamental phenomena such as wave-particle duality.