Measuring Quantum Correlations of Polarization, Spatial Mode, and Energy-Time Entangled Photon Pairs
Optical quantum technologies have found applications in all facets of quantum information. Single photons are actively being researched for quantum computation, communication, and sensing, due to their robustness against decoherence stemming from their minimal interaction with the environment. For communication and networking applications, specifically, photons are lauded for their speed and coherence over long distances. While clear benefits arise from the lack of photon-environment interaction, measurement and control of all photonic degrees of freedom is made challenging. Each degree of freedom, be it polarization, space, time, or frequency, comes with its own advantages and drawbacks. The potential that single photons bring to future quantum technologies may only be realized by full control over each of these properties of light.
The polarization degree of freedom can be used for high fidelity preparations and measurements and is experimentally controlled with high precision. The spatial degree of freedom, on the other hand, while comparatively trickier to work with, provides access to a large Hilbert space for encoding information that polarization falls short of. Together, these properties of light are combined in structured waves to use the advantages of both degrees of freedom simultaneously. One particularly popular spatial encoding, orbital angular momentum, has received a lot of attention for its high-dimensionality and experimental realizations. However, these states are not preserved by fiber and decohere in turbulence. Correlations between polarization and orbital angular momentum have shown robustness in scattering and turbulent media, demonstrating the advantage of their partnership.
The energy-time degree of freedom of light also provides a large Hilbert space for encoding, along with preservation of quantum information through fiber transmission. The accessible state space is determined by the resolution of controls and measurements in both frequency and time. Specifically, single photon manipulation on ultrafast timescales has become more practical in recent years, enabling measurement on timescales faster than state-of-the-art single photon detectors.
In the first experiments presented in this thesis, novel single-photon structured waves are experimentally demonstrated and imaged with a single photon emICCD camera. First, these states are propagated in free space and used to demonstrate a Talbot effect with single photons. Imaging at different fractional Talbot distances shows the near-field interference patterns of a two-dimensional Talbot carpet. Next, the correlations between the polarization of one photon and the spatial mode of its partner entangled photon are utilized to remotely prepare complex spatial arrays by means of heralded polarization measurements.
The final chapter of this thesis moves focus to the energy-time degree of freedom. The optical Kerr effect, a third order nonlinear optical effect, is used to gate energy-time entangled photons with sub-picosecond resolution, therefore surpassing the timing limitations of single photon detectors. With this fast optical gating technique, the temporal correlations of two energy-time entangled photons are measured. In addition to spectral correlation measurements, these are used to verify energy-time entanglement. This demonstration adds the optical Kerr effect to the short list of available methods in ultrafast quantum optics, further advancing experimental control of the energy-time degree of freedom of single photons.
Supervisor:
Kevin Resch