Xiaohang Sun

Quality of spatial entanglement propagation

We explore, both experimentally and theoretically, the propagation dynamics of spatially entangled photon pairs (biphotons). Characterization of entanglement is done via the Schmidt number, which is a universal measurement of the degree of entanglement directly related to the nonseparability of the state into its subsystems. We develop expressions for the terms of the Schmidt number that depend on the amplitude and phase of the commonly used double-Gaussian approximation for the biphoton wave function, and demonstrate migration of entanglement between amplitude and phase upon propagation. We then extend this analysis to incorporate both phase curvature in the pump beam and higher spatial frequency content of more realistic non-Gaussian wave functions. Specifically, we generalize the classical beam quality parameter

Biphoton transmission through non-unitary objects

{M}^{2}

Measurement of Biphoton Wigner Function Using a Lenslet Array

to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics.

Quantum Imaging and Spatial Entanglement Characterization with an EMCCD Camera

Losses should be accounted for in a complete description of quantum imaging systems, and yet they are often treated as undesirable and largely neglected. In conventional quantum imaging, images are built up by coincidence detection of spatially entangled photon pairs (biphotons) transmitted through an object. However, as real objects are non-unitary (absorptive), part of the transmitted state contains only a single photon, which is overlooked in traditional coincidence measurements. The single photon part has a drastically different spatial distribution than the two-photon part. It contains information both about the object, and, remarkably, the spatial entanglement properties of the incident biphotons. We image the one- and two-photon parts of the transmitted state using an electron multiplying CCD array both as a traditional camera and as a massively parallel coincidence counting apparatus, and demonstrate agreement with theoretical predictions. This work may prove useful for photon number imaging and lead to techniques for entanglement characterization that do not require coincidence measurements.

Propagation of Spatial Entanglement in Quantum Beams

We measure the Wigner distribution function of an entangled photon pair using a lenslet array. We experimentally characterize its second-order coherence properties and discuss issues of entanglement and commutation of variables in phase space.

Imaging High-dimensional Spaces with Spatially Entangled Photon Pairs

We utilize a single-photon sensitive electron multiplying CCD camera as a massively parallel coincidence counting apparatus to study spatial entanglement of photon pairs. This allows rapid measurement of transverse spatial entanglement in a fraction of the time required with traditional point-scanning techniques. We apply this technique to quantum experiments on entangled photon pairs: characterization of the evolution of entanglement upon propagation, and measurement of one- and two-photon portions of the state transmitted through non-unitary (lossy) objects, and quantum phase imaging.

METHOD AND SYSTEM FOR QUANTUM INFORMATION PROCESSING AND COMPUTATION

We quantify separately the degree of entanglement in the amplitude and phase parts of the biphoton wave function, and observe its evolution from amplitude to phase, and back, upon propagation.

Evolution of Spatial Entanglement of Realistic Biphotons

We directly measure the biphoton probability distribution within a 373 million dimensional Hilbert space using an electron multiplying CCD camera. These data allow for simultaneous characterization of correlations and their application for sub-diffraction-limited imaging.