Self-referenced hologram of a single photon beam

Wiktor Szadowiak, Sanjukta Kundu, Jerzy Szuniewicz, and Radek Lapkiewicz

Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5,02-093 Warszawa, Poland

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Quantitative characterization of the spatial structure of single photons is essential for free-space quantum communication and quantum imaging. We introduce an interferometric technique that enables the complete characterization of a two-dimensional probability amplitude of a single photon. Importantly, in contrast to methods that use a reference photon for the phase measurement, our technique relies on a single photon interfering with itself. Our setup comprises of a heralded single-photon source with an unknown spatial phase and a modified Mach-Zehnder interferometer with a spatial filter in one of its arms. The spatial filter removes the unknown spatial phase and the filtered beam interferes with the unaltered beam passing through the other arm of the interferometer. We experimentally confirm the feasibility of our technique by reconstructing the spatial phase of heralded single photons using the lowest order interference fringes. This technique can be applied to the characterization of arbitrary pure spatial states of single photons.

The measurements of the spatial wavefunction of photons are important for applications in quantum imaging, metrology, communication, and computation. However, the indeterminate global phase of single photons was believed to constitute an obstacle for characterizing their spatial phase profile using classical interferometric techniques. Weak measurements, tomography, and two-photon interferometry have been used instead, but they are not as straightforward, robust, and precise as the classical holographic techniques. We demonstrate a novel approach to determining the spatial phase profile of a single photon beam based on self-referenced interferometry which relies on a single photon interfering with itself. We experimentally confirm the feasibility of our technique by reconstructing the two-dimensional spatial phase profile of single photons using the lowest-order interference fringes. Our technique does not require the generation of reference photons and coincidence detection and it can tolerate more losses than methods using two-photon interference. Owing to its simplicity, our method can facilitate quantum technology applications that rely on the spatial degree of freedom of photons.

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