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Reconstruction of single photon’s transverse spatial wave function

Piotr Leszek Kolenderski, Adam Czerwiński, Carmelo Scarcella, Simone Bellisai, Alberto Tosi, Thomas D. Jennewein

Published Jan 1, 2012• 0 citations
OpenAlex

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The quantum wave function of multiple particles provides additional information which is inaccessible to detectors working alone. Here, we introduce the coincidence wave-front sensing (CWS) method to reconstruct the phase of the multiphoton transverse spatial wave function. The spatially resolved coincidence photon counting is involved. Numerical simulations of two-photon cases using the weak measurement wave-front sensor are performed to test its correctness, and the phase information hidden in the correlation is revealed. Our work provides a direct spatial way to characterize multipartite quantum systems and leads to fundamental studies like experimental Bohmian mechanics and applications in quantum optical technologies.
We have demonstrated the loss of transverse spatial coherence of an atomic wave function after a single spontaneous emission. He∗{\mathrm{He}}^{*}He∗ atoms were both diffracted and excited by a standing light wave with a variable period. After the interaction, the excited atoms decay by a single spontaneously emitted photon. By changing the period of the standing light wave, we have mapped the loss of spatial coherence as a function of the transverse coordinate. By detecting the emitted photon one could "erase" the position information available and recover the transverse coherence in a correlation experiment, or realize a Heisenberg microscope.
Spatial qudit states can be realized by using multislits to discretize the transverse momentum of a photon. The merit of this kind of spatial qudit states is that the implementation of higher-dimensional qudits is relatively easy. As we have recently shown, the quantum states of these spatial qudits can be analyzed by scanning a single interference pattern. This method of single scan tomography can also be applied at higher dimensions, but the reconstruction becomes more sensitive to smaller details of the scanned patterns as the dimensions increase. In this paper, we investigate the effect of finite measurement resolution on the single scan tomography of spatial qutrits. Realistic measurement operators describing the spatial resolution of the measurement are introduced and the corresponding pattern functions for quantum state reconstruction are derived. We use the pattern functions to analyze experimental results for entangled pairs of spatial qutrits generated by spontaneous parametric downconversion. It is shown that a reliable reconstruction of the quantum state can be achieved with finite measurement resolution if this limitation of the measurement is included in the pattern functions of single scan tomography.