Dirk Puhlmann

Wave-particle dualism and complementarity unraveled by a different mode

The precise knowledge of one of two complementary experimental outcomes prevents us from obtaining complete information about the other one. This formulation of Niels Bohr’s principle of complementarity when applied to the paradigm of wave-particle dualism—that is, to Young’s double-slit experiment—implies that the information about the slit through which a quantum particle has passed erases interference. In the present paper we report a double-slit experiment using two photons created by spontaneous parametric down-conversion where we observe interference in the signal photon despite the fact that we have located it in one of the slits due to its entanglement with the idler photon. This surprising aspect of complementarity comes to light by our special choice of the TEM01 pump mode. According to quantum field theory the signal photon is then in a coherent superposition of two distinct wave vectors giving rise to interference fringes analogous to two mechanical slits.

A two-photon double-slit experiment

We employ a photon pair created by spontaneous parametric down conversion (SPDC) where the pump laser is in the TEM01 mode to perform a Youngs double-slit experiment. The signal photon illuminates the two slits and displays interference fringes in the far-field while the idler photon measured in the near-field in coincidence with the signal photon provides us with ‘which-slit’ information. We explain the results of these experiments with the help of an analytical expression for the second-order correlation function derived from an elementary model of SPDC. Our experiment emphasizes the crucial role of the mode function in the quantum theory of radiation.

Quantum diffraction of biphotons at a blazed grating

Correlations between photons are interesting for a number of applications and concepts in metrology, in particular for resolution improvements in different methods of quantum imaging. We demonstrate the application of a blazed grating for the characterization of the degree of spatial correlation of biphotons. The biphotons are generated by type II parametric downconversion. Compared to an ordinary transmission grating, a blazed grating shows a high diffraction efficiency only for a single order of diffraction. Thus, higher intensities in the Fraunhofer far field behind the grating, and easier photon counting, can be achieved. The distribution of the two-photon rate in the Fraunhofer far field of the blazed grating can show one additional order of diffraction with a visibility related to the degree of correlation of the biphotons. The number of spatial modes that are populated by the biphoton beam can be directly altered in our experiments. The relation of the spatial mode order of the photon propagation to the observable degree of spatial correlation of the biphotons is investigated and related to the Schmidt number of spatially entangled modes.

Spatial entanglement characterization in a biphoton beam

Spatial entanglement is investigated for applications in quantum imaging relying on multi-photon absorption. A product of variances in space and momentum shows strong violation of the classical correlation bound.

Tomography of spatially entangled biphotons

Correlations in light can be used for a variety of applications in metrology and imaging. Several schemes in quantum imaging rely on multi-photon absorption. Therefore a detailed knowledge of the temporal and spatial correlations of the photons used is desired.

Characterization of the spatial correlation of biphotons using a blazed grating

An exact knowledge and the possiblity of manipulating the spatial correlations of multi photon objects are of great interest for a number of applications in metrology and imaging. Since Fock-states of N-photons of wavelength λ propagate through phase shifts N-times faster as coherent states [1] they can appear as if they had a de Broglie wavelength of λ/N. This has been studied for diffraction at ordinary gratings in [2].