Spatial antibunching of photons with parametric down-conversion

Abstract

The theoretical framework behind a recent experiment by Nogueira et al. [Phys. Rev. Lett. 86, 4009 (2001)] of spatial antibunching in a two-photon state generated by collinear type II parametric down-conversion and a birefringent double-slit is presented. The fourth-order quantum correlation function is evaluated and shown to violate the classical Schwarz-type inequality, ensuring that the field does not have a classical analog. We expect these results to be useful in the rapidly growing fields of quantum imaging and quantum information.

Spatial correlations in parametric down-conversion

“…A more comprehensive study of these far field correlations were made by Grayson and Barbosa [10]. Experiments exploring interference at a double slit experiment using twin photons and coincidence counting came in 1994 [13] and 1995 [14] and was further investigated in later work [50,34,19,17,51,52,53,18,54,55]. In this section, we review some of the key experiments exploring aspects of interference of photon pairs using a double slit.…”

“…The π/2 phase factors are due to the delay introduced by the zero-order quarter-wave plates. The coincidence probability is [18,19] …”

“…Monken et al [16] demonstrated that the spatial correlations could be controlled through the shaping of the angular spectrum of the pump beam. This control allowed the use of the spatial correlations in a series of applications, ranging from fundamental aspects of Quantum Mechanics such as the measurement of the photonic de Broglie wavelength of a two-photon wave packet [17] and the observation of the spatial anti-bunching of photons [18,19], to applications to quantum information such as, for instance, the production of spatial qudits [20]. Howell et al [21] and D'Angelo et al [22] formally demonstrated entanglement between the spatial properties of the twin photons.…”

Multimode Hong–ou–mandel Interferometry

“…It has been shown that spatial antibunching is a purely quantum property with no classical analog. 30,31 Thus the singlet-beam is inherently nonclassical.…”

Generation of a Two-Photon Singlet Beam

“…However, because of the antisymmetry of the transverse spatial component, which is provided by the odd pump beam together with the reflection of one photon at the beam splitter, the photons are spatially separated in the y-direction and thus do not occupy the same plane wave mode. Interestingly enough, this characteristic guarantees that the singlet beam exhibits spatial antibunching, a quantum effect with no classical analog [13,14].…”