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Topologica

Observing Quantum Correlation of Photons in Laguerre-Gauss Modes Using the Gouy Phase

Daisuke Kawase, Y. Miyamoto, Mitsuo Wada Takeda, Koichi Sasaki, Shigeki Takeuchi

Published Jan 1, 2009• 1 citation
Publisher

Abstract

The effect of the Gouy phase, which is one of the geometrical phases of photons, is observed through quantum correlation in Laguerre-Gaussian (LG) modes. In an experiment, the relative phase of two different LG modes of measurement basis states is manipulated via the Gouy phase, and the observed coincidence count rates agree well with theoretical predictions. This result suggests that the Gouy phase can be used as a new tool to manipulate multidimensional photonic quantum states.

DOI
10.3731/topologica.2.017

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The effect of the Gouy phase, which is one of the geometrical phases of photons, is observed through quantum correlation in Laguerre-Gaussian (LG) modes. In an experiment, the relative phase of two different LG modes of measurement basis states is manipulated via the Gouy phase, and the observed coincidence count rates agree well with theoretical predictions. This result suggests that the Gouy phase can be used as a new tool to manipulate multidimensional photonic quantum states.
Quantum correlations encoded in photonic Laguerre-Gaussian modes were shown to be related to the Gouy-phase shifts [Kawase et al., Phys. Rev. Lett. 101, 050501 (2008)], allowing for a nondestructive manipulation of photonic quantum states. In this work, we exploit the relation between phase-space correlations of biphotons produced by spontaneously parametric down-conversion (SPDC) as encoded in the logarithmic negativity (LN) and the Gouy phase as they are diffracted through an asymmetrical double-slit setup. Using an analytical approach based on a double-Gaussian approximation for type-I SPDC biphotons, we show that measurements of Gouy-phase differences provide information on their phase-space entanglement variation, governed by the physical parameters of the experiment and expressed by the LN via covariance matrix elements.
Abstract We experimentally demonstrate the quantum entanglement in various spatial modes of the correlated photons generated via spontaneous parametric down-conversion in a type-II phase-matched periodically-poled KTP crystal. The two-fold coincidence measurement reveals the spatial entanglement between the photon pairs by projecting one of the correlated photons onto a Gaussian mode while scanning the spatial mode of its partner photon through selective projection (Gaussian, Laguerre–Gaussian (LG), Bessel-Gaussian (BG), and Airy–Gaussian (AG)) using a spatial light modulator (SLM). We also show the spatially resolved measurement of the non-conservation of orbital angular momentum via modal decomposition of the correlated photon in LG and BG bases.
Hong-Ou-Mandel (HOM) interference is demonstrated experimentally for entangled photon pairs in the Hermite-Gauss (HG) basis. We use two Dove prisms in one of the paths of the photons to manipulate the entangled quantum state that enters the HOM interferometer. It is demonstrated that, when entangled photon pairs are in a symmetric Bell state in the Laguerre-Gauss (LG) basis, they will remain symmetric after decomposing them into the HG basis, thereby resulting in no coincidence events after the HOM interference. On the other hand, if the photon pairs are in an antisymmetric Bell state in the LG basis, then they will also be antisymmetric in the HG basis, thereby producing only coincidence events as a result of the HOM interference.
In this work, we demonstrate the effect of self-splitting spatial quantum correlations induced by Gouy phase engineering. In the process of spontaneous parametric down conversion the pump beam is structured with a mode superposition that produces a dynamical splitting and recombination of the light beam. This structure is transferred to the quantum correlations between signal and idler photons. As a result the joint two-photon probability distribution propagates like a self-splitting and recombining light beam, implementing a Mach-Zehnder-like interferometer. We observe heralded single-photon interference and two-photon NOON state interference. These results open new avenues for applications in quantum metrology.
Abstract Controlling the evolution of photonic quantum states is crucial for most quantum information processing and metrology tasks. Due to its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood; however, the fundamental phase anomaly of evolving waves, called the Gouy phase, has had a limited number of studies in the context of elementary quantum states of light, especially in the case of photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception attributing the increased phase sensitivity of multi-photon quantum states solely to an effective de Broglie wavelength.