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Physical Review A

Measuring dispersion of biphotons

Assaf Barak, Mordechai Segev

Published Oct 26, 2012• 4 citations
Publisher

Abstract

We study the interference pattern of biphotons passing through a dispersive medium, and devise a method for measuring dispersion in coincidence counting of entangled photons. By measuring the Gouy phase shift accompanying dispersion, we show that it fundamentally differs from the Gouy phase expected from classical models. Finally, we show that the second-order correlation function of the dispersed biphoton can be much wider than the pattern predicted from classical analog.

DOI
10.1103/physreva.86.043838

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We study the interference pattern of biphotons passing through a dispersive medium, and devise a method for measuring dispersion in coincidence counting of entangled photons. By measuring the Gouy phase shift accompanying dispersion, we show that it fundamentally differs from the Gouy phase expected from classical models. Finally, we show that the second-order correlation function of the dispersed biphoton can be much wider than the pattern predicted from classical analog.
In classical optics, Young's double-slit experiment with colored coherent light gives rise to individual interference fringes for each light frequency, referring to single-photon interference. However, two-photon double-slit interference has been widely studied only for wavelength-degenerate biphoton, known as subwavelength quantum lithography. In this work, we report double-slit interference experiments with two-color biphoton. Different from the degenerate case, the experimental results depend on the measurement methods. From a two-axis coincidence measurement pattern we can extract complete interference information about two colors. The conceptual model provides an intuitional picture of the in-phase and out-of-phase photon correlations and a complete quantum understanding about the which-path information of two colored photons.
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.
We present the first observation of two-photon polarization interference structure in the second-order Glauber correlation function of two-photon light generated via type-II spontaneous parametric down-conversion. In order to obtain this result, two-photon light is transmitted through an optical fiber and the coincidence distribution is analyzed by means of the start-stop method. Beyond the experimental demonstration of an interesting effect in quantum optics, these results also have considerable relevance for quantum communications.
We discuss how to use coincidence detection to generate unusual, nonsinusoidal interference curves by using not a single detector, but several in coincidence. The method works for both strong (classical) and weak (on the few-photon level) light, although in the latter case the detection becomes probabilistic with low efficiency. Using the method, one can tailor the coincidence measurement setup to obtain essentially any interference pattern. We then use the method to experimentally demonstrate phase-difference state interference patterns in the few-photon regime that are highly nonsinusoidal. We also discuss optimal implementation of the method with regard to fluctuations and success probability, and we analyze the origin and magnitude of errors.
Two-photon interferometry started to play an important role in quantum optics since 1980’s. In that time, Dirac was criticized to be mistaken because he stated in his book, The Principles of Quantum Mechanics , that “photon only interferes with itself. Interference between two different photons never occurs”. Two-photon interference was considered as the interference between two photons. In fact, neither classical theory nor quantum theory suggested the interference between different photons. Classical theory views optical interference the result of coherent superposition between electromagnetic waves. The two-photon interference picture provided reasonable interpretation to that observation too: under the condition of complete overlapping, when the two biphoton amplitudes superpose in phase the joint-detection of the two distant photodetectors reaches its maximum counting rate as the sign of “correlation”. When the optical path difference is increased from zero to unbalanced values, a coincidence curve of “dip” is observed.
High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.