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Journal of the Optical Society of America B

Experimental evaluation of a two-photon wave packet in type-II parametric downconversion

Alexander V. Sergienko, Yanhua H. Shih, Morton H. Rubin

Published May 1, 1995• 84 citations
Publisher

Abstract

A two-photon wave packet (a biphoton) produced by type-II parametric downconversion is studied in a simple beam-splitting experiment for its natural shape in space–time. The measured triangular shape of a two-photon correlation function is the signature of a rectangular-shaped biphoton. Inserting a birefringent sample into the beam causes a displacement of the vertex of the notch pattern, which can be used to measure the optical delay between the ordinary and the extraordinary rays in the sample with femtosecond resolution.

DOI
10.1364/josab.12.000859

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A two-photon wave packet (a biphoton) produced by type-II parametric downconversion is studied in a simple beam-splitting experiment for its natural shape in space–time. The measured triangular shape of a two-photon correlation function is the signature of a rectangular-shaped biphoton. Inserting a birefringent sample into the beam causes a displacement of the vertex of the notch pattern, which can be used to measure the optical delay between the ordinary and the extraordinary rays in the sample with femtosecond resolution.
One-photon and two-photon wave packets of entangled two-photon states in spontaneous parametric downconversion (SPDC) fields are calculated and measured experimentally. For type II SPDC, measured one-photon and two-photon wave packets agree well with theory. For type I SPDC, the measured one-photon wave packet agrees with the theory. However, the two-photon wave packet is much bigger than the expected value, and the visibility of interference is low. We identify the sources of this discrepancy as the spatial filtering of the two-photon bandwidth and nonpair detection events caused by the detector apertures and the tuning-curve characteristics of the type I SPDC.
In this work we present a simple method to reconstruct the complex spectral wave function of a biphoton, and hence gain complete information about the spectral and temporal properties of a photon pair. The technique, which relies on quantum interference, is applicable to biphoton states produced with a monochromatic pump when a shift of the pump frequency produces a shift in the relative frequencies contributing to the biphoton. We demonstrate an example of such a situation in type-II parametric down conversion allowing arbitrary paraxial spatial pump and detection modes. Moreover, our test cases demonstrate the possibility to shape the spectral wave function. This is achieved by choosing the spatial mode of the pump and of the detection modes, and takes advantage of spatiotemporal correlations.
Correlated pairs of photons generated in Type-II nonlinear spontaneous parametric down conversion (SPDC) were used to develop a new approach for the measurement of time delay between two orthogonally polarized waves (linear or circular) in optical materials with femtosecond time resolution. This technique can be used to improve the accuracy of measurement of polarization properties of optical fibers, birefringent materials including nonlinear crystals, waveguides, Pockel’s cells and Faraday rotators in the visible and IR spectrum.
Einstein–Podolsky–Rosen (EPR) correlations produced for two-photon entangled wave packets are analyzed by use of optical Wigner functions. In particular, type-II optical parametric downconversion systems are used, and the effects of the length of the crystal and the filter bandwidth on the Wigner functions are studied. The relation between the optical Wigner functions and the interference experiment with a beam splitter is studied. We find that, whereas in first-order correlation experiments (typified, for example, by Young’s interference experiment) the “photon interferes with itself” [ P. A. M. Dirac , The Principles of Quantum Mechanics (Clarendon, Oxford, UK, 1958), p. 9], in the EPR correlations the two-photon amplitude function interferes with itself. Such interference is analyzed by use of the optical Wigner functions.
The entangled photon pairs (biphotons) produced from parametric down-conversion (PDC) in a χ(2)crystal are the key element for several quantum information and communication schemes. Recent theoretical investigations [1–2] have revealed the peculiar structure of the biphotonic correlation characterizing the entanglement of twin beams in the space-time domain. The biphotonic correlation in type I PDC is characterized in the near field by a X-shaped geometry, which turns out to be non-factorable in space and time, offering thus the relevant possibility of manipulating the temporal bandwidth of biphoton entanglement by acting on their spatial degrees of freedom. The name “X-entanglement” was coined to describe this geometry [1]. An other key feature which emerged is the extreme spatial and temporal localization of the biphotonic correlation, on the micrometer and femtosecond range, respectively.