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arXiv:quant-ph/0111024 · Physical Review A

Multiparameter entanglement in quantum interferometry

Mete Atatüre, Giovanni Di Giuseppe, Matthew D. Shaw, Alexander V. Sergienko, Bahaa E. A. Saleh, Malvin Carl Teich

Published Aug 30, 2002• 43 citations
arXivHTMLPDF

Abstract

The role of multiparameter entanglement in quantum interference from collinear Type-II spontaneous parametric down-conversion is explored using a variety of aperture shapes and sizes, in regimes of both ultrafast and continuous-wave pumping. We have developed and experimentally verified a theory of down-conversion which considers a quantum state that can be concurrently entangled in frequency, wavevector, and polarization. In particular, we demonstrate deviations from the familiar triangular interference dip, such as asymmetry and peaking. These findings improve our capacity to control the quantum state produced by spontaneous parametric down-conversion, and should prove useful to those pursuing the many proposed applications of down-converted light.

DOI
10.1103/physreva.66.023822

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The role of multiparameter entanglement in quantum interference from collinear Type-II spontaneous parametric down-conversion is explored using a variety of aperture shapes and sizes, in regimes of both ultrafast and continuous-wave pumping. We have developed and experimentally verified a theory of down-conversion which considers a quantum state that can be concurrently entangled in frequency, wavevector, and polarization. In particular, we demonstrate deviations from the familiar triangular interference dip, such as asymmetry and peaking. These findings improve our capacity to control the quantum state produced by spontaneous parametric down-conversion, and should prove useful to those pursuing the many proposed applications of down-converted light.
A theory of spontaneous parametric down-conversion, which gives rise to a quantum state that is entangled in multiple parameters, such as three-dimensional wave vector and polarization, allows us to understand the unusual characteristics of fourth-order quantum interference in many experiments, including ultrafast type-II parametric down-conversion, the specific example illustrated in this paper. The comprehensive approach provided here permits the engineering of quantum states suitable for quantum-information schemes and quantum technologies.
Summary form only given. Pairs of entangled photons display a complex quantum state that cannot be represented through a product of single-particle states. The spontaneous parametric down-conversion (SPDC) process, that takes place when a laser pulse pumps a second-order nonlinear crystal has become recently a convenient source of such nonclassical states of light in quantum optics experiments. Nonstationary effects are mainly observed when the pump pulse temporal duration is significantly shorter than the characteristic interaction time in the nonlinear crystal. We introduce a nonstationary theory of SPDC to describe the results of fourth-order quantum-interference experiments when no spectral filtering is applied to the down-converted fields. Experiments involving nonlinear SPDC crystals with three different lengths were performed. The ultraviolet laser pulses were obtained from a Ti:sapphire femtosecond laser with a second-harmonic generator. These pulses were used to pump nonlinear crystals to initiate the process of nonstationary spdc and generate orthogonally-polarized photon pairs. These pairs then went into a polarization interferometer, and the coincidence counts of the detectors at the two output ports of the interferometer were recorded.
Spectral properties of entangled photons generated via type-I frequency-nondegenerate spontaneous parametric down-conversion are studied theoretically and experimentally. For monochromatic pumping, the joint spectral intensity function for the photon pair is found to be symmetric even though each photon has a different central wavelength. The single-photon (first-order) interference shows the familiar triangular interferogram, usually associated with the cw-pumped frequency-degenerate type-II spontaneous parametric down-conversion. For broadband (ultrafast) pumping, on the other hand, the joint spectral intensity function is shown to be asymmetric, similar to the case of ultrafast-pumped frequency-degenerate type-II spontaneous parametric down-conversion. The spectral studies reported here are expected to play an important role in developing ultrabright two-color entangled photon sources.
Theory and experiment of two-photon lquotlquotlquotdirectrquotrquotrquot interference for type-II spontaneous parametric down-conversion with an ultrafast pulse laser pump
Fourth-order spatial interference of entangled photon pairs generated in the process of spontaneous parametric down-conversion pumped by a femtosecond pulse laser has been performed for the first time. In theory, it takes into account the transverse correlation between the two photons and is used to calculate the dependence of the visibility of the interference pattern obtained in Young’s double-slit experiment. In this experiment, a short focal length lens and two narrow band interference filters were adopted to eliminate the effects of the broadband pump laser and improve the visibility of the interference pattern under the condition of nearly collinear light and degenerate phase matching.
Quantum entanglement has been a topic of much research in modern physics, and an application in quantum computing is envisioned. This thesis address the use of polarization entangled photon pairs produced by spontaneous parametric down-conversion (SPDC) in entanglement transfer process and quantum computing. The simplicity of SPDC entanglement relative to other quantum phenomena is first emphasized by developing a complete classical theory of the photon-crystal interactions characteristic of SPDC. The methods of achieving polarization superposition via the Type-I and Type-II SPDC are described. A combination of superposition and polarization correlation between down-converted photons is shown to violate Bell’s inequality, thus revealing the entangled nature of the photon pairs. Finally, the possibility of controlling entangled photons through the manipulation of surface plasmons is highlighted as a way to transfer entanglement from photons to material particles.