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A Bi-Photon Quantum Interferometer for Complete Measurement of the Bi-Photon Wave Function

Roey Pomerantz, Yaakov Shaked, Avi Pe’er

Published Sep 19, 2012• 0 citations
OpenAlex

Abstract

We observe at record-high speed the nonclassical nature of ultra-broadband bi-photons, reducing the measurement time by four orders of magnitude compared to standard techniques of Hong-Ou-Mandel interference or sum-frequency generation. We measure the quantum state of the broadband bi-photons, amplitude and phase, with a pairwise Mach-Zehnder quantum interferometer, where bi-photons that are generated in one nonlinear crystal are enhanced (constructive interference) or diminished (destructive interference) in another crystal, depending on the bi-photon phase. We verify the quantum nature of the interference by observing the dependence of the fringe visibility on internal loss. Since destructive interference is equivalent to an attempt to annihilate in the second crystal (by up-conversion) the bi-photons that were created in the first crystal (by down-conversion), the fringe visibility is a measure for the quantum bi-photon purity of the broadband light. The measurement speed-up is due to the large homodyne-like gain from the strong pump ($\!\sim\!10^{7-9}$) in the up-conversion efficiency of single bi-photons, which enables the use of simple photo-detection of the full, ultra-high photon flux instead of single-photon / coincidence counting.

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We observe at record-high speed the nonclassical nature of ultra-broadband bi-photons, reducing the measurement time by four orders of magnitude compared to standard techniques of Hong-Ou-Mandel interference or sum-frequency generation. We measure the quantum state of the broadband bi-photons, amplitude and phase, with a pairwise Mach-Zehnder quantum interferometer, where bi-photons that are generated in one nonlinear crystal are enhanced (constructive interference) or diminished (destructive interference) in another crystal, depending on the bi-photon phase. We verify the quantum nature of the interference by observing the dependence of the fringe visibility on internal loss. Since destructive interference is equivalent to an attempt to annihilate in the second crystal (by up-conversion) the bi-photons that were created in the first crystal (by down-conversion), the fringe visibility is a measure for the quantum bi-photon purity of the broadband light. The measurement speed-up is due to the large homodyne-like gain from the strong pump ( ⁣∼ ⁣107−9\!\sim\!10^{7-9}∼107−9) in the up-conversion efficiency of single bi-photons, which enables the use of simple photo-detection of the full, ultra-high photon flux instead of single-photon / coincidence counting.
We observe at record-high speed the nonclassical nature of ultra-broadband bi-photons, reducing the measurement time by four orders of magnitude compared to standard techniques of Hong–Ou–Mandel interference or sum-frequency generation. We measure the quantum wave-function of the broadband bi-photons, amplitude and phase, with a pairwise 'Mach–Zehnder' quantum interferometer, where bi-photons that are generated in one nonlinear crystal are enhanced (constructive interference) or diminished (destructive interference) in another crystal, depending on the bi-photon phase. We verify the quantum nature of the interference by observing the dependence of the fringe visibility on internal loss. Since destructive interference is equivalent to an attempt to annihilate in the second crystal (by up-conversion) the bi-photons that were created in the first crystal (by down-conversion), the fringe visibility is a measure of the quantum bi-photon purity of the broadband light. The measurement speed-up is due to the large homodyne-like gain from the strong pump (∼10 7–9 ) in the up-conversion efficiency of single bi-photons, which enables the use of simple photo-detection of the full, ultra-high photon flux instead of single-photon/coincidence counting.
The visibility of nonlinear SU(1,1) interference directly reflects the nonclassical properties of entangled bi-photons and squeezed light with practically unlimited bandwidth, high efficiency and ultra-high photon flux, orders of magnitude beyond the abilities of standard photo-detectors. We study experimentally the dependence of the SU(1,1) visibility on the phase matching conditions and beam parameters in a free-space configuration, and show that maximal SU(1,1) visibility requires extreme collinear conditions, which deviate from the conditions for maximal nonlinear conversion. We demonstrate near-ideal visibility of ∼95% (limited only by internal loss) in an ultra-broadband SU(1,1), interferometer with over 120 THz of squeezed light bandwidth. Utilizing this analysis we demonstrate efficient detection of the spectral phase of single-cycle bi-photons and precise compensation of the dispersion over a full octave of bandwidth.
A pair of light quanta with different colors (155.9-nm difference in center wavelength) generated from parametric down-conversion was injected collinearly into one input port of a Mach-Zehnder interferometer. Coincidence interference behavior was studied over a wide range of optical path differences of the interferometer. A measurement of 75% interference visibility with oscillation of the pump frequency for a large optical path difference of the interferometer (43 cm) is the signature of a quantum two-photon entangled state, which reflects both particle and wave nature of the light quanta in one experiment.
We study both theoretically and experimentally the interference pattern in a nonlinear Mach–Zehnder interferometer formed by two aperiodically-poled crystals, where broadband squeezed light is generated by both crystals via parametric down-conversion with a common quasi-monochromatic pump. This configuration is important for measuring the squeezing produced by the first crystal and also for measuring a small phase shift introduced by a sample between the crystals. On the basis of the approximate quantum Rosenbluth formula for each crystal we develop an analytic model for the field evolution in the interferometer. We report an experimental observation of the interference fringes, caused by the dispersion of the generated PDC waves in both crystals forming the interferometer. We observe a displacement of the interference pattern caused by a sample between the crystals and infer the phase shift within a band of 20 nm. The experimental data are in a good agreement with the predictions of the developed model, up to imperfections of the samples.