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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Interferometric phase measurement with two-photon states

M. Kacprowicz, Wojciech Wasilewski, Rafał Demkowicz-Dobrzański, Konrad Banaszek

Published Jun 1, 2009• 2 citations
Publisher

Abstract

We demonstrate experimentally a phase measurement using general two-photon superposition states in a multiport interferometer shown schematically. A pair of photons, produced in the process of spontaneous parametric down-conversion, is transformed into the desired superposition state using beam splitters BS1 and BS2, provided that no photon escapes through the unmonitored port of BS2. In the signal arm, the photon pair experiences losses introduced by the beam splitter BS3 and monitored by a detector C, and subsequently probes the phase shift phi. The phase information is read out by sending the photons onto the beam splitter BS4, whose output ports are monitored by detectors A and B.

DOI
10.1109/cleoe-eqec.2009.5191544

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We demonstrate experimentally a phase measurement using general two-photon superposition states in a multiport interferometer shown schematically. A pair of photons, produced in the process of spontaneous parametric down-conversion, is transformed into the desired superposition state using beam splitters BS1 and BS2, provided that no photon escapes through the unmonitored port of BS2. In the signal arm, the photon pair experiences losses introduced by the beam splitter BS3 and monitored by a detector C, and subsequently probes the phase shift phi. The phase information is read out by sending the photons onto the beam splitter BS4, whose output ports are monitored by detectors A and B.
Quantum theory predicts that two indistinguishable photons incident on a beam-splitter interferometer exit together (the pair emerges randomly from one port or the other). We use a special photon-number-resolving energy detector for a direct observation of this quantum-interference phenomenon. Simultaneous measurements from two such detectors, one at each beam-splitter-interferometer output port, confirm the absence of cross coincidences. Photon-number-resolving detectors are expected to find use in other quantum-optics and quantum-information-processing experiments.
An interferometric arrangement utilizing a pair of twin photons, generated by parametric down-conversion, is devised to show second-order interferences revealing de Broglie's wavelength of the photon pair as a whole and the Pancharatnam phase depending on the number of photons. This proposed experiment utilizes the phenomenon ``induced coherence without stimulated emission'' to generate a coherent superposition of states distinct from the usual superposition with beam splitters, where the photons are independently scattered. In this experiment interference occurs due to recombination of photon trajectories on a beam splitter and also through frustration or enhancement of the down-conversion processes.
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In this paper, we investigate the influence of the symmetry of the biphoton wave function on the coincidence measurement of the generalized Mach-Zehnder (MZ) interferometer, where there are a temporal and frequency shift operations between the two beam splitters. We show that the generalized MZ interferometer allows the measurement of the short-time Fourier transform of the function modeling the energy conservation of a spontaneous parametric down-conversion process if the full biphoton state is symmetric, and of the symmetric characteristic distribution of the phase-matching function if the state is antisymmetric. Thus, this technique is phase sensitive to the spectral distribution of the photon pairs. Finally, we investigate in detail the signature of a pair of anyons whose peculiar statistics can be simulated by engineering the spectrum of photon pairs.