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arXiv:0904.3923 · Physical Review A

Control, measurement, and propagation of entanglement in photon pairs generated through type-II parametric down-conversion

Yasser Jerónimo-Moreno, Alfred B. U’Ren

Published Mar 25, 2009• 18 citations
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Abstract

We present a study of the effects of dispersion on the properties of photon pairs generated by type-II collinear spontaneous parametric down-conversion. Specifically, we take into consideration the effects of a chirped pump, as well as of dispersive propagation of the photon pairs. We present expressions for the joint amplitude both in the spectral and temporal domains, as well as for the chronocyclic Wigner function of heralded single photons, which fully characterizes the single-photon spectral (temporal) properties. On the one hand, we show that unwanted effects of pump chirp in terms of the heralded single-photon duration can be suppressed for states designed to be factorable and spectrally elongated. On the other hand, we show that pump chirp constitutes an effective tool for the control of the degree of photon-pair entanglement. We show that when frequency-entangled photon pairs propagate through a dispersive medium, entanglement can ``migrate'' between the modulus and phase of the joint temporal amplitude.

DOI
10.1103/physreva.79.033839

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We present a study of the effects of dispersion on the properties of photon pairs generated by type-II collinear spontaneous parametric down-conversion. Specifically, we take into consideration the effects of a chirped pump, as well as of dispersive propagation of the photon pairs. We present expressions for the joint amplitude both in the spectral and temporal domains, as well as for the chronocyclic Wigner function of heralded single photons, which fully characterizes the single-photon spectral (temporal) properties. On the one hand, we show that unwanted effects of pump chirp in terms of the heralded single-photon duration can be suppressed for states designed to be factorable and spectrally elongated. On the other hand, we show that pump chirp constitutes an effective tool for the control of the degree of photon-pair entanglement. We show that when frequency-entangled photon pairs propagate through a dispersive medium, entanglement can ``migrate'' between the modulus and phase of the joint temporal amplitude.
We report the complete measurement of the spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion pumped by a cw laser in both the collinear and the noncollinear regimes. The measurement includes the single-photon spectra as well as the two-photon joint spectra. Our results reveal interesting yet subtle differences between the collinear and the noncollinear regimes of frequency-degenerate type-I spontaneous parametric down-conversion. The single-photon and two-photon spectral measurements are in good agreement with the numerical simulation taking into account the tuning curve and the experimental geometry.
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.
In this paper we describe theoretically quantum control of temporal correlations of entangled photons produced by collinear type II spontaneous parametric down-conversion. We examine the effect of spectral phase modulation of the signal or idler photons arriving at a 50/50 beam splitter on the temporal shape of the entangled-photon wave packet . The coincidence count rate is calculated analytically for photon pairs in terms of the modulation depth applied to either the signal or idler beam with a spectral phase filter. It is found that the two-photon coincidence rate can be controlled by varying the modulation depth of the spectral filter.
Spontaneous parametric down-conversion (SPDC) is the most often used source of entangled photon states in quantum optics. Recently, it has been suggested in theory that the reduction of polarization entanglement between the photon pair generated via the type-II SPDC process pumped by a ultrafast laser is due to the asymmetry in the joint spectrum function, which is the indicative of the frequency entanglement between the two photons. In this paper, we report the measurement of the joint spectrum function (i.e., direct observation of the degree of frequency entanglement) of the two-photon state of type-II SPDC in both cw- and ultrafast-laser pumping conditions. We observed that, in agreement with the theory, the degree of frequency entanglement (the shape of the joint spectrum function) is indeed different for cw- and ultrafast-pumped type-II SPDC. Our results are of importance in "engineering" the two-photon state for specific quantum applications, such as quantum cryptography.