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arXiv:0709.3517 · Physical Review A

Generation of Fourier-transform-limited heralded single photons

Alfred B. U’Ren, Yasser Jerónimo-Moreno, Hipolito Garcia-Gracia

Published Feb 15, 2007• 28 citations
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Abstract

In this paper we study the spectral (temporal) properties of heralded single photon wave packets, triggered by the detection of an idler photon in the process of parametric down conversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier-transform-limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfillment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wave packets.

DOI
10.1103/physreva.75.023810

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In this paper we study the spectral (temporal) properties of heralded single photon wave packets, triggered by the detection of an idler photon in the process of parametric down conversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier-transform-limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfillment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wave packets.
We experimentally demonstrate temporal shaping of a heralded single-photon wave packet, prepared by conditional measurement of the idler photon of the entangled photon pair in the process of spontaneous parametric down-conversion. The heralded single-photon wave packet for the signal photon, after being tailored with the help of chirp broadening and interference effects, was observed directly by measuring the time-correlated single-photon-counting histogram. We also demonstrate remote control of the temporal shaping effect by spectral filtering of the idler photon.
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.
In this paper, we describe how introducing angular dispersion into the pump beam and the downconverted photons in spontaneous parametric downconversion allows us to manipulate the joint spectrum of the paired photons. In particular, when collinear geometries are used, we demonstrate an increase of the photons' bandwidth and discuss the implications of this method for the generation of narrow temporal Fourier transform limited biphotons. Additionally, we describe the situation in which angular dispersion is combined with noncollinear geometries. In this case, a full control of the joint spectrum is achieved and heralded pure single photons with controllable bandwidth can be obtained.
We present a theoretical analysis of the process of spontaneous parametric down conversion (SPDC) in a nonlinear crystal characterized by a linearly-chirped χ(2) grating along the direction of propagation. Our analysis leads to an expression for the joint spectral amplitude, based on which we can derive various spectral–temporal properties of the photon pairs and of the heralded single photons obtained from the photon pairs, including: The single-photon spectrum (SPS), the chronocyclic Wigner function (CWF) and the Schmidt number. The simulations that we present are for the specific case of a collinear SPDC source based on a PPLN crystal with the signal and idler photons emitted close to the telecom window. We discuss the mechanism for spectral broadening due to the presence of a linearly chirped χ(2) grating, showing that not only the width but also to some extent the shape of the SPDC spectrum may be controlled. Also, we discuss how the fact that the different spectral components are emitted on different planes in the crystal leads to single-photon chirp.