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International Journal of Quantum Information

ANGULAR DISPERSION IN SPONTANEOUS PARAMETRIC DOWN CONVERSION: A TOOL TO GENERATE NARROW TEMPORAL BIPHOTONS AND PURE HERALDED SINGLE PHOTONS

Alejandra Valencia, Martin Hendrych, Xiaojuan Shi, Juan P. Torres

Published Jan 1, 2009• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749909004906

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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.
One of the goals of quantum optics is to implement new sources of quantum light with tunable control of the relevant photonic properties. Here, we add to the toolkit of available techniques in quantum optics for the full control of the properties of quantum light, new strategies to manage the spectrum of photons, namely, type of frequency correlations, bandwidth and waveform. As a source of quantum light, spontaneous parametric downconversion (SPDC) is considered. Interestingly, the techniques presented might be used in any nonlinear medium and frequency band of interest. One of the schemes to control the frequency correlations makes use of light pulses with pulse-front tilt. The method is based on the proper tailoring of the group velocities of all the waves that interact in the nonlinear process, through the use of beams with angular dispersion. Noncollinear SPDC is the other strategy that is considered, since it allows mapping the spatial characteristics of the pump beam into the frequency properties of the downconverted photons.
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.
The bandwidth and the frequency correlations of quantum light can be considered as a resource for the implementation of new quantum information algorithms, and it should enable the applicability of quantum techniques not yet implemented. For that purpose, the control of the frequency correlations, and the bandwidth, of single and paired photons is an essential ingredient, since the optimum bandwidth, as well as the most appropriate type of frequency correlations for a specific quantum application, depend on the specific quantum information application under consideration. Here we elucidate and implement new strategies to tailor the frequency properties of quantum light. Such strategies, which are based on the use of non collinear spontaneous parametric down conversion (SPDC) configurations, include the generation of narrow and enhanced bandwidth quantum light, the control of the frequency correlations of paired photon, and the generation of heralded single photons with a high degree of purity from pairs of uncorrelated photons.
The nonlinear optical process of spontaneous parametric down-conversion (SPDC) is widely studied for applications in quantum information science due to its ability to produce two photons that can be entangled in many degrees of freedom. For applications in quantum communication, two metrics of this process are particularly important: heralding efficiency and total joint rate. Here, we derive expressions for both quantities for a variety of different beam geometries and frequencies. We pay specific attention to the spectrum of both biphotons and individual photons. We reveal the underlying mechanisms responsible for the spectral shape and show they differ for different geometries and frequencies. We then use these spectra to calculate heralding efficiency and joint count rate and examine how each of these metrics changes with different geometries, frequencies, spectral filtering, and beam parameters. Interestingly, we find very high heralding efficiencies are achievable for collinear geometries without spectral filtering, while noncollinear geometries require spectral filtering to achieve the same values. We also find that the spectrum is narrower for nondegenerate SPDC than for degenerate SPDC, leading to lower joint count rates and higher heralding efficiency in the former. In addition to the theory, we verify selected predictions with experimental results.
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.