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Conference on Lasers and Electro-Optics

Heralded Single Photon Partial Coherence

P. Ben Dixon, Gregory A. Howland, Mehul Malik, David J. Starling, Robert W. Boyd, E. Wolf, John C. Howell

Published Jan 1, 2010• 0 citations
Publisher

Abstract

Optical spatial coherence, characterizing correlations between optical fields at distinct points, plays a key role in the understanding of classical and quantum phenomena. Recent decades’ technological advances, such as powerful lasers and fast, efficient photon counters enabled the study of nonclassical optical fields. Here, we describe single photon partial coherence, providing a theoretical model from quantum coherence theory and experimental observation. In particular, we make clear the role of quantum birth-zones for SPDC sources. These birth-zones are the quantum analog of classical emitters; they characterize the heralded single photon’s coherence properties. We make the first observation of the predicted inversion of the single photon degree of coherence.

DOI
10.1364/cleo.2010.cmcc2

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•Jan 16, 2016•111 citations
Optical spatial coherence, characterizing correlations between optical fields at distinct points, plays a key role in the understanding of classical and quantum phenomena. Recent decades’ technological advances, such as powerful lasers and fast, efficient photon counters enabled the study of nonclassical optical fields. Here, we describe single photon partial coherence, providing a theoretical model from quantum coherence theory and experimental observation. In particular, we make clear the role of quantum birth-zones for SPDC sources. These birth-zones are the quantum analog of classical emitters; they characterize the heralded single photon’s coherence properties. We make the first observation of the predicted inversion of the single photon degree of coherence.
The achievement of sufficiently fast interactions between two optical fields at the few-photon level would provide a key enabler for a broad range of quantum technologies. One critical hurdle in this endeavor is the lack of a comprehensive quantum theory of the generation of nonlinearities by ensembles of emitters. Distinct approaches applicable to different regimes have yielded important insights: i) a semiclassical approach reveals that, for many-photon coherent fields, the contributions of independent emitters add independently allowing ensembles to produce strong optical nonlinearities via EIT; ii) a quantum analysis has shown that in the few-photon regime collective coupling effects prevent ensembles from inducing these strong nonlinearities. Rather surprisingly, experimental results with around twenty photons are in line with the semi-classical predictions. Theoretical analysis has been fragmented due to the difficulty of treating nonlinear many-body quantum systems. Here we are able to solve this problem by constructing a powerful theory of the generation of optical nonlinearities by single emitters and ensembles. The key to this construction is the application of perturbation theory to perturbations generated by subsystems. This theory reveals critical properties of ensembles that have long been obscure. The most remarkable of these is the discovery that quantum effects prevent ensembles generating single-photon nonlinearities only within the rotating-wave regime; outside this regime single-photon nonlinearities scale as the number of emitters. The theory we present here also provides an efficient way to calculate nonlinearities for arbitrary multi-level driving schemes, and we expect that it will prove a powerful foundation for further advances in this area.
Single photons exhibit nonclassical, counterintuitive behavior that can be exploited in the developing field of quantum technology. They are needed for various applications such as quantum key distribution, optical quantum information processing, quantum computing, intensity measurement standards, and others yet to be discovered in this developing field. This drives the current intensive research into the realization of true deterministic sources of single photons on demand. Lacking such a source, many researchers default to the well-established workhorse: spontaneous parametric down-conversion that generates entangled signal-idler pairs. Since this source is thermal statistical in nature, it is common to use a detected idler photon to herald the production of a signal photon. The need exists to determine the quality of the single photons generated in the heralded signal beam. Quite often, the literature reports a heralded second-order coherence function of the signal photons conditioned on the idler photons using readily available single-photon detectors. In this work we examine the applicability of this technique to single-photon characterization and the consequences of the fact that the most commonly used single-photon detectors are not photon-number resolving. Our results show that this method using non-photon-resolving detectors can only be used to characterize the signal-idler correlations rather than the nature of the signal-photon state alone.
Abstract As a tutorial to the spatial aspects of spontaneous parametric downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.
As a tutorial to the spatial aspects of Spontaneous Parametric Downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a Double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such Double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.