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Physical Review A

Heralded single-photon partial coherence

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

Published Aug 2, 2010• 6 citations
Publisher

Abstract

We study transverse spatial coherence of approximately localized single-photon states. We demonstrate nonlocal control over single-photon spatial coherence via projective measurements of an entangled twin and provide a theoretical interpretation from quantum coherence theory. Our results show that the spatial coherence of a single-photon state behaves similarly to that of a classical optical field, although the coincidence measurement adds a degree of freedom.

DOI
10.1103/physreva.82.023801

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We study transverse spatial coherence of approximately localized single-photon states. We demonstrate nonlocal control over single-photon spatial coherence via projective measurements of an entangled twin and provide a theoretical interpretation from quantum coherence theory. Our results show that the spatial coherence of a single-photon state behaves similarly to that of a classical optical field, although the coincidence measurement adds a degree of freedom.
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.
Partially coherent quantum-entangled beams combine quantum correlation with partial coherence, allowing them to maintain quantum characteristics while being more resistant to distortions caused by random media during propagation. In this study, we investigate the effect of coherence variation of such beams on non-local double-slit quantum interference. The spatial coherence variation is achieved by controlling the transverse coherence length of the Gaussian Schell model pump in the spontaneous parametric down conversion process. For a fixed beam size, the momentum correlation width of partially coherent biphotons increases with the decrease in the transverse coherence length. This results in a biphoton beam exhibiting multiple spatial modes, making it more suitable for studying the non-local features of quantum states in imaging, interference, and diffraction experiments. Our findings infer both high-quality and near-unity visibility of nonlocal interference using the partially coherent twin beams, even with the substantial decrease in the coherence of the pump. We believe these results can enhance robustness against the deleterious effects of the medium during propagation and can have potential applications in optical image cryptography, biomedical imaging, quantum lithography, and quantum holography.
According to Schrödinger, the laws of quantum mechanics obliges us to admit that by suitable measurement taken on one of the two system only1 the state of the other system can not only be determined but steered too. That is, it conveys the potential ability to steer the state of another physical system without interacting with it by implementing independent measurements, this nonlocal phenomenon was named steering. On the other hand, the first proposals about the nonlocality of a single photon focus on showing the Bell nonlocality by using a single photon path entanglement. This path entanglement of a single photon was also used for analyzing and experimentally produce the steering of a single photon. However, these established facts have been recently called into question suggesting that single-photon entanglement is not non-local. In this letter, we show that by incorporating and manipulating the internal degrees of freedom of the photon, together with the external path, it is easy to demonstrate the nonlocal effect of steering of a single photon's state. In this sense, the experimental set-up that we propose differs from the one reported in the quantum optics literature which only uses, to the best of our knowledge, the path entanglement of photons for showing the steering phenomenon, i.e. here we exploit the entanglement between the internal and external degrees of freedom of the photon to show this nonlocal effect. The introduction of the photon's internal degrees of freedom in the experimental set-up gives us new insight, advantages and possibilities to control the nonlocal character of the single-photon entangled state.
We present an experimental method to measure the transverse spatial quantum state of an optical field in coordinate space at the single-photon level. The continuous-variable measurements are made with a photon-counting, parity-inverting Sagnac interferometer based on all-reflecting optics. The technique provides a large numerical aperture without distorting the shape of the wavefront, does not introduce astigmatism, and allows for characterization of fully or partially coherent optical fields at the single-photon level. Measurements of the transverse spatial Wigner functions for highly attenuated coherent beams are presented and compared with theoretical predictions.
We present an experimental method to measure the transverse spatial quantum state of an optical field in coordinate space at the single-photon level. The continuous-variable measurements are made with a photon-counting, parity-inverting Sagnac interferometer based on all-reflecting optics. The technique provides a large numerical aperture without distorting the shape of the wave front, does not introduce astigmatism, and allows for characterization of fully or partially coherent optical fields at the single-photon level. Measurements of the transverse spatial Wigner functions for highly attenuated coherent beams are presented and compared to theoretical predictions.
Summary form only given. The spatial structure of a photon has proved to be indispensable resource allowing the experimental realization of free-space quantum cryptography or high dimensional entanglement. Although efficient methods for manipulating spatial characteristic of individual photons can be easily transferred from the field of classical optics, their spatial structure cannot be measured using the standard interferometric reference-based methods such as optical holography due to their completely undefined-global phase. Hence, the full recovery of a transverse photon wavefunction still remains a challenging task tackled so far exclusively using indirect methods such as the quantum tomography [1] and weak values measurements [2].Here we present and experimentally demonstrate a different approach based on spatially resolved detection of two-photon interference [3,4]. Although such measurements are usually perceived to be insensitive to the relative phase between two interfering photons we show that rarely considered local phase dependence can be still observed and utilized for direct recovery of a single photon quantum wavefunction. In particular we experimentally show that the complex transversal wavefunction of the unknown photon can be fully recovered from the 2D spatial coincidence pattern resulting from its two-photon interference with the reference photon [5].