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Physical Review A

Intense nonclassical light: Controllable two-photon Talbot effect

C. H. Raymond Ooi, Boon Leong Lan

Published Jun 28, 2010• 18 citations
Publisher

Abstract

We study the spatial interference pattern of two-photon correlation function for a coherently phased linear array of $N$ emitters with a double-Raman scheme, each producing nonclassically correlated photon pairs. The ${N}^{2}$ dependence in the two-photon correlation serves as a coherent amplification method for producing intense nonclassical light. The spatial distribution of the correlation can be controlled by lasers, and depends on the detection configuration. For two coincident detectors, the nonclassical correlation displays the spatial Talbot pattern, but modulated by quantum interference effect. The image revival distance is found to be twice the usual Talbot length. For symmetrically located detectors (${X}_{1}=\ensuremath{-}{X}_{2}$), the correlation displays a distorted Talbot pattern with intricate features and lack of symmetry.

DOI
10.1103/physreva.81.063832

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We study the spatial interference pattern of two-photon correlation function for a coherently phased linear array of NNN emitters with a double-Raman scheme, each producing nonclassically correlated photon pairs. The N2{N}^{2}N2 dependence in the two-photon correlation serves as a coherent amplification method for producing intense nonclassical light. The spatial distribution of the correlation can be controlled by lasers, and depends on the detection configuration. For two coincident detectors, the nonclassical correlation displays the spatial Talbot pattern, but modulated by quantum interference effect. The image revival distance is found to be twice the usual Talbot length. For symmetrically located detectors (X1=\ensuremath−X2{X}_{1}=\ensuremath{-}{X}_{2}X1​=\ensuremath−X2​), the correlation displays a distorted Talbot pattern with intricate features and lack of symmetry.
We report the first experimental observation of quantum Talbot effects with single photons and entangled photon pairs. Both the first- and second-order quantum Talbot self-images are observed experimentally. They exhibit unique properties, which are different from those produced by coherent and incoherent classical light sources. In particular, our experiments show that the revival distance of two-photon Talbot imaging is twice the usual classical Talbot length and there is no net improvement in the resolution, due to the near-field effect of Fresnel diffraction, which is different from the case of previous proof-of-principle quantum lithography experiments in the far field.
We demonstrate the existence of nonclassical correlations in the radiation of two atoms, that are coherently driven by a continuous laser source. The photon-photon correlations of the fluorescence light show a spatial interference pattern not present in a classical treatment. A feature of this phenomenon is that bunched and antibunched light is emitted in different spatial directions. The calculations are performed analytically. It is pointed out that the correlations are induced by state reduction due to the measurement process when the detection of the photons does not distinguish between the atoms. It is interesting to note that the phenomena show up even without any interatomic interaction.
Two‐photon “ghost” imaging, based on the second‐order intensity correlation, was first realized with entangled light, but has now been demonstrated with true thermal light. Following our work on lensless and high‐order ghost imaging with thermal light, we have recently shown that both entangled and thermal light may be used to produce two‐photon correlation Talbot effects. In the Talbot effect, first observed in 1836, a periodic object illuminated with coherent light can give rise to repeated self‐images at specific positions within the Fresnel diffraction field without any lens. Using an incoherent thermal light source, we have experimentally observed second and higher order Talbot self‐images, including fractional and phase‐reversal images, at multiples of the Talbot length in a lensless setup containing two optical paths. We have also recently observed another surprising imaging phenomenon which does not depend on the second‐order correlation function, and can produce both negative and positive images of a nonlocal object. It is expected that these types of imaging will find novel applications in both the microscopic and macroscopic regimes.
In this thesis we discuss an extension of the historical Hanbury Brown and Twiss experiment and investigate spatial intensity correlations of higher-orders in the radiation field of statistically independent light sources. The light sources can be non-classical like single-photon emitters or classical, obeying thermal or coherent statistics. Although the light sources are assumed to emit the photons in an incoherent manner, we find spatial photon correlations in the far field which can be explained by the quantum mechanical concept of multi-photon interferences. We demonstrate that spatial correlation measurements between indistinguishable photons based on linear optical detection techniques can be used to overcome the resolution limit of classical optics (Abbe/Rayleigh limit) and also to manipulate the spatial radiation characteristic of the light sources. Both remarkable properties of higher-order intensity correlations have been experimentally verified using statistically independent pseudothermal light sources. Due to the fact that the reported correlation measurements require neither special quantum tailoring of light nor N-photon absorbing media, they are of particular interest for the field of quantum imaging and quantum information processing. The thesis is divided into three main parts: In the first part (Chapter 2 and 3) we introduce a quantum path formalism which allows to describe multi-photon interferences arising in both classical and nonclassical light fields. This quantum path approach explains the origin of the underlying interference mechanism of the higher-order spatial intensity correlation functions in a transparent and simple manner. Moreover, it enables us to compare the multi-photon interferences obtained by nonclassical single-photon emitters with those generated by classical light sources. In the course of this discussion it appears that Dirac's famous statement “Each photon interferes only with itself. Interference between two different photons never occurs.” should better read “A multi-photon state of independent photons only interferes with itself. Interference between different multi-photon states never occurs.” This general statement summarizes the physics behind all multi-photon interference phenomena investigated in this thesis. In the second part of the thesis (Chapter 4) we investigate particular multi-photon interference measurements of independent light sources in the context of quantum imaging. We demonstrate that the Nth-order spatial intensity correlation functions display at specific ‘magic’ detector positions the ability to filter sub-wavelength information out of the light fields arising from N incoherently radiating light sources. These multi-photon interference patterns achieve a higher resolution for N>2 than the classical Abbe/Rayleigh limit for imaging the light source. In case of N single-photon emitters we theoretically show that the super-resolving interference patterns obtained for the ‘magic’ detector positions are identical to the ones generated by NOON states with N-1 photons. Quite unexpected, the same is true for N thermal light sources, except for a reduced visibility. Experimental results with up to eight independent thermal light sources confirm this approach to improve the spatial resolution in imaging. In the last part of this thesis (Chapter 5) we finally demonstrate that multi-photon detections can lead to a strong angular focussing of incoherent photons emitted again by either uncorrelated single-photon sources or statistically independent classical light sources. For this effect the sources can be far away from each other and do not interact. The mth-order intensity correlation measurement causes source correlations which produce a heralded peaked emission pattern for the initially uncorrelated light sources. In particular, we show that if m-1 photons have been detected in a particular direction, the conditional probability to detect the mth photon in the same direction can be as high as 100 %. Owing to the great flexibility of detector positions for the correlation measurement, a wide variety of additional detection schemes exists which produces similar directional photon emission patterns. This theoretically predicted measurement-induced focussing was experimentally confirmed with up to eight pseudothermal light sources for three particular detection schemes.
We study the interference patterns obtained from the superposition of two Bessel beams originated from a quantum two-photon state produced by a spontaneous parametric down-conversion process. Due to the nondiffracting character of the light beam, a self-imaging effect is found along the propagation direction for second-order interference patterns with periodicity proportional to $\ensuremath{\lambda}∕2$, characterizing a two-photon Talbot effect. Conditional interference patterns in the longitudinal plane are theoretically shown as well.
The generation and manipulation of single- and multi-photon states play a central role in numerous quantum optics applications, including quantum communication, imaging, sensing, and information processing. The transverse spatial degrees of freedom of photons are particularly attractive because they provide access to high-dimensional quantum states. Optical systems that inherently support spatially structured modes therefore provide compact and versatile platforms for manipulating such states. Ring-core fibers naturally support azimuthal modes whose interference produces cylindrical Talbot self-imaging. At half the Talbot length, this propagation performs a transformation analogous to that of a balanced beam splitter between diametrically opposite angular positions. In this thesis, the cylindrical Talbot effect is experimentally investigated using the full transverse output of a spontaneous parametric down conversion source, with the goal of observing two-photon interference occurring inside a ring-core fiber. Degenerate photon pairs were generated in a periodically poled potassium titanyl phosphate crystal. The transverse momentum anti-correlations of the generated photons were determined with a single-photon avalanche diode camera utilizing the reconstructed joint probability distributions from sequences of short-exposure frames. Near- and far field measurements after the nonlinear crystal verified the expected transverse momentum anti-correlations and transverse position correlation properties of the generated biphoton state. The annular far field distribution was subsequently shaped and coupled into a ring-core fiber with a length corresponding to half of the cylindrical Talbot length. Intensity acquisitions at the fiber output confirmed the expected beam splitting of an angularly localized input distribution into two diametrically opposite outputs. Two-photon interference was investigated at discrete temporal delays by observing the coincidence counts between opposite output ports of the ring-core fiber. No reduction in coincidences between opposite outputs was observed at zero temporal delay. The statistical uncertainty, poor signal-to-noise ratio, and deviation from the correct Talbot length most likely prevent the observation of the interference effect. The correlation structure of the biphoton state after the fiber was likewise insufficient to determine an expected transformation from momentum anti-correlation to correlation. These results establish that the cylindrical Talbot effect can be employed for manipulating the spatial output of an SPDC source to observe beam splitting. The two-photon interference measurements can be utilized for identifying the main experimental limitations affecting the visibility of the observed effect. These results provide a framework for further investigations of the cylindrical Talbot effect for compact beam splitting and quantum state manipulation.