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arXiv:1911.10983 · Physical Review Letters

Light of Two Atoms in Free Space: Bunching or Antibunching?

Sebastian Wolf, Stefan Richter, Joachim von Zanthier, Ferdinand Schmidt‐Kaler

Published Feb 13, 2020• 50 citations
arXivHTMLPDF

Abstract

Photon statistics divides light sources into three different categories, characterized by bunched, antibunched, or uncorrelated photon arrival times. Single atoms, ions, molecules, or solid state emitters display antibunching of photons, while classical thermal sources exhibit photon bunching. Here we demonstrate a light source in free space, where the photon statistics depends on the direction of observation, undergoing a continuous crossover between photon bunching and antibunching. We employ two trapped ions, observe their fluorescence under continuous laser light excitation, and record spatially resolved the autocorrelation function g^{(2)}(τ) with a movable Hanbury Brown and Twiss detector. Varying the detector position we find a minimum value for antibunching, g^{(2)}(0)=0.60(5) and a maximum of g^{(2)}(0)=1.46(8) for bunching, demonstrating that this source radiates fundamentally different types of light alike. The observed variation of the autocorrelation function is understood in the Dicke model from which the observed maximum and minimum values can be modeled, taking independently measured experimental parameters into account.

DOI
10.1103/physrevlett.124.063603

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•Jan 1, 2012•0 citations
Photon statistics divides light sources into three different categories, characterized by bunched, antibunched, or uncorrelated photon arrival times. Single atoms, ions, molecules, or solid state emitters display antibunching of photons, while classical thermal sources exhibit photon bunching. Here we demonstrate a light source in free space, where the photon statistics depends on the direction of observation, undergoing a continuous crossover between photon bunching and antibunching. We employ two trapped ions, observe their fluorescence under continuous laser light excitation, and record spatially resolved the autocorrelation function g^{(2)}(τ) with a movable Hanbury Brown and Twiss detector. Varying the detector position we find a minimum value for antibunching, g^{(2)}(0)=0.60(5) and a maximum of g^{(2)}(0)=1.46(8) for bunching, demonstrating that this source radiates fundamentally different types of light alike. The observed variation of the autocorrelation function is understood in the Dicke model from which the observed maximum and minimum values can be modeled, taking independently measured experimental parameters into account.
Understanding the boundary between classical and nonclassical phenomena is important for both fundamental researches in quantum optics and applications in quantum information. One of the most interesting research directions in this field is exploring nonclassical effects with classical light. In this paper, we will show that it is possible to observe antibunching with thermal light in a Hanbury Brown-Twiss interferometer by treating single-photon detectors as photon-number-resolving detectors to perform photon-number projection measurements. Both temporal and spatial antibunching is observed via the correlation of two detectors detecting one and zero photon, respectively. By comparing the measured results of thermal and laser light, it is found that the observed antibunching arises from the combined effect of photon statistics of thermal light and photon-number projection measurement.The classical and nonclassical nature of the observed antibunching is analyzed. The results are helpful to understand the connection between classical and nonclassical correlation and may find applications in multiphoton interference and quantum imaging.
We investigate the photon statistics of an ensemble of coherently driven non-interacting two-level atoms in the weak driving regime. As it turns out, the system displays unique emission characteristics that are strongly in contrast to the emission of classical oscillating dipoles. By deriving the second-order autocorrelation function, we show that extraordinary two-photon correlations are obtained, ranging from strong antibunching to superbunching. These features are enhanced by disorder in the emitter positions, and the control parameter is the number of excitations in the system. We observe the appearance of bunching and antibunching when the light is scattered by the atoms predominantly coherently, i.e., mimicking classical Rayleigh scattering, whereas thermal photon statistics is obtained when the light is scattered via spontaneous decay, a well-known quantum effect. The underlying mechanism is the interplay between coherent scattering, which exhibits spatial fluctuations due to interference, and dissipation in the form of isotropic spontaneous decay.
The photon statistics of the light emitted from an atomic ensemble into a single field mode of an optical cavity is investigated as a function of the number of atoms. The light is produced in a Raman transition driven by a pump laser and the cavity vacuum, and a recycling laser is employed to repeat this process continuously. For weak driving, a smooth transition from antibunching to bunching is found for about one intracavity atom. Remarkably, the bunching peak develops within the antibunching dip. The observed behavior is well explained by a model describing an ensemble of independent emitters.
Since Hanbury Brown and Twiss revealed the photon bunching effect of a thermal light source in 1956, almost all studies in correlation optics have been based on light’s intensity fluctuation, regardless of fact that the polarization fluctuation is a basic attribute of natural light. In this work, we uncover the veil of the polarization fluctuation and corresponding photon correlations by proposing a new light source model, termed pseudo-natural light, embodying both intensity and polarization fluctuations. Unexpectedly, the strong antibunching and superbunching effects can be simultaneously realized in such a new source, whose second-order correlation coefficient g ( 2 ) can be continuously modulated across 1. For the symmetric Bernoulli distribution of the polarization fluctuation, particularly, g ( 2 ) can be in principle from 0 to unlimitedly large. In pseudo-natural light, while the bunching effects of both intensity and polarization fluctuations enhance the bunching to superbunching photon correlation, the antibunching correlation of the polarization fluctuation can also be extracted through the procedure of division operation in the experiment. The antibunching effect and the combination with the bunching one will arouse new applications in quantum imaging. As heuristic examples, we carry out high-quality positive or negative ghost imaging, and devise high-efficiency polarization-sensitive and edge-enhanced imaging. This work, therefore, sheds light on the development of multiple and broad correlation functions for natural light.
Recently single photon emission has been observed for systems in which multiple excitons are generated by pulsed excitation. When fast pair annihilation of excitons takes place, finally a single exciton remains and single photon can be emitted. Its efficiency depends on the competition among pair annihilation, unimolecular nonradiative, and radiative processes. The efficiency of single photon emission is usually studied by measuring the correlation of emitted photons after pulsed excitation by the Hanbury-Brown and Twiss method. The photon correlation measured in this method is different from that calculated by taking into account all pairs of emitted photons, which was presented in a previous paper. We calculate the former rigorously for the first time in the case of multiple excitations and compare it with the latter. We also calculate correlation of arrival times of two photons by the Hanbury-Brown and Twiss method. These results should be useful for the analysis of the antibunching measurement by the Hanbury-Brown and Twiss method.
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.