Hanbury Brown and Twiss

With the advent of extremely large aperture telescopes, there is a growing interest in the statistical properties of the field emitted by astronomical sources (Dravins, 2001). The goal is to obtain important physical information concerning the source by looking at the statistical characteristics of the light it emits. This domain was pioneered by two radio astronomers, Hanbury Brown and Twiss (1956) who measured the intensity correlation function + r))... 

The characteristic property of the autocorrelation function was first demonstrated experimentally by Hanbury Brown and Twiss (1956) using two radiotelescopes. As T goes to zero, (r) goes to two. 

The analysis of the interference phenomenon can be extended into higher-order correlation functions. The first experimental demonstration that such correlations exist in optical fields was given by Hanbury-Brown and Twiss [14], who measured the second-order correlation function of a thermal held. 

Figure 8. Photon-pair correlation analysis of single molecule emission, (a) The temporal separation of photon pairs can be analyzed by a Hanbury-Brown and Twiss experiment, where the fluorescence photon flux is divided by a 50/50 beamsplitter and detected by two avalanche photo diodes (APDs). By delaying the arrival time of signals from one detector, simultaneous photon events can be detected if the delay time is known, (b) Photon-pair correlation analysis of - 1000 molecules of Rhodamine 6G probed individually by the setup shown in (a). Single fluorescent molecules can only emit one molecule at a time (photon antibunching), which results in an anti-correlation of photon events for times shorter than the fluorescence lifetime. By fitting such a histogram, the fluorescence lifetime and the number of molecules probed in the excitation spot can be extracted. For an increasing number of molecules, the dip at time zero begins to become less well expressed, because the probability for simultaneous photon emission increases.

Hanbury-Brown, R. and Twiss, R. (1956) Correlation between photons in two coherent beams of light. Nature, 177, 27-29. 

Let us stress that the operational definition of the quantum phase of radiation [47] is also based on the use of bilinear forms in the photon operators. In the simplest form, the idea of the operational approach to the phase difference can be illustrated with the aid of the two-port interferometer shown in Fig. 11 (see Refs. 14 and 47 for more detailed discussion). The two incident monochromatic (or quasimonochromatic) light beams are combined by a symmetric beamsplitter oriented at 45° to each beam. The resultant intensities emerging from each output port are measured by the two photodetectors connected with a comparator (computer) as in the Hanbury-Brown-Twiss interferometer [85] (also see Refs. 14, 15, and 86). Following Noh et al. [47], we denote by a and 2 the photon annihilation operators, describing the field at the two input ports, and by a and 04 the corresponding operators at the two output ports. Then... 

A famous example for the application of intensity-correlation interferometry in astronomy is the Hanbury Brown-Twiss interferometer sketched in Fig. 7.33. In its original form it was intended to measure the degree of spatial coherence of starlight (Vol. 1, Sect. 2.8) [945] from which diameters of stars could be determined. In its modern version it measures the degree of coherence and the photon statistics of laser radiation in the vicinity of the laser threshold [946]. 

Fig. 7.33 (a) Basic principle of the Hanbury Brown-Twiss intensity-correlation interferometer in astronomy (b) its application to measurements of spectral characteristics and statistics of laser radiation... 

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