Ghost Imaging with Thermal Light: Comparing Entanglement and ClassicalCorrelation

Abstract

We analytically show that it is possible to perform coherent imaging by using the classical correlation of two beams obtained by splitting incoherent thermal radiation. The case of such two classically correlated beams is treated in parallel with the configuration based on two entangled beams produced by parametric down-conversion, and a basic analogy is pointed out. The results are compared in a specific numerical example.The topic of entangled imaging has attracted noteworthy attention in recent years [1,2,3,4,5,6,7,8]. This tecnique exploits the quantum entaglement of the state generated by parametric down-conversion (PDC), in order to retrieve information about an unknown object. In the regime of single photon pair production of PDC, the photons of a pair are spatially separated and propagate through two distinct imaging systems. In the path of one of the photons an object is located. Information about the spatial distribution of the object is not obtained by detection of this photon, but rather by registering the coincidence counts as a function of the other photon position [1,2,3,4,5]. In the regime of a large number of photon pairs, this procedure is generalized to the measurement of the signal-idler spatial correlation function of intensity fluctuations [6]. Such a two-arm configuration provides more flexibility in comparison with standard imaging procedures, as e.g. the possibility of illuminating the object with one light frequency and performing a spatially resolved detection in the other arm with a different light frequency, or of processing the information from the object by only operating on the imaging system of arm 2 [5,6]. In addition, it opens the possibility of performing coherent imaging by using, in a sense, spatially incoherent light, since each of the two down-converted beams taken separately is described by a thermal-like mixture and only the two-beam state is pure(see e.g. [5] and [6]).In this paper we show that it is possible to implement such a scheme using a truly incoherent light, as the radiation produced by a thermal (or quasi-thermal) source. A comparison between thermal and biphoton emission is performed in [9], where an underlying duality accompanies the mathematical similarity between the two cases. Here, we considerCorrelated imaging with incoherent thermal light. The thermal beam a is splitted into two beams which travel through two distinct imaging systems, described by their impulse response functions h1 and h2. Arm 1 includes an object. Detector D1 is either a point-like detector or a bucket detector. Beam 2 is detected by an array of pixel detectors. v is a vacuum field. a different scheme (Fig.1), appropriate for correlated imaging, in which a thermal beam is divided by a beam-splitter (BS) and the two outgoing beams are handled in the same way as the PDC beams in entangled imaging. A basic analogy between the PDC and the thermal case emerges from our analysis. Currently there is a debate whether quantum entanglement is necessary to perform correlated imaging [5,6,7,8]. ...

Frequency doubling of incoherent light from a superluminescent diode in a periodically poled lithium niobate waveguide crystal

“…The ASE yielded a measured thermal-like photon statistics with a measured DSOC of g (2) (0) = 1.9±0.1. Although we were not able to measure the DSOC of the frequency doubled light, we want to point out that the bunching is possibly enhanced for the SHG light.…”

“…The resulting autocorrelation function was filtered and the DSOC was extracted as a function of the time delay. The extracted DSOC g (2) (τ ) is shown in Fig. 3.…”

“…We determine the DSOC function g (2) (0) of the ASE to be 1.9±0.1, validating the thermal-like photon statistics of the light source and therefore its temporal incoherence. Despite the non optimized scenario, our results show that efficient nonlinear frequency conversion of thermal-like light without the aid of coherent radiation can be achieved.…”

“…This enhanced bunching would be of high interest for applications like microscopy [9] or ghost imaging [2] as well as fundamental quantum optical experiments.…”

“…Some of these applications [2][3][4] exploit the quantum nature of light via the photon statistics, which can be determined by the degree of second order coherence (DSOC) g (2) (0). Light with thermal-like photon statistics will yield a DSOC g (2) (0) of 2 which is called photon bunching [6], while coherent light will give a value of 1. Due to the short coherence times of thermal-like radiation a measurement of the DSOC could not be demonstrated until recently.…”