Volume 54, number 5 OPTICS COMMUNICATIONS 1 July 1985 INTENSITY DEPENDENCE OF THE NORMALIZED INTENSITY CORRELATION FUNCTION IN PARAMETRIC DOWN-CONVERSION ~ S. FRIBERG, C.K. HONG and L. MANDEL Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA Received 27 February 1985 The question under what conditions a normalized intensity correlation function 2~12(r) depends strongly on the average light intensity is discussed. It is shown that in the process of spontaneous parametric down-conversion the strong correlation between signal and idler photons makes )~lz(r) inversely proportional to the light intensity of either the signal or idler beam. This conclusion is then confirmed experimentally by two-time photoelectric correlation measurements. 1. Introduction It is well known that when a fluctuating, quasi- monochromatic light beam of instantaneous light in- tensity I(t) falls on a photoelectric detector, the dif- ferential probability P(1)(t) for the emission of a pho- toelectron and its detection within a short time inter- val At is given by [1,2] p(1)( t ) = ~(I( t)) At. (1) a is a constant characteristic of the detector, and ( ) denotes the average over the ensemble. Despite the fact that I(t) here represents a classical field in- tensity, it is often convenient to express I(t) in units of photons per second, in which case a is a dimension- less measure of detector quantum efficiency. More generally, when two light beams of intensi- ties Ii(t) and I2(t) fall on two photodetectors of quantum efficiencies cq, a2, the joint probability of photoelectric detections at both detectors at times t 1 within At 1 and t 2 within At 2 is given by e!2)( t" ,~z • t2) = al ct2 (I1 (tl)I2(t2))Atl At2" (2) It is often convenient to introduce the normalized in- tensity correlation function This work was supported by the National Science Founda- tion and by the Office of Naval Research. 0 030-4018/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) (/1 (tl) I2(t2) ) X12(t I , t2) --= (ii(t1))(i2(t2)) -- 1 (A/1 (t 1 ) A/2(t2)) = (/l(tl))(I2(t2)) ' (3) which allows us to rewrite the joint probability in the form P(12)(tl , t2) =P~l)(tl)t~21)(t2)[1 + ~12(tl, t2) 1. (4) The first term represents the random contribution to the joint probability attributable to uncorrelated events, whereas the second describes correlated detec- tions. If the electromagnetic field is quantized instead of being classical, then the light intensity becomes a Hilbert space operator [(t) (all Hilbert space operators are labelled by the caret ~), and the ensemble average (/(t)) has to be interpreted as a quantum mechanical expectation. Moreover, in the two-time correlation function, the operators have to be written in normal order and in time order [3], so that P(11 )(tl ) = t~l (I1 (tl))Atl, P(21)(t2) = ct2(/2(t2))At2, (5) P(12)(tl , t2) = C~l c~2(: 11 (tl)]2(t2):)Atl At2" (6) With these changes and with X12(tl, t2) defined by 311