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1 = (. use visual .net code 128 code set a maker tocreate uss code 128 with .net iPhone OS H 1 . H 2. + . V 1 . V 2 ).. (9.54). Optical test of quantum mechanics Fig. 9.14.

Schematic fo r Franson s experiment. The path lengths of the interferometer are adjustable as indicated..

The two-crystal scheme VS .NET barcode 128 described is an ef cient method of generating polarization states and was rst used by Kwiat et al. [24].

Their results violated Bell s inequality by 21 standard deviations. Not all experiments demonstrating a violation of a Bell-type inequality using down-converted light have involved polarization entanglement. Rarity and Tapster [25] have done experiments with momentum entanglement of the beams.

Another, proposed by Franson [26], involves time energy uncertainty. We now discuss this experiment..

Franson s experiment Consider the experiment Code 128 Code Set A for .NET al setup pictured in Fig. 9.

14. A pair of photons, signal and idler, is simultaneously produced by the down-converter and directed toward the interferometers. There is no single-photon interference inside a single interferometer as the photon coherence lengths are much shorter than the differences between path lengths of the arms of the interferometers.

However, there is two-photon interference in the coincidence detection between the detectors D1 and D2 . To see how this comes about, consider the following. To reach the detectors, the photons can both take the short paths (S, S), both take the long paths (L, L), the short long (S, L) or the long short (L, S) paths.

The rst two cases are indistinguishable as we do not know when the photons are created. Both detectors will tend to re simultaneously, assuming identical path lengths in the two interferometers. The last two cases are distinguishable because of the delay between the clicking of the two detectors, the detector of the photon taking the short path will click rst.

So, the last two cases are distinguishable from each other and from the rst two cases in which the detectors click simultaneously. Under experimental conditions, the fast electronics of the correlator can be set for a suf ciently narrow timing window such that counts from the. 9.8 Applications of down-converted light to metrology two distinguishable pro Code128 for .NET cesses are rejected. This has the effect of post-selecting (reducing) the two-photon output state to be.

= 1 (. S 1 . S 2 . + ei L 1 1 . L 2 2 ),. (9.55). evidently another form visual .net Code128 of Bell state, where we have assumed that S1 = S2 = S but that L 1 and L 2 can be adjusted as indicated in Fig. 9.

14. The phase , the relative phase between the (S, S) and (L, L) processes, is the sum of the relative phases acquired by the individual photons:. = s L 1 /c + i L 2 /c s + i s i = ( L 1 + L 2) + ( L1 2 2 p ( L 1 + L 2) 2. L 2) (9.56). valid as L 1 L 2 is t aken to be small compared to the inverse bandwidth of the signal and idler frequencies s and i . The frequency p = s + i is, of course, the frequency of the pump eld. If we now use the Feynman dictum of adding amplitudes associated with indistinguishable processes, the probability for coincident two-photon detection is.

Pcoin = 1 1 1 + ei 2 = [1 + cos ] 4 2 p 1 ( L 1 + L 2) 1 + cos = 2 2 (9.57). This result exhibits 10 Visual Studio .NET Code 128A 0% visibility, meaning that the minimum of the probability of coincident detection is zero. This in turn means that the photons entering the two interferometers become anti-correlated: if one takes the short path the other takes the long path, and vice versa.

The meaning of the maximum is that the photons become correlated in the interferometers: either both take the short path or both take the long. No classical or hidden variable model can predict a visibility greater that 50%. Fringes of visibility greater than 70.

7% violate a Bell-type inequality. The experiments of Kwiat et al. [27] exhibit a visibility of 80.

4 0.6%. Other experimental realizations of the Franson experiment are those of Ou et al.

[28], Brendel et al. [29], and Shih et al. [30].

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