Polarization Correlation and Coherence Lengths of Two-Photon Radiation

Frederik Jozef Belinfante

Alan J. Duncan, H. Kleinpoppen, Z. A. Sheikh

The Paper first summarizes fundamental aspects and results of the quantum electrodynamical theory of the two-photon radiationfromthe decay of the metastable 2 2 S 1/2 atomic hydrogen state. After a brief description of the second improved Stirling two-photon coincidence experiment polarization correlations of the two-photon decay are described in which both two or three linear polarizers are applied in order to test predictions of such correlations based upon quantum mechanics and local realistic theories (i.e., Einstein-Podolsky-Rosen type experiments). It is particularly noticeable that the three-polarizer coincidence measurement provided the largest difference (about 40%) between the Bell limits of local realistic theories and quantum mechanics so far. Apart from confirming in addition the correlations of right-right and left-left circularly polarized two-photon correlations a new type of coherence analysis of the two-photon radiation has been carried out experimentally and theoretically. A result of it is the measured coherence time of τ coh = 1.2 · 10 −15 s and coherence length of l coh = c · τ coh = 350 nm of the two-photon emission. By applying a theoretical model of the two-photon radiation linked to cascade transitions the coherence length can be estimated to l coh ≈ 100 nm in agreement by order of magnitude with the experimental data.

Giuseppe Faraci, A. Pennisi

Hans Kleinpoppen, Alan J. Duncan, H. J. Beyer +1 more

The Stirling two-photon source based upon the decay of metastable atomic hydrogen has been applied to study angular and polarization correlations and the photon coherence length, and to an experimental confirmation of the Breit-Teller hypothesis. Selecting opposite directions for the detection of the two photons in coincidence, polarization correlations were measured with both linear and circular polarizers inserted into the photon paths. The results of these Einstein-Podolski-Rosen (EPR) type experiments favour quantum mechanics over local realistic theories in common with all other published studies. By inserting an additional linear polarizer in one detection arm it was, further-more, possible to test for the first time (and exclude) a new class of local realistic theories. The coherence length of the photons in one detection arm was measured by the introduction (in that arm) of retardation ("multiwave") plates oriented with their fast axes at 45° with respect to the linear polarization which in turn is determined by the linear polarizer in the other detection arm. If the retardation is just sufficient to prevent the two orthogonal components emerging from the multiwave plate from interfering as a result of their path difference, the polarization of the coincidence signal is destroyed. The coherence length of 350 nm found in this way is extremely short, only approximately 1.5 times the median wavelength of 243 nm of the two-photon decay. The corresponding coherence time t coh = l coh / c is approximately 10 −15 s which confirms that it is not determined by the long lifetime of the 2S state (~ 1/8 s) but by the virtual states which mediate the two-photon decay. Given measurements at enough values of retardation this method can, in principle, be used to determine the spectral distribution of the two-photon decay. The current measurements also confirm the Breit-Teller hypothesis that the two-photon decay is unaffected by fine structure and hyperfine structure interactions.

E. Wolf

Z. A. Sheikh

We report a novel method of determining the coherence length of photons produced in the two-photon decay of metastable atomic deuterium by observing the depolarization of the photons in what is essentially a true single-photon interference experiment. In the Stirling source two photons propagating in the ±z directions are detected in coincidence. The degree of polarization of the radiation emerging from a multiwave plate placed on one side of the source as a function of the optical path difference 6 introduced by the multiwave plate between the orthogonally polarized components is determined by measuring the Stokes' parameters. The results confirm the dependence of the depolarizing effect of the multiwave plate on 6, agree with the quantum mechanical predictions and allow a measurement to be made of the coherence length of single photons of the two-photon pair. \nWe also report the results t>f an experiment which, for the first time, demonstrates the action of an achromatic half-wave plate on the polarization state of the two-photon radiation emitted by atomic deuterium in the metastable 2Sv, state The results agree with the quantum mechanical predictions and confirm the hypothesis of Breit and Teller that the fine and hyperfine interaction play no role in the emission process.