Quantum interference photon correlations

We concentrate on the role of quantum interference in the correlation of photons emitted from a coherently driven V-type atom, recently analyzed by Swain et al. [58]. We calculate the normalized second-order two-time correlation function g (R, t R, t + x) for the fluorescent field emitted from a three-level V-type atom driven by a coherent laser field coupled to both atomic transitions. The fluorescence field is observed by a single detector located at a point R = RR, where R is the unit vector in the direction of the observation. 

In Fig. 16, we plot the correlation functions (148) and (149) for nondegenerate transitions with A = 5T. Again, the solid line represents p = 0.99 and the dashed line, p 0. It is apparent from the graphs that with quantum interference (p = 0.99), there are very strong correlations of photons on the, v) —> 12) transition, whereas the photons are strongly anticorrelated on the ja) > 2) transition. The correlation function g (x) oscillates with 2 /2i l and attains the maximum value at time r = (2 /20) V. Moreover, the correlations decay at a very low rate and it takes a time in excess of 30071 before it gets close to unity. The correlation function 15 (x) oscillates with /2il and in the presence of quantum interference is smaller than unity for all times, whereas the values can be larger than unity, with the maximum value of around 2.8, for... 

As we have seen from Figs. 14-16, the effect of quantum interference on the second-order correlation function, is very sensitive to the splitting A of the excited levels. For degenerate excited levels (A = 0), the photon emissions are similar to those of a two-level atom, independent of quantum interference. For large splittings, the correlation functions g (x) and gj (x). ij = 1,3 are smaller than unity for all times x, while (x) exhibits strong correlations (gj (x) 3> 2) for x (2 20,)-17i, which decay at a very low rate. 

Interest in the polarization correlation of photons goes back to the early measurements of the linear polarization correlation of the two photons produced in the annihilation of para-positronium which were carried out as a result of a suggestion by Wheeler that these photons, when detected, have orthogonal polarizations. Yang subsequently pointed out that such measurements are capable of giving information on the parity state of nuclear particles that decay into two photons. In addition, the polarization correlation observed in the two-photon decay of atoms is considered to be one of the few phenomena where semiclassical theories of radiation are inadequate and it is necessary to invoke a full quantum theory of radiation. The effect has also been used to demonstrate the phenomenon of quantum interference. ... 

Let us quote the text from Ref. [15] "...a, Quantum eraser configuration in which electro-optic shutters separate microwave photons in two cavities from the thin-film semiconductor (detector wall) which absorbs microwave photons and acts as a photodetector, b, Density of particles on the screen depending upon whether a photocount is observed in the detector wall ( yes ) or not ( no ), demonstrating that correlations between event on the screen and the eraser photocount are necessary to retrieve the interference pattern."... 

It is not difficult to associate various second-order correlation functions G - x Xf,XcX ) = abcd] with (7.15). (When two beams are present, we must consider a space-time point for each of the beams so that the index in takes on two values [7.34].) Thus, the first term, ls may be associated with [1111], the second with [2222], the third with [1221] and [2112], the fourth with the four permutations of [1112], the fifth with the four permutations of [2221], and the sixth with the four permutations of [1212], with h + c. The coefficient of each term in (7.15) is there fore equal to the number o f permutations in the appropriate form of the correlation function for that term. The physical interpretation follows immediately the first two dc terms in (7.15) arise from the absorption of two monochromatic photons, both from the same beam. The third dc term, which exists in two permutations with b = c, arises from the two ways in which two single monochromatic photons can be absorbed, one from each beam. The fourth and fifth terms correspond to the absorption of a single monochromatic photon from one of the beams plus a single nonmonochromatic photon which must be associated with both beams. These terms therefore contribute currents at the difference frequency (tOi —analogy with the single-quantum heterodyne interference term [7.12-14]. The final term corresponds to the absorption of two nonmonochromatic photons, and therefore varies at double the difference frequency, i.e., at 2(o), —coj) clearly there is no analogous process possible in the one-quantum case. 

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