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Physical Review A

Generating mutual coherence from incoherence with the help of a phase-conjugate mirror

Carlos Henrique Monken, Augusto Garuccio, David A. Branning, J. R. Torgerson, Frank A. Narducci, L. Mandeļ

Published Mar 1, 1996• 8 citations
Publisher

Abstract

Although the signal and idler light beams produced in the process of spontaneous parametric down-conversion are mutually incoherent and exhibit no one-photon interference, interference effects should be observable after either the signal or the idler is reflected by a phase-conjugate mirror. The degree of coherence can, in principle, be as large as unity. We refer to the relationship between the signal and the idler produced by down-conversion as anticoherent and introduce a natural measure for the degree of anticoherence. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.1782

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Physical Review A•Jun 1, 1996•27 citations
Although the signal and idler light beams produced in the process of spontaneous parametric down-conversion are mutually incoherent and exhibit no one-photon interference, interference effects should be observable after either the signal or the idler is reflected by a phase-conjugate mirror. The degree of coherence can, in principle, be as large as unity. We refer to the relationship between the signal and the idler produced by down-conversion as anticoherent and introduce a natural measure for the degree of anticoherence. \textcopyright{} 1996 The American Physical Society.
Normally, the signal and idler photons produced in the process of parametric down- conversion exhibit no second-order interference. However, in the presence of an external laser beam that follows the path of the signal photon and induces stimulated down-conversions, one would expect coherence to develop between the down-converted signal and idler beams. We have demonstrated the existence of this phenomenon in an experiment with two down-converters pumped by similar pump beams, in which two mutually coherent laser beams followed the paths of the two down-converted signal photons and induced coherence between the two down- converted idler beams. The induced coherence gives rise to observable interference effects, which are presented.
We discuss the situation in which idler beams from two parametric down-converter crystals are allowed to interfere. We show that, when two mutually coherent signal beams derived from a common laser are injected into the down-converters, the two idler beams can become mutually coherent also. Moreover, the resulting interference pattern can, in principle, have 100% visibility when the number of injected photons per unit down-converter bandwidth is large. This is just the condition for stimulated down-conversion to dominate over spontaneous down-conversion.
Although induced coherence is generally associated with induced or stimulated emission, in the process of spontaneous parametric downconversion of light induced coherence can be generated on its own. This is demonstrated in an experiment in which the signal beams from two coherently pumped downconverters come together and interfere whenever the idler beam from the first downconverter (DC1) passes through and is aligned with the second downconverter (DC2). Misaligning the idlers, or blocking the first idler, makes the interference disappear. More generally, the degree of coherence can be controlled by varying the amplitude of the idler from DC1 that reaches DC2. The interpretation of this nonclassical interference is discussed in terms of the interpretation of the wave function or state vector of the emitted photon.
The correlation properties of the pump field in spontaneous parametric down-conversion are crucial in determining the degree of entanglement of generated signal and idler photons. We find theoretically that continuous-variable entanglement of the transverse positions and momenta of these photons can be achieved only if the coherence of the pump beam is sufficiently high. The positions of signal and idler photons are found to be correlated, even for an incoherent pump. However, the momenta of the signal and idler photons are not anti-correlated, even though transverse momentum is conserved.
A theory of two-photon down-conversion in the presence of mirrors is developed and applied to recent observations of Herzog et al. [Phys. Rev. Lett. 72, 629 (1994)]. The experimentally observed results for counting and coincidence rates as functions of mirror-crystal separations are obtained, and it is shown how the same results may be derived in a simplified formulation that presumes phase-matched signal and idler modes. We account for the observed effects of the finite coherence length of the pump field as well as the signal and idler coherence lengths, which are much shorter than the pump coherence length and have a different physical origin. Our analysis also supports the interpretation of the phenomena observed as being analogous to the modification of single photon spontaneous emission of atoms in cavity QED. \textcopyright{} 1996 The American Physical Society.