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Conference on Lasers and Electro-Optics

Influence of walk-off and dispersion on the coherence of parametric fluorescence

Antonio Picozzi, Marc Haelterman

Published Aug 29, 2005• 0 citations
Publisher

Abstract

Summary form only given. We consider the basic problem of spontaneous parametric generation from quantum noise fluctuations. Various experiments revealed that in the parametric fluorescence process a transition occurs between two regimes respectively characterized by the incoherence of the initial quantum noise and the coherence of the generated signal and idler fields. We investigate the mechanism responsible for the incoherence-to-coherence transition.

DOI
10.1109/iqec.2000.908144

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Summary form only given. We consider the basic problem of spontaneous parametric generation from quantum noise fluctuations. Various experiments revealed that in the parametric fluorescence process a transition occurs between two regimes respectively characterized by the incoherence of the initial quantum noise and the coherence of the generated signal and idler fields. We investigate the mechanism responsible for the incoherence-to-coherence transition.
We consider the basic problem of spontaneous parametric generation from quantum noise fluctuations in the presence of a continuous plane-wave pump. We show, both numerically and analytically, that the walk-off between the down-converted fields is the key ingredient that leads to the generation of coherent fields in the parametric process. Along these lines, our theory reveals that, in the absence of walk-off, diffraction and chromatic dispersion in usual quadratically nonlinear materials only lead to incoherent erratic dynamics. Moreover, a two-dimensional study shows that, when the walk-off is exclusively temporal (or spatial), the parametric process is not able to yield the generation of spatially (or temporally) coherent fields. This study sheds light on the problem of coherence in parametric fluorescence and, in particular, allows us to explain various recent experimental observations.
Pumping a nonlinear crystal by an intense radiation results in the optical parametric generation of photons in two modes (the signal and the idler). The quantized electromagnetic field in these modes is described by a continuous-variable quantum state, which is entangled if the pump is a coherent state produced by a laser. The signal and the idler modes remain populated by photons even if the pump becomes incoherent (dephased by a medium, superposed with a thermal state, or produced by an alternative source such as the superluminescent diode). However, the incoherent pump does effect the entanglement and purity of the signal and the idler modes, which is of vital importance for quantum information applications and interferometry. Here we develop an approach to infer the signal-idler entanglement and purity for a general quantum incoherent pump with the given Glauber-Sudarshan function. We show that the signal-idler entanglement is extremely sensitive to the phase distribution of the pump and illustrate our findings by physically relevant examples of the incoherent pump: the noisy coherent state, slightly dephased and phase-averaged coherent states, the thermal state, and states modulated by the Kerr medium. The effect of an incoherent pump on the combined quadratures is discussed as well.
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.
We investigate the appearance of spontaneous coherence in the parametric emission from planar semiconductor microcavities in the strong coupling regime. Calculations are performed by means of a quantum Monte Carlo technique based on the Wigner representation of the coupled exciton and cavity-photon fields. The numerical results are interpreted in terms of a nonequilibrium phase transition occurring at the parametric oscillation threshold: below the threshold, the signal emission is incoherent, and both the first and the second-order coherence functions have a finite correlation length which becomes macroscopic as the threshold is approached. Above the threshold, the emission is instead phase coherent over the whole two-dimensional sample and intensity fluctuations are suppressed. Similar calculations for quasi-one-dimensional microcavities show that in this case the phase coherence of the signal emission has a finite extension even above the threshold, while intensity fluctuations are suppressed.