The law of propagation of coherence function

Ulvi Yurtsever

The lossy propagation law (generalization of Lambert-Beer's law for classical radiation loss) for non-classical, dual-mode entangled states is derived from first principles, using an infinite-series of beam splitters to model continuous photon loss. This model is general enough to accommodate stray-photon noise along the propagation, as well as amplitude attenuation. An explicit analytical expression for the density matrix as a function of propagation distance is obtained for completely general input states with bounded photon number in each mode. The result is analyzed numerically for various examples of input states. For N00N state input, the loss of coherence and entanglement is super exponential, as predicted by a number of previous studies. However, for generic input states, where the coefficients are generated randomly, the decay of coherence is very different; in fact no worse than the classical Beer-Lambert law. More surprisingly, there is a plateau at a mid-range interval in propagation distance where the loss is in fact sub-classical, following which it resumes the classical rate. The qualitative behavior of the decay of entanglement for two-mode propagation is also analyzed numerically for ensembles of random states using the behavior of negativity as a function of propagation distance.

Jan Peřina

Rémi Carminati, John C. Schotland

George L. Lamb, Marlan O. Scully, F. A. Hopf

The description of coherent optical pulse propagation in terms of coupled Maxwell and Schroedinger- Bloch equations in slowly varying envelope approximation possesses conservation laws in addition to those of field energy and field momentum. Comparison with preliminary numerical results has shown that these higher conservation laws can be used to predict the amplitude of each of the 2pi pulses into which an intense coherent pulse may decompose as it propagates through an attenuator. In the present paper a comparison with more extensive numerical results is carried out. It is shown that over a wide range of variation of the parameters involved the conservation laws yield results in agreement with those obtained through numerical computation.

Wei Wang, Mitsuo Wada Takeda

For a complete and lucid discussion of quantum correlation, we introduced two new first-order correlation tensors defined as linear combinations of the general coherence tensors of the quantized fields and derived the associated coherence potentials governing the propagation of quantum correlation. On the basis of these quantum optical coherence tensors, we further introduced new concepts of scalar, vector and tensor densities and presented some related properties, such as conservation laws and the wave-particle duality for quantum correlation, which provide new insights into photon statistics and quantum correlation.

Soma, Gaius