Fresnel–Hadamard complementary transformation in quantum optics

Abstract

Based on the newly-developed coherent-entangled state representation we propose the so-called Fresnel–Hadamard complementary transformation, which is unitary. The new unitary operator plays the role of both Fresnel transformation for and Hadamard transformation for respectively. Physically, and could be a symmetric beamsplitter's two output fields. We show that the two transformations are concisely expressed in the coherent-entangled state representation as a projective operator in integration form.

Keywords:

• Hadamard–Fresnel complementary transform
• IWOP technique
• beamsplitter

Acknowledgement

This work was supported by the National Natural Science Foundation of China under Grant 10874174 and the President Foundation of Chinese Academy of Science specialized research fund for the doctoral program of higher education (No. 20070358009).