Uncertainty relations in quantum optics. Is the photon intelligent?

TL;DR

This paper explores various quantum uncertainty relations involving phase and photon number, analyzing states that minimize uncertainty products or sums, with implications for understanding quantum optical states.

Contribution

It extends uncertainty relations to arbitrary functions of phase and photon number, and investigates states that minimize these uncertainties in quantum optics.

Findings

Derived uncertainty relations for functions of phase and photon number.

Identified states that minimize uncertainty products and sums.

Analyzed properties of intelligent states in quantum optics.

Abstract

The Robertson -- Schr\"{o}dinger, Heisenberg -- Robertson and Trifonov uncertainty relations for arbitrary two functions $f_{1}$ and $f_{2}$ depending on the quantum phase and the number of photons respectively, are given. Intelligent states and states which minimize locally the product of uncertainties $(\Delta f_{1})^{2}\cdot (\Delta f_{2})^{2}$ or the sum $(\Delta f_{1})^{2}+(\Delta f_{2})^{2}$ are investigated for the cases $f_{1}=\phi,\exp{(i\phi)}, \exp{(-i\phi)}, \cos{\phi}, \sin{\phi}$ and $f_{2}=n$.