Two-photon coherent states of the radiation field

TLDR

Two‑photon coherent states generalize minimum‑uncertainty wave packets and correspond to the radiation states of ideal two‑photon lasers far above threshold under the self‑consistent‑field approximation. The paper introduces two‑photon coherent states for quantum‑optics applications and develops their properties, distinguishing them from ordinary coherent states. The authors generate two‑photon coherent states by applying unitary operators tied to quadratic Hamiltonians to ordinary coherent states, thereby deriving their detailed properties. These states exhibit minimum‑uncertainty noise, remain robust to small losses, and produce distinct photocount distributions, enabling applications beyond those of coherent states or one‑photon lasers.

Abstract

The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.