Quantum Analysis of Subharmonic Generation Via First-Order Hamiltonian

TL;DR

This paper demonstrates that a unified Hamiltonian approach effectively describes subharmonic generation, accurately predicting photon statistics and quadrature squeezing in twin light beams with either same or different frequencies.

Contribution

It establishes that the same Hamiltonian can be used for subharmonic generation regardless of the frequency relationship, providing new insights into photon statistics and squeezing.

Findings

Mean photon number for same-frequency beams is half that of different-frequency beams.

Maximum quadrature squeezing reaches 50% below vacuum level.

Maximum local quadrature squeezing is 74.9% below vacuum level.

Abstract

We have established that the mean photon number obtained employing the conventional Hamiltonian for the twin light beams with the same frequency, produced by a subharmonic generator, is half that of the twin light beams with different frequencies. In view of this, we have found it to be quite appropriate to describe the process of subharmonic generation by the same Hamiltonian regardless of whether the twin light beams have the same or different frequencies. Applying this Hamiltonian, we have calculated the photon statistics and quadrature squeezing for the signal-signal and the signal-idler modes. Obviously, this time the mean photon number of the signal-signal modes is exactly the same as that of the signal-idler modes. In addition, we have found that the maximum global quadrature squeezing of the signal-signal or the signal-idler modes is 50$\%$ below the vacuum-state level and the maximum local quadrature squeezing of the signal-signal modes is 74.9$\%$ below the same level.