Time evolution of interacting bosons through squeezing Hamiltonians

TL;DR

This paper analyzes the complete time evolution of interacting bosonic systems with squeezing Hamiltonians, revealing a formal equivalence between single- and two-mode cases and predicting a critical coupling transition causing exponential mode population growth.

Contribution

It demonstrates the formal equivalence of single- and two-mode squeezing dynamics and derives differential equations for their evolution, applicable across various quantum systems.

Findings

Single- and two-mode squeezing cases are mathematically equivalent.

Identifies a critical coupling value causing exponential growth in mode populations.

Provides analytical tools for predicting system dynamics in quantum applications.

Abstract

We study the full time evolution of one- and two-mode bosonic quantum systems that interact through single- and two-mode squeezing Hamiltonians. We establish that the single- and two-mode cases are formally equivalent, leading to the same differential equations encoding the full time evolution. These differential equations can be easily employed in any application. We analytically predict a dramatic transition in the population of the modes when the coupling takes a specific critical value, leading to exponential growth of the excitation population. We discuss the validity, scope and generality of our results.