Squeezing with classical Hamiltonians

TL;DR

This paper derives a simple formula for the maximum squeezing rate in classical Hamiltonian systems, providing rules for optimal phase space rotation to achieve fastest squeezing, applicable to various quantum models.

Contribution

It introduces a universal formula for the initial squeezing rate based on classical Hamiltonian second derivatives and optimal phase space rotations.

Findings

Maximum squeezing rate depends on second derivatives of Hamiltonian.

Optimal phase space rotation aligns the state for fastest squeezing.

Results apply to models like Kerr, Jaynes-Cummings, and spin squeezing.

Abstract

A simple formula is derived for the maximum squeezing rate which occurs at the initial stages of the squeezing process: the rate only depends on the second partial derivatives of a classical Hamiltonian. Rules for optimum rotation of the phase space are found to keep the state optimally located and oriented for fastest squeezing. These operations transform the phase-space point of interest into a saddle point with opposite principal curvatures. Similar results are found for the Bloch-sphere phase space and spin squeezing. Application of the general formulas is illustrated by several model examples including parametric downconversion, Kerr nonlinearity, Jaynes-Cummings interaction, and spin squeezing by one-axis twisting and two-axis countertwisting.