Quantum dynamics generated by the two-axis counter-twisting Hamiltonian

TL;DR

This paper investigates the quantum dynamics of a spin ensemble under the two-axis counter-twisting Hamiltonian, revealing fixed points, squeezing, and quantum states relevant for high-precision metrology, with exact Fisher information and scaling analysis.

Contribution

It provides exact results for quantum Fisher information and squeezing, and explains system size scaling using a Gaussian approach, advancing understanding of quantum metrological states.

Findings

Presence of four neutrally stable fixed points and two saddle points influences dynamics.

High levels of squeezing are generated, useful for quantum metrology.

Exact quantum Fisher information and squeezing parameters are computed.

Abstract

We study the quantum dynamics generated by a two-axis counter-twisting Hamiltonian from an initial spin coherent state in a spin-$1/2$ ensemble. A characteristic feature of the two-axis counter-twisting Hamiltonian is the existence of four neutrally stable and two saddle unstable fixed points. The presence of the last one is responsible for a high level of squeezing. The squeezing is accompanied by the appearance of several quantum states of interest in quantum metrology with Heisenberg-limited sensitivity, and we show fidelity functions for some of them. We present exact results for the quantum Fisher information and the squeezing parameter. Although, the overall time evolution of both changes strongly with the number of particles, we find that they have regular dynamics for short times. We explain scaling with the system size by using a Gaussian approach.