Heisenberg Operator Approach for Spin Squeezing Dynamics

TL;DR

This paper develops a Heisenberg operator method to analyze spin squeezing dynamics under the one-axis twisting Hamiltonian, providing more accurate approximations than traditional frozen spin methods.

Contribution

It introduces a perturbative Heisenberg operator approach for spin squeezing dynamics, improving accuracy over existing approximations.

Findings

The method yields more accurate results than the frozen spin approximation.

Perturbative solutions effectively describe the time evolution of spin squeezing.

Comparison with exact numerics validates the improved accuracy.

Abstract

We reconsider the one-axis twisting Hamiltonian, which is commonly used for generating spin squeezing, and treat its dynamics within the Heisenberg operator approach. To this end we solve the underlying Heisenberg equations of motion perturbatively and evaluate the expectation values of the resulting time-dependent Heisenberg operators in order to determine approximately the dynamics of spin squeezing. Comparing our results with those originating from exact numerics reveals that they are more accurate than the commonly used frozen spin approximation.