Twisting tensor and spin squeezing

TL;DR

This paper introduces a unified tensor framework for quadratic spin squeezing interactions, deriving equations of motion and identifying optimal squeezing rates, with a proposed optical implementation.

Contribution

It presents a general tensor-based description of spin squeezing, encompassing single- and two-axis twisting, and analyzes optimal squeezing generation conditions.

Findings

Optimal squeezing rate depends on eigenvalue differences of the twisting tensor.

Derived equations of motion for spin squeezing in Gaussian approximation.

Proposed a cascaded optical interferometer with Kerr media as a realization.

Abstract

A unified tensor description of quadratic spin squeezing interactions is proposed, covering the single- and two-axis twisting as special cases of a general scheme. A closed set of equations of motion of the first moments and variances is derived in Gaussian approximation and their solutions are discussed from the prospect of fastest squeezing generation. It turns out that the optimum rate of squeezing generation is governed by the difference between the largest and the smallest eigenvalues of the twisting tensor. A cascaded optical interferometer with Kerr nonlinear media is proposed as one of possible realizations of the general scheme.