Four-mode quantum sensing and Fisher information in a spin-orbit-coupled Bose gas

TL;DR

This paper explores four-mode quantum sensing in spin-orbit-coupled Bose gases, revealing enhanced entanglement and measurement control capabilities beyond traditional two-mode systems, approaching the Heisenberg limit.

Contribution

It introduces a four-mode model for spin-orbit-coupled Bose gases, demonstrating richer entanglement and sensing capabilities compared to previous two-mode studies.

Findings

Four-mode model spans an $4$su(4)$4$ algebra with six SU(2) subspaces.

SOC-induced four-mode couplings enable entanglement-enhanced sensing near the Heisenberg limit.

Tuning the Raman Rabi frequency allows control over optimal measurement directions.

Abstract

Multi-mode squeezing and entanglement are important resources in quantum metrology and sensing. For spin-1/2 Bose-Einstein condensates subject to spin-orbit coupling (SOC), previous studies on spin squeezing have been limited to two-mode systems. In this work, we demonstrate that such a system can naturally construct a four-mode model spanning an $\mathfrak{su}(4)$ algebra with six SU(2) subspaces. Using spin squeezing parameters and quantum Fisher information matrices, we analyze the dynamical evolution of coherent spin states. The results show that, beyond two-mode models, the SOC-induced four-mode couplings give rise to richer entanglement-enhanced sensing approaching the Heisenberg limit across various SU(2) subspaces. Additionally, by tuning a single system parameter (the Raman Rabi frequency), one can selectively control the optimal measurement directions across different subspaces.