Higher-Order Adiabatic Elimination in Atom-Cavity Systems and Its Impact on Spin-Squeezing Generation

TL;DR

This paper develops higher-order adiabatic elimination techniques for atom-cavity systems to accurately model spin-squeezing generation, revealing effects missed by standard approximations and improving understanding of scalability limitations.

Contribution

It introduces a third-order adiabatic elimination method for open quantum systems and extends it to conditional dynamics under continuous measurement.

Findings

Higher-order adiabatic elimination captures spin squeezing loss.

Numerical simulations confirm the accuracy of the extended model.

The approach improves understanding of scalability in quantum metrology.

Abstract

Spin-squeezed states are metrologically useful quantum states where entanglement allows for enhanced sensing with respect to the standard quantum limit. Key challenges include the efficient preparation of spin-squeezed states and the scalability of estimation precision with the number $N$ of probes. Recently, in the context of the generation of spin-squeezed states via coupling of three-level atoms to an optical cavity, it was shown that increasing the atom-cavity coupling can be detrimental to spin squeezing generation, an effect that is not captured by the standard second-order adiabatic cavity removal approximation. We describe adiabatic elimination techniques to derive an effective Lindblad master equation up to third order for the atomic degrees of freedom. Numerical simulations show that the spin squeezing scalability loss is correctly reproduced by the reduced open system dynamics, highlighting the role of higher-order contributions. Furthermore, we conjecture an extension beyond leading order of the adiabatic elimination technique to the case of conditional dynamics under quantum non-demolition continuous measurement and fast cavity loss, whose reliability is again confirmed by numerical simulation of the dynamics and the corresponding behavior of spin squeezing as a function of $N$.