Driven-dissipative four-mode squeezing of multilevel atoms in an optical cavity

TL;DR

This paper develops a theoretical framework for generating multi-mode squeezed states using multilevel atoms in optical cavities, revealing the potential for up to four quadrature squeezing and analyzing finite-size effects.

Contribution

It generalizes previous models to multilevel systems, providing analytic methods to predict multi-mode squeezing and its scaling in realistic experimental setups.

Findings

Up to four quadrature squeezing can be achieved.

Finite-size effects limit the maximum squeezing attainable.

Scaling of squeezing with atom number N is analytically derived.

Abstract

We utilize multilevel atoms trapped in a driven resonant optical cavity to produce scalable multi-mode squeezed states for quantum sensing and metrology. While superradiance or collective dissipative emission by itself has been typically a detrimental effect for entanglement generation in optical cavities, in the presence of additional drives it can also be used as an entanglement resource. In a recent work [Phys. Rev. Lett. 132, 033601 (2024)], we described a protocol for the dissipative generation of two-mode squeezing in the dark state of a six-level system with only one relevant polarization. There we showed that up to two quadratures can be squeezed. Here, we develop a generalized analytic treatment to calculate the squeezing in any multilevel system where atoms can collectively decay by emitting light into two polarization modes in a cavity. We show that in this more general system up to four spin squeezed quadratures can be obtained. We study how finite-size effects constrain the reachable squeezing, and analytically compute the scaling with $N$. Our findings are readily testable in current optical cavity experiments with alkaline-earth-like atoms.