# One- and two-axis squeezing of atomic ensembles in optical cavities

## TL;DR

This paper compares one-axis and two-axis squeezing schemes for atomic ensembles in optical cavities, showing that two-axis provides more squeezing in ideal conditions, but both are limited by decoherence, with specific advantages depending on initial states.

## Contribution

It extends previous work by demonstrating how to realize a two-axis twisting Hamiltonian in a cavity setup and compares its performance to the one-axis scheme under various conditions.

## Key findings

- Two-axis scheme achieves more squeezing without decoherence.
- Both schemes scale as (NC)^(1/2) under decoherence.
- Dissipative one-axis scheme attains higher fidelity for certain initial states.

## Abstract

The strong light-matter coupling attainable in optical cavities enables the generation of highly squeezed states of atomic ensembles. It was shown in [Phys. Rev. A 66, 022314 (2002)] how an effective one-axis twisting Hamiltonian can be realized in a cavity setup. Here, we extend this work and show how an effective two-axis twisting Hamiltonian can be realized in a similar cavity setup. We compare the two schemes in order to characterize their advantages. In the absence of decoherence, the two-axis Hamiltonian leads to more squeezing than the one-axis Hamiltonian. If limited by decoherence from spontaneous emission and cavity decay, we find roughly the same level of squeezing for the two schemes scaling as (NC)^(1/2) where C is the single atom cooperativity and N is the total number of atoms. When compared to an ideal squeezing operation, we find that for specific initial states, a dissipative version of the one-axis scheme attains higher fidelity than the unitary one-axis scheme or the two-axis scheme. However, the unitary one-axis and two-axis schemes perform better for general initial states.