Rapid Generation of a Macroscopic Schr\"odinger Cat State of Atoms with Parity-Independent Orientation

TL;DR

This paper demonstrates a rapid method to generate macroscopic Schr"odinger cat states of atoms using one-axis-twist squeezing, enabling control of atomic ensemble orientation and entanglement with a single atom, independent of atom number parity.

Contribution

It introduces a novel technique combining echo configuration and one-axis-twist squeezing to quickly produce large-scale Schr"odinger cat states with parity-independent orientation control.

Findings

The squeezing propagator can be expressed as a sum of rotation operators under specific conditions.

A hidden order exists in the squeezed state even when the Husimi distribution appears irregular.

The method allows for deterministic entanglement between an atom and an ensemble.

Abstract

We show that using the process of one-axis-twist squeezing in an echo configuration, it is possible to control the orientation of the macroscopic magnetic moment of a large number of atoms by manipulating the quantum state of a single atom that is physically isolated from the ensemble. With this control technique, it is also possible to entangle an ensemble with a single atom deterministically, which mimics the thought experiment known as the Schr\"odinger cat. In addition, this technique would make it possible to generate a mesoscopic Schr\"odinger cat state for a large number of atoms far more rapidly that the conventional process for generating such a state, with an orientation that is independent of the parity of the number of atoms. Apart from the echo configuration, we have also investigated the behavior of one-axis-twist squeezing for some special values of the squeezing parameter. We find that the squeezing propagator can be expressed as the sum of n rotation operators if the product of n and the squeezing parameter equals pi, where n is a non-zero integer. A direct consequence of this property of one-axis-twist squeezing is that there is a hidden order in a squeezed state generated under this condition even if its Husimi quasi-probability distribution looks irregular.