NOON state of Bose atoms in the double-well potential via an excited state quantum phase transition

TL;DR

This paper proposes a straightforward method to generate NOON states of Bose atoms in a double-well potential using an excited state quantum phase transition, analyzing the process's fidelity and scalability.

Contribution

It introduces a two-step protocol leveraging excited state quantum phase transition to create NOON states in Bose atoms, with analysis of fidelity and scaling behavior.

Findings

Fidelity depends on ramp rate, atom number, and parameter fluctuations.

Ramp rate scales algebraically with atom number for fixed fidelity.

Protocol effectively produces high-fidelity NOON states.

Abstract

We suggest a simple scheme for creating a NOON state of repulsively interacting Bose atoms in the double-well potential. The protocol consists of two steps. First, by setting atom-atom interactions to zero, the system is driven to the upper excited state. Second, the interactions is slowly increased and, simultaneously, the inter-well tunneling is decreased to zero. We analyze fidelity of the final state to the NOON state depending on the number of atoms, ramp rate, and fluctuations of the system parameters. It is shown that for a given fidelity the ramp rate scales algebraically with the number of atoms.