Creation of NOON states by double Fock-state/Bose-Einstein condensates

TL;DR

This paper proposes a theoretical method to generate NOON states using two Bose-Einstein condensates in a modified interferometer, enabling superposition and interference effects useful for quantum metrology and tests of quantum mechanics.

Contribution

It introduces a novel approach to create NOON states from Bose-Einstein condensates via conditional measurements and a modified interferometer setup.

Findings

The method successfully produces NOON states with condensates.

Interference patterns confirm superposition of phase states.

Detection of which-path information destroys interference.

Abstract

NOON states (states of the form $|N>_{a}|0>_{b}+|0>_{a}|N>_{b}$ where $a$ and $b$ are single particle states) have been used for predicting violations of hidden-variable theories (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state/Bose-Einstein condensates as sources in a modified Mach Zender interferometer can lead to the creation of the NOON state in which $a$ and $b$ refer to arms of the interferometer and $N$ is the total number of particles in the two condensates. The modification of the interferometer involves making conditional ``side'' measurements of a few particles near the sources. These measurements put the remaining particles in a superposition of two phase states, which are converted into NOON states by a beam splitter. The result is equivalent to the quantum experiment in which a large molecule passes through two slits. The NOON states are combined in a final beam splitter and show interference. Attempts to detect through which ``slit'' the condensates passed destroys the interference.