NOON-state formation from Fock-state Bose-Einstein condensates

TL;DR

This paper proposes a theoretical method to generate NOON states using two Fock state Bose-Einstein condensates in a modified interferometer with side measurements and feedforward correction, enabling high-precision phase measurements.

Contribution

It introduces a novel scheme for creating NOON states from Bose-Einstein condensates using side measurements and feedforward, advancing quantum metrology techniques.

Findings

Successful theoretical scheme for NOON state generation from BECs.

Conversion of phase superpositions into NOON states via beam splitter.

Application of NOON states for enhanced phase measurement precision.

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 local realism (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-Zehnder interferometer can lead to the creation of the NOON state in which $a$ and $b$ refer to arms of the interferometer and $N$ is a subset of the total number of particles in the two condensates. The modification of the interferometer involves making {}"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 if the phase states are orthogonal. When they are not orthogonal, a {}"feedforward" correction circuit is shown to convert them into proper form so a NOON results. We apply the NOON to the measurement of phase. Here the NOON experiment is equivalent to one in which a large molecule passes through two slits. The NOON components can be recombined in a final beam splitter to show interference.