Quantifying the mesoscopic quantum coherence of approximate NOON states and spin-squeezed two-mode Bose-Einstein condensates

TL;DR

This paper develops criteria to quantify mesoscopic quantum coherence in approximate NOON states and spin-squeezed BECs, enabling verification of high-fidelity quantum states and revealing atomic coherence with over ten atoms.

Contribution

It introduces two criteria for verifying and quantifying mesoscopic quantum coherence in NOON states and BECs, applicable to experimental data and theoretical models.

Findings

Criteria successfully verify quantum coherence in lossy interferometers.

Application to BEC experiments demonstrates atomic coherence with n≈10.

Correlation measurement relates to interference fringes and spin squeezing.

Abstract

We examine how to signify and quantify the mesoscopic quantum coherence of approximate two-mode NOON states and spin-squeezed two-mode Bose-Einstein condensates (BEC). We identify two criteria that verify a nonzero quantum coherence between states with quantum number different by $n$. These criteria negate certain mixtures of quantum states, thereby signifying a generalised $n$-scopic Schrodinger cat-type paradox. The first criterion is the correlation $\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle\neq0$ (here $\hat{a}$ and $\hat{b}$ are the boson operators for each mode). The correlation manifests as interference fringes in $n$-particle detection probabilities and is also measurable via quadrature phase amplitude and spin squeezing measurements. Measurement of $\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle$ enables a quantification of the overall $n$-th order quantum coherence, thus providing an avenue for high efficiency verification of a high-fidelity photonic NOON states. The second criterion is based on a quantification of the measurable spin-squeezing parameter $\xi_{N}$. We apply the criteria to theoretical models of NOON states in lossy interferometers and double-well trapped BECs. By analysing existing BEC experiments, we demonstrate generalised atomic "kitten" states and atomic quantum coherence with $n\gtrapprox10$ atoms.