Mesoscopic Quantum Superposition of Generalized Cat State: A Diffraction limit

TL;DR

This paper investigates the properties of mesoscopic quantum superpositions of generalized cat states, analyzing their orthogonality and phase space interference, and draws parallels with diffraction patterns and the van Cittert-Zernike theorem.

Contribution

It provides an asymptotic expression for the overlap function of large-scale generalized cat states and links quantum superposition properties with classical diffraction phenomena.

Findings

Overlap function matches diffraction patterns for large numbers of states.

Large phase space support ensures distinguishability of constituent states.

Overlap function behavior aligns with the van Cittert-Zernike theorem.

Abstract

The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The mesoscopic superposition of the generalized cat state is correlated with the corresponding state overlap function, controlled by the sub-Planck structures arising from phase space interference. The asymptotic expression of this overlap function is evaluated and the validity of large phase space support and distinguishability of the constituent states, in which context the asymptotic limit is achieved, are discussed in detail. For large number of coherent states, uniformly located on a circle, the overlap function significantly matches with the diffraction pattern for a circular ring source with uniform angular strength. This is in accordance with the van Cittert-Zernike theorem, where the overlap function, similar to the mutual coherence function, matches with a diffraction pattern. The physical situation under consideration is delineated in phase space by utilizing Husimi-Q function.