Uncovering a Nonclassicality of the Schr\"odinger Coherent State up to the Macro-Domain

TL;DR

This paper demonstrates that the Schrödinger coherent state, traditionally viewed as classical-like, exhibits nonclassical behavior through Leggett-Garg inequality violations, persisting up to macroscopic scales under certain conditions.

Contribution

It reveals a new nonclassicality of the Schrödinger coherent state via LGI violations without ancillary systems, extending the understanding of quantum behavior to macroscopic regimes.

Findings

LGI violation observed in coherent states without ancillary systems

Nonclassicality persists for large mass and amplitude, but becomes harder to detect

Proposes an experimental setup with nano-objects for testing LGI violations

Abstract

The Leggett-Garg inequality (LGI), based on the notions of realism and noninvasive measurability, is applied in the context of a linear harmonic oscillator. It is found that merely through observing at various instants which region of the potential well, the oscillating quantum object is in, the LGI can be violated without taking recourse to any ancillary quantum system. Strikingly, this violation reveals an unexplored nonclassicality of the state which is considered the most "classical-like" of all quantum states, namely the Schr\"odinger coherent state. In the macrolimit, the extent to which such nonclassicality persists for large values of mass and classical amplitudes of oscillation is quantitatively investigated. It is found that while for any given mass and oscillator frequency, a significant quantum violation of LGI can be obtained by suitably choosing the initial peak momentum of the coherent state wave packet, as the mass is sufficiently increased, actual observability of this violation becomes increasingly difficult. A feasible experimental setup for testing the predicted quantum mechanical violation of LGI is suggested using a trapped nano-object of $\sim 10^6-10^9$ amu mass.