NMR investigation of contextuality in a quantum harmonic oscillator via pseudospin mapping

TL;DR

This paper uses NMR techniques to experimentally demonstrate quantum contextuality in a quantum harmonic oscillator by encoding its states into nuclear spins and testing inequalities that distinguish quantum from classical behavior.

Contribution

It is the first experimental demonstration of quantum contextuality in a QHO using NMR and pseudospin mapping, including both state-dependent and state-independent inequalities.

Findings

Violation of state-dependent inequality confirming quantum contextuality.

Experimental violation of state-independent inequality with thermal states.

Assessment of quantumness in nuclear spin systems.

Abstract

Physical potentials are routinely approximated to harmonic potentials so as to analytically solve the system dynamics. Often it is important to know when a quantum harmonic oscillator (QHO) behaves quantum mechanically and when classically. Recently Su et. al. [Phys. Rev. A {\bf 85}, 052126 (2012)] have theoretically shown that QHO exhibits quantum contextuality (QC) for a certain set of pseudospin observables. In this work, we encode the four eigenstates of a QHO onto four Zeeman product states of a pair of spin-1/2 nuclei. Using the techniques of NMR quantum information processing, we then demonstrate the violation of a state-dependent inequality arising from the noncontextual hidden variable model, under specific experimental arrangements. We also experimentally demonstrate the violation of a state-independent inequality by thermal equilibrium states of nuclear spins, thereby assessing their quantumness.