English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The Leggett-Garg (LG) inequalities were introduced to test for the possiblepresence of macroscopic quantum coherence. Since such effects may be found invarious types of macroscopic oscillators, we consider the application of the LGapproach to the one-dimensional quantum harmonic oscillator and also to moregeneral bound systems, using a single dichotomic variable $Q$ given by the signof the oscillator position. We present a simple method to calculate thetemporal correlation functions appearing in the LG inequalities for any boundsystem for which the eigenspectrum is (exactly or numerically) known. We applythis result to the quantum harmonic oscillator for a variety of experimentallyaccessible states, namely energy eigenstates, and superpositions thereof. Forthe subspace of states spanned by only the ground state and first excitedstate, we readily find substantial regions of parameter space in which the LGinequalities at two, three and four times can each be independently violated orsatisfied. We also find that the violations persist, although are reduced, whenthe sign function defining $Q$ is smeared to reflect experimental imprecision.For higher energy eigenstates, we find that LG violations diminish, showing theexpected classicalization. With a $Q$ defined using a more general type ofposition coarse graining, we find two-time LG violations even in the groundstate. We also show that two-time LG violations in a gaussian state are readilyfound if the dichotomic variable at one of the times is taken to be the parityoperator. To demonstrate the versatility of the approach, we repeat much of theLG analysis for the Morse potential, finding qualitatively similar physicalresults.

Leggett-Garg tests for macrorealism in the quantum harmonic oscillator and more general bound systems