Pendulum beams: a window into the quantum pendulum

Galvez, Enrique J.; Auccapuclla, Fabio J.; Wittler, Kristina L.; Qin, Yingsi

doi:10.1117/12.2510822

Cited by 1 publication

(2 citation statements)

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“…10(a). At first glance, this correlator is qualitatively very similar to the |1 correlator for the QHO, and hence similar to the simple cosine correlator for spin- There are several other systems for which the Schrödinger equation may be solved exactly, including the Hydrogen-like atom [37], the linear potential [30], and the quantum pendulum [29]. The result presented in Sec.…”

Section: B Lg Violations Using the Parity Operatorsupporting

confidence: 60%

“…We also note in passing that this formula unlocks the result of several indefinite integrals in the form of partial spatial overlaps of special functions, which we have not been able to find in the literature. These include, generalised Laguerre polynomials (Morse potential [28]), Mathieu functions (quantum pendulum [29]), Airy functions (triangular potential [30]), and Hypergeometric functions (transformation technique [31]), with the exactly soluble potential leading to the result bracketed.…”

Section: Quasi-probability For Energy Eigenstatesmentioning

confidence: 99%

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

Mawby,

Halliwell

2021

Preprint

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Macrorealism (MR) is the world-view that at all moments of time, a system is definitely in one of the observable states available to it, irrespective of past or future measurements. The Leggett-Garg (LG) inequalities were introduced to test MR and therefore assess for the presence of macroscopic quantum coherence. Since such effects could plausibly be found in various types of macroscopic oscillators, we consider the application of the LG approach to the one-dimensional quantum harmonic oscillator and more general bound systems, using a single dichotomic variable Q given by the sign of the oscillator position. We present a simple method to calculate the temporal correlation functions appearing in the LG inequalities for any bound system for which the eigenspectrum is (exactly or numerically) known. We then apply this result to the quantum harmonic oscillator for a variety of experimentally accessible states, namely energy eigenstates, and superpositions thereof. For the subspace of states spanned by only the ground state and first excited state, we readily find substantial regions of parameter space in which the two and threetime LG inequalities can each be independently violated or satisfied. Similar results are found for four-time LG inequalities. We find that the violations persist (although are reduced) when the sign function defining Q is smeared to reflect experimental imprecision. We also find that LG violations diminish for higher energy eigenstates, showing the expected classicalization. With a Q defined using a more general type of position coarse graining, we find two-time LG violations even in the ground state, a simple example of a feature recently noted by Bose et al. [Phys. Rev. Lett. 120, 210402 (2018)]. We also show that two-time LG violations in a gaussian state are also readily found if the dichotomic variable at one of the times is taken to be the parity operator. To demonstrate the versatility of the technique we developed, we also calculate temporal correlators for the Morse potential, and present a brief analysis of the LG inequalities in this system, where we find significant violations for the first excited state.

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Section: B Lg Violations Using the Parity Operatorsupporting

confidence: 60%