Coherent States, Superpositions of Coherent States and Uncertainty Relations on a M\"obius Strip

TL;DR

This paper explores coherent states and their superpositions on a M"obius strip, analyzing their topological properties, periodic behaviors, and uncertainty relations, with implications for quantum computation.

Contribution

It extends previous work by analyzing periodic behaviors and uncertainty relations of coherent states on a M"obius strip, highlighting their advantages for quantum computation.

Findings

Coherent states on M"obius strip exhibit unique periodic behaviors.

Superpositions of coherent states show distinct uncertainty relations.

Potential applications in continuous variable quantum computation are identified.

Abstract

Since symmetry properties of coherent states (CS) on M\"obius strip (MS) and fermions are closely related, CS on MS are naturally associated to the topological properties of fermionic fields. Here we consider CS and superpositions of coherent states (SCS) on MS. We extend a recent propose of CS on MS (Cirilo-Lombardo, 2012 [25]), including the analysis of periodic behaviors of CS and SCS on MS and the uncertainty relations associated to angular momentum and the phase angle. The advantage of CS and SCS on MS with respect to the standard ones and potential applications in continuous variable quantum computation are also addressed.