Multicomponent cat states with sub-Planckian structures and their optomechanical analogues

TL;DR

This paper introduces generalized superpositions of coherent states with enhanced and isotropic sub-Planckian phase-space structures, demonstrating their potential for quantum information and their realization in optomechanical systems.

Contribution

It presents new generalized compass states with improved phase-space features and shows their feasibility in optomechanical systems, extending prior superposition states.

Findings

Generalized states exhibit isotropic sub-Planckian structures.

Superpositions with at least six coherent states maintain phase-space sensitivity.

Optomechanical systems can generate these states with similar phase-space features.

Abstract

We investigate the superposition of coherent states, emphasizing quantum states with distinct Wigner phase-space features relevant to quantum information applications. In this study, we introduce generalized versions of the compass state, which display enhanced phase-space characteristics compared with the conventional compass state, typically a superposition of four coherent states. Our findings reveal that, unlike sub-Planckian structures and phase-space sensitivity of the compass state, these generalized states produce isotropic sub-Planckian structures and sensitivity to phase-space displacements. We demonstrate that these desirable phase-space characteristics are maintained in superpositions comprising at least six distinct coherent states. Furthermore, we show that increasing the number of coherent states in the superposition preserves these characteristics, provided the number remains even. We examine an optomechanical system capable of generating the proposed quantum states, resulting in optomechanical counterparts with nearly identical phase-space structures, thereby suggesting the feasibility of physically realizing these generalized compass states.