Coherent-State Approach for Majorana representation

TL;DR

This paper generalizes the Majorana representation using coherent states to describe quantum states with various symmetries, enabling intuitive visualization and analysis of their evolution and properties.

Contribution

It introduces a unified method to extend the Majorana representation to systems with different symmetries using coherent states, applicable to both finite and infinite systems.

Findings

Star distributions vary with squeezing parameters.

Stars form two orthogonal large circles at specific evolution times.

Method applies to Heisenberg-Weyl, SU(2), and SU(1,1) symmetries.

Abstract

By representing a quantum state and its evolution with the majorana stars on the Bloch sphere, the Majorana representation (MR) provide us an intuitive way to study a physical system with SU(2) symmetry. In this work, based on coherent states, we propose a method to establish generalization of MR for a general symmetry. By choosing a generalized coherent state as a reference state, we give a more general MR for both finite and infinite systems and the corresponding star equations are given. Using this method, we study the squeezed vacuum states for three different symmetries, Heisenberg-Weyl, SU(2) and SU(1,1), and express the effect of squeezing parameter on the distribution of stars. Furthermore, we also study the dynamical evolution of stars for an initial coherent state driven by a nonlinear Hamiltonian, and find that at a special time point, the stars are distributed on two orthogonal large circles.