Generalized Dicke States

TL;DR

This paper introduces a group-theoretical superoperator method leveraging SU(4) symmetry to analytically solve quantum master equations for systems of atoms or qubits, generalizing Dicke states and reducing computational complexity.

Contribution

It develops a novel superoperator approach based on SU(4) symmetry to generalize Dicke states, enabling analytical solutions and simplifying complex quantum optical problems.

Findings

Analytical solutions for quantum master equations using the new method

Reduction in computational complexity for solving these equations

Illustrative examples demonstrating the effectiveness of the approach

Abstract

Quantum master equations are an important tool in quantum optics and quantum information theory. For systems comprising a small to medium number of atoms (or qubits), the non-truncated equations are usually solved numerically. In this paper, we present a group-theoretical superoperator method that helps solving these equations. To do so, we exploit the SU(4)-symmetry of the respective Lindblad operator and construct basis states that generalize the well-known Dicke states. This allows us to solve various problems analytically and to considerably reduce the complexity of problems that can only be solved numerically. Finally, we present three examples that illustrate the proposed method.