Mean-field phase diagrams of spinor bosons in an optical cavity

TL;DR

This paper investigates the phase diagrams of spinor bosons in an optical cavity using mean-field theory, revealing various magnetic and supersolid phases, including density-modulated quantum superpositions, with implications for experiments.

Contribution

It introduces a comprehensive mean-field analysis of spinor bosons in a cavity, identifying new supersolid phases and detailed phase diagrams for both homogeneous and trapped systems.

Findings

Identified antiferromagnetic Mott insulator and ferromagnetic density wave phases.

Discovered three types of supersolid phases with different spin and density patterns.

Mapped phase diagrams for systems with and without total magnetization constraints.

Abstract

The plethora of possible ground states of spinor bosons placed in an external lattice and a cavity is revisited. We discuss the simplest case when the external lattice nodes coincide with the antinodes of the cavity field. We analyze the problem within the grand-canonical mean-field approach, considering both the homogeneous system and the nonhomogeneous case with a harmonic trapping potential. Due to the spin degree of freedom, in the homogeneous case we treat the system in a twofold manner: we impose the physically relevant total-magnetization constraint, while also discussing the minimization landscape for the full unconstrained problem. In the latter, by combining analytical arguments with numerical calculations based on the Gutzwiller ansatz, we show that the system exhibits two types of magnetic phases: an antiferromagnetic Mott insulator (AFM) and a ferromagnetic density wave (FDW). In addition, three distinct supersolid phases emerge, characterized by different patterns of spin and density imbalances. In case of the zero total magnetization, only two of the three supersolid regimes survive, and the FDW phases are replaced by NOON density waves (NDW). These new ground states present density-modulated quantum superpositions of the underlying spin components of the bosons. Finally, we present the phase diagram of the trapped system, which is directly relevant for future experiments.