Hörmann and Colleagues Models Self-Consistent Functional for Understanding Dicke Mode Interactions

Max Hörmann, and colleagues present a thermodynamic account of Dicke models, revealing how collective coupling between cavity modes and interacting matter dictates the emergence of superradiance. Integrating out the cavity mode results in a self-consistent functional linking magnetisation and matter energy, demonstrating that photon creation relies solely on pre-existing phases within the matter itself. Superradiant phase transitions arise not from crossing energy sheets, but as folds within a single equation of state, and a framework is provided for understanding these transitions through local rules and spectral signatures. Specifically, the analysis of the Dicke-Ising model yields exact Landau coefficients and maps out four distinct phases, while investigations into other magnetic systems, including Rydberg-blockade chains, triangular antiferromagnets, and Heisenberg chains, reveal diverse behaviours ranging from persistent antiferromagnetic phases to spectrally silent onsets.

Exact Landau coefficients reveal origins of superradiant phase transitions and antiferromagnetic

Landau coefficients are now exact for the Dicke-Ising model, representing a significant improvement over previous approximations that depended on perturbative methods. Previously, achieving this precision was difficult due to the complexity of accurately mapping the interaction between collective coupling and magnetic interactions; a closed-form solution now circumvents these limitations. Superradiant first-order transitions originate from folds within a single equation of state, fundamentally altering the understanding of how these transitions occur, rather than from crossings of separate energy sheets.

Investigations into diverse magnetic systems, including Rydberg-blockade chains, demonstrate the antiferromagnetic superradiant phase persists as a finite one-dimensional wedge, exhibiting varied behaviours and expanding the model’s applicability. The Dicke-Ising model’s exact Landau coefficients provide a precise description of its phase transitions, defining the boundaries between magnetic states and dictating whether transitions are continuous or abrupt. Detailed analysis of the model’s ‘stationarity curve’, a graphical representation of all possible self-consistent states, confirms superradiant transitions arise from folds within this single curve, a fundamentally new understanding of the process. Extending investigations to other magnetic systems, such as Rydberg-blockade chains, reveals the antiferromagnetic superradiant phase persists as a finite one-dimensional wedge; the compass chain exhibits a BKT-functional onset, while the Heisenberg and XX chains display spectrally silent first-order onsets. Although these results provide a thorough thermodynamic account, they currently do not extend to finite-temperature effects or the impact of disorder, limiting their direct application to real-world experimental systems.

Deriving Magnetisation Functionals via Cavity Mode Elimination

By integrating out the cavity mode, effectively removing its influence from the calculations, an exact self-consistent functional relating magnetisation to the bare energy of the matter was derived; this is a mathematical description of how the material’s internal energy changes with its magnetic order. This technique simplifies the complex interactions within the Dicke model, a simplified model of light and matter interactions, by focusing on the collective behaviour of the matter itself. A method to understand the collective behaviour of matter interacting with light was developed, utilising a simplified model known as the Dicke model.

Removing the influence of a ‘cavity mode’, the space where light and matter interact, created a precise relationship between a material’s magnetisation and its internal energy. This approach avoids the need to calculate complex interactions directly, instead focusing on the overall properties of the material. Phase boundaries were mapped and the order of transitions determined through calculations, utilising a functional derived from previous theoretical work and refined through numerical analysis.

Mapping superradiance beyond phase transitions and towards realistic material systems

The precise mapping of these superradiant transitions offers a compelling alternative to established models reliant on identifying distinct phases separated by sharp boundaries. However, the analysis remains firmly rooted in the thermodynamic limit, a simplification that neglects the influence of finite system sizes and temperature fluctuations. This limitation raises a key tension; while the theoretical framework elegantly describes collective behaviour in idealised conditions, its direct relevance to real-world materials, where imperfections and thermal noise are unavoidable, remains an open question.

Despite relying on an idealised system that simplifies complex realities, the detailed mapping of superradiant transitions remains valuable. The work provides a new theoretical language for understanding how collective behaviour emerges in materials, which is important even if real materials deviate from the perfect conditions assumed in the modelling. The analysis reveals superradiant transitions, shifts in a material’s collective behaviour triggered by light, arise from a single, continuous relationship between a material’s properties, not abrupt changes between separate states. Establishing an exact mathematical description of how collective coupling between light and interacting matter dictates these transitions simplifies previous models that relied on identifying distinct phases. By focusing on the internal energy of the matter itself, photon creation requires only pre-existing phases within the material, opening new avenues for understanding and potentially controlling these phenomena.

The research demonstrated that superradiant transitions, shifts in a material’s collective behaviour triggered by light, arise from a single, continuous relationship between a material’s properties rather than abrupt changes between separate states. This finding offers a new theoretical language for understanding collective behaviour in materials, simplifying previous models that identified distinct phases. Calculations mapped these transitions using a functional derived from theoretical work and refined through numerical analysis, revealing that photon creation requires only pre-existing phases within the material. The authors established the boundaries between phases and the order of transitions, finding the antiferromagnetic superradiant phase persists as a finite one-dimensional wedge.