Role of Matter Interactions in Superradiant Phenomena

Abstract

The superradiant phenomenon, usually described by the Dicke model, is a hallmark of strong light-matter interaction. We explore how matter-matter interactions influence this phenomenon by performing ground-state simulations of Dicke-like models with both isotropic and anisotropic spin couplings. We find that Ising-type interactions produce two qualitatively distinct phase boundaries, one of which gives rise to an antiferromagnetic-normal phase connected to the superradiant regime via a first-order phase transition. Under anisotropic couplings, we uncover a strongly correlated phase where in-plane spin order coexists with superradiance, exhibiting sublinear scaling of the photon occupation per site and power-law decay of spin correlations. Furthermore, superradiance can be strengthened by tuning either isotropic or anisotropic interactions, highlighting the role of intrinsic many-body correlations in shaping light-matter quantum phases.

Figures (4)

• Figure 1: Schematic of the Dicke-Heisenberg model. The system comprises an ensemble of two-level qubits, embedded in an optical cavity. They interact anisotropically with their nearest neighbors through an exchange interaction $\vb{J}$ and couple collectively to a single cavity mode with strength $g$. Dissipative effects include photon loss at rate $\kappa$ and spontaneous emission at rate $\gamma$, both of which are assumed to be slow compared to the coherent coupling (i.e., $g^2\gg 2\gamma\kappa$).
• Figure 2: Ground-state properties of the Dicke model obtained via the hybrid variational method: (a) average energy, (b) average photon occupation and absolute magnetization. Simulations are performed for $N = 200$. The insets show the iteration errors at each step of the self-consistent iterations for the representative case $g = 0.25$ system. The energy is converged to a threshold of $10^{-12}$, while photon number and magnetization are converged to $10^{-8}$.
• Figure 3: (a) Representative spin configurations in phases of the Dicke--Ising model. (b) Magnetization and average photon number calculated for $g=0.5$ and $N=100$. (c) Phase diagram of the Dicke--Ising model, where the solid (dashed) lines denote second-order (first-order) transitions between the normal and superradiant phases. The normal phase is further divided by a critical coupling $J_c$ into regions with distinct spin configurations. The vertical arrow marks the Dicke model.
• Figure 4: Phases of the Dicke--XXZ model. (a) Photon number per site $\langle n \rangle /N$ for various $J_z$ and $g$, obtained use $N=24$. The two arrows indicate the critical couplings at zero light-matter coupling ($g=0$). (b) Scaling laws of $\langle n \rangle /N$ in different phases: the normal phase (red: $J_z=1$, $g=0.01$) exhibit a $\langle n \rangle/N \propto 1/N$ decay; the superradiant phase (blue: $J_z=-1.6$, $g=0.4$) shows $\langle n \rangle \propto N$; a sublinear scaling arises in the intermediate regime (purple: $J_z=-1.6$, $g=0.01$). (c) Spatial profile of the spin-spin correlation $\langle s_i^x s_{i+r}^x \rangle$ for $N=32$. Deep in the normal phase (red: $J_z=-5$, $g=0.01$) it decays exponentially, while the superradiant phase supports long-range order. The intermediate regime displays power-law decay, consistent with quasi-long-range XY-type order [blue and purple the same as in (b)].