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The Journal of Chemical Physics

Superradiant quantum phase transition can be easier with disorder

Bing Gu

Published Sep 16, 2026• 0 citations
Publisher

Abstract

We investigate the influence of strong static disorder on the transition frequency of molecules to the superradiant quantum phase transition in the Dicke model. A spin-fermion mapping is employed to recast the Dicke model into a coupled fermion-boson problem, which is subsequently treated by the non-equilibrium Green's function formalism. An analytical expression for the critical point as a function of the disorder strength is derived. In particular, there exists a regime where increasing the disorder strength reduces the critical coupling strength.

DOI
10.1063/5.0331821

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arXiv:1104.0648•Apr 4, 2011•1 citation
We investigate the influence of strong static disorder on the transition frequency of molecules to the superradiant quantum phase transition in the Dicke model. A spin-fermion mapping is employed to recast the Dicke model into a coupled fermion-boson problem, which is subsequently treated by the non-equilibrium Green's function formalism. An analytical expression for the critical point as a function of the disorder strength is derived. In particular, there exists a regime where increasing the disorder strength reduces the critical coupling strength.
We introduce and study the disordered Dicke model in which the spin-boson couplings are drawn from a random distribution with some finite width. Regarding the quantum phase transition, we show that, when the standard deviation $\ensuremath{\sigma}$ of the coupling strength gradually increases, the critical value of the mean coupling strength $\ensuremath{\mu}$ gradually decreases, and after a certain $\ensuremath{\sigma}$ there is no quantum phase transition at all; the system always lies in the superradiant phase. We derive an approximate expression for the quantum phase transition in the presence of disorder in terms of $\ensuremath{\mu}$ and $\ensuremath{\sigma}$, which we numerically verify. Studying the thermal phase transition in the disordered Dicke model, we obtain an analytical expression for the critical temperature in terms of the mean and standard deviation of the coupling strength. We observe that, even when the mean of the coupling strength is zero, there is a finite temperature transition if the standard deviation of the coupling is sufficiently high. Disordered couplings in the Dicke model will exist in quantum dot superlattices, and we also sketch how they can be engineered and controlled with ultracold atoms or molecules in a cavity.
We introduce and study the disordered Dicke model in which the spin-boson couplings are drawn from a random distribution with some finite width. Regarding the quantum phase transition we show that when the standard deviation σσσ of the coupling strength gradually increases, the critical value of the mean coupling strength μμμ gradually decreases and after a certain σσσ there is no quantum phase transition at all; the system always lies in the super-radiant phase. We derive an approximate expression for the quantum phase transition in the presence of disorder in terms of μμμ and σσσ, which we numerically verify. Studying the thermal phase transition in the disordered Dicke model, we obtain an analytical expression for the critical temperature in terms of the mean and standard deviation of the coupling strength. We observe that even when the mean of the coupling strength is zero, there is a finite temperature transition if the standard deviation of the coupling is sufficiently high. Disordered couplings in the Dicke model will exist in quantum dot superlattices, and we also sketch how they can be engineered and controlled with ultracold atoms or molecules in a cavity.
We investigate a generalized Dicke model by introducing two interacting spin ensembles coupled with a single-mode bosonic field. Apart from the normal to superradiant phase transition induced by the strong spin-boson coupling, interactions between the two spin ensembles enrich the phase diagram by introducing ferromagnetic, antiferromagnetic and paramagnetic phases. The mean-field approach reveals a phase diagram comprising three phases: paramagnetic-normal phase, ferromagnetic-superradiant phase, and antiferromagnetic-normal phase. Ferromagnetic spin-spin interaction can significantly reduce the required spin-boson coupling strength to observe the superradiant phase, where the macroscopic excitation of the bosonic field occurs. Conversely, antiferromagnetic spin-spin interaction can strongly suppress the superradiant phase. To examine higher-order quantum effects beyond the mean-field contribution, we utilize the Holstein-Primakoff transformation, which converts the generalized Dicke model into three coupled harmonic oscillators in the thermodynamic limit. Near the critical point, we observe the close of the energy gap between the ground and the first excited states, the divergence of entanglement entropy and quantum fluctuation in certain quadrature. These observations further confirm the quantum phase transition and offer additional insights into critical behaviors.
In this study, the energy spectrum and thermal equilibrium states of the finite-size Dicke-Stark model were numerically obtained within the extended coherent state space by solving the dressed master equation for strongly coupled light-atom systems. The critical point of the superradiant phase transition in the infinite-size Dicke-Stark model was analytically derived using the mean-field approach and confirmed with numerical calculation. Under thermal equilibrium conditions, analyses of the negativity, zero-time-delay two-photon correlation function, and atom-spin squeezing parameters in the finite-size Dicke-Stark model reveal that as the coupling strength increases, the light field undergoes a transition from photon bunching to anti-bunching and then back to bunching. The Stark field can modulate both the maximum and minimum values of the two-photon correlation function and their corresponding coupling strengths. At low temperatures, the system exhibits entanglement and spin squeezing. As temperature rises, entanglement gradually diminishes, while strong coupling facilitates the preservation of entanglement in the system state. Atom-spin squeezing spin squeezing is highly sensitive to temperature and vanishes rapidly with increasing temperature. This work contributes to the fundamental understanding of quantum phenomena in Dicke-Stark systems.
The Dicke model can exhibit quantum phase transition between the normal and the superradiant phases when the strength of the light-matter coupling exceeds the ultrastrong-coupling regime. However, it is challenging to observe this phase transition in practical systems due to limited coupling strength or finite two-photon A2{A}^{2}A2 terms. Here we show that by applying a periodic modulation to the frequency of the two-level systems in a standard Dicke model in the strong-coupling regime, an anisotropic Dicke model with tunable rotating and counter-rotating terms in the ultrastrong-coupling regime can be achieved. We calculate the ground state and the excitation spectrum of this model in terms of the modulation parameters. Our result shows that the superradiant phases can be observed in cavity- or circuit-quantum electrodynamics systems with strong coupling.
The Dicke Hamiltonian describes the simplest quantum system with atoms interacting with photons: N two level atoms inside a perfectly reflecting cavity which allows only one electromagnetic mode. It has also been successfully employed to describe superconducting circuits which behave as artificial atoms coupled to a resonator. The system exhibits a transition to a superradiant phase at zero temperature. When the interaction strength reaches its critical value, both the number of photons and of atoms in excited states in the cavity, together with their fluctuations, exhibit a sudden increase from zero. Employing symmetry-adapted coherent states it is shown that these properties scale with the number of atoms, that their reported divergences at the critical point represent the limit when this number goes to infinity, and that in this limit they remain divergent in the superradiant phase. Analytical expressions are presented for all observables of interest, for any number of atoms. Comparisons with exact numerical solutions strongly support the results.