Quantum phases and entanglement properties of an extended Dicke model

Abstract

We study a simple model describing superradiance in a system of two-level atoms interacting with a single-mode bosonic field. The model permits a continuous crossover between integrable and partially chaotic regimes and shows a complex thermodynamic and quantum phase structure. Several types of excited-state quantum phase transitions separate quantum phases that are characterized by specific energy dependences of various observables and by different atom-field and atom-atom entanglement properties. We observe an approximate revival of some states from the weak atom-field coupling limit in the strong coupling regime.

Excited-state quantum phase transitions and their manifestations in an extended Dicke model

“…At zero temperature, there is a purely quantum phase transition (second-order qpt) at a critical coupling λ c [37]. Recently, the model was also used as an example of various types of esqpts [14,18,38,39,40,41,42]. Note that experimental realization of the Dicke Hamiltonian with a strong coupling [43,44] puts the model to the forefront of present theoretical and experimental interest.…”

“…The advantage of taking the δ = 0 limit is that an additional conserved quantity appears, namely M = n + m + j = n + n ⋆ , where n is the number of photons, m the pseudo-spin z-projection, and n ⋆ = m + j the number of excitations in the atomic ensemble. Whereas the model for δ 0 has f = 2 degrees of freedom, the limiting δ = 0 dynamics can be reduced to f = 1 [14,18,42], hence is integrable. We also note that the extended Dicke Hamiltonian (15) commutes with a parity operator Π = e iπM for all values of both parameters λ and δ.…”

“…z , we restrict our present analysis to the single irreducible representation with j = N/2, which is fully symmetric with respect to exchange of atoms (for the discussion of other choices of j see, e.g., [18,42]). The strength of interaction is controlled by parameter λ ranging from zero (non-interacting limit) to infinity (strongcoupling limit).…”

“…Its energy spectrum is split into mutually noninteracting subsets numbered by the conserved quantity M. As a result we can restrict our analysis on a single-M case. To do so, we apply a suitable canonical transformation [18] on (17) and obtain new classical Hamiltonian of the form…”

“…This singularity is present in the spectral level density and in related quantities, e.g., in the flow rate, which is an average slope of the quantum spectrum when λ is varied. The existence of an esqpt also influences the canonical and microcanonical thermodynamics [9,10,11,12], decoherence and relaxation processes [13,14,15], driven and dissipative dynamics [16,17], and entanglement properties [18].…”