The thermodynamic equilibrium properties of the Dicke Hamiltonian for a collection of spin- 1 / 2 particles interacting via magnetic dipole interaction with a single mode of the radiation field and with each other by spin-spin interaction are analysed and the conditions for the existence of a super-radiant phase transition are derived. It is shown, using the approximate long-range spin-spin interaction (MI), in the Dicke Hamiltonian, that the conditions for the existence of the super-radiant phase transition are invariant with respect to isotropic MI whether or not the A 2 term is included.The thermodynamic equilibrium properties of the Dicke Hamiltonian for a collection of spin- 1 / 2 particles interacting via magnetic dipole interaction with a single mode of the radiation field and with each other by spin-spin interaction are analysed and the conditions for the existence of a super-radiant phase transition are derived. It is shown, using the approximate long-range spin-spin interaction (MI), in the Dicke Hamiltonian, that the conditions for the existence of the super-radiant phase transition are invariant with respect to isotropic MI whether or not the A 2 term is included.

Journal of Physics A Mathematical and GeneralJan 1, 19787 citations

Phase States in Quantum Optics

F. Rocca

Springer eBooksJan 1, 19780 citations

Nonequilibrium phase transition in a spin-1 Dicke model

Zhang Zhiqiang, Chern Hui Lee, Ravi Kumar +4 more

We realize a spin-1 Dicke model using magnetic sub-levels of the lowest F=1 hyperfine level of $^{87}$ Rb atoms confined to a high finesse cavity. We study this system under conditions of imbalanced driving, which is predicted to have a rich phase diagram of nonequilibrium phases and phase transitions. We observe both super-radiant and oscillatory phases from the cavity output spectra as predicted by theory. Exploring the system over a wide range of parameters, we obtain the boundaries between the normal, super-radiant and the oscillatory phases, and compare with a theoretical model.We realize a spin-1 Dicke model using magnetic sub-levels of the lowest F=1 hyperfine level of $^{87}$Rb atoms confined to a high finesse cavity. We study this system under conditions of imbalanced driving, which is predicted to have a rich phase diagram of nonequilibrium phases and phase transitions. We observe both super-radiant and oscillatory phases from the cavity output spectra as predicted by theory. Exploring the system over a wide range of parameters, we obtain the boundaries between the normal, super-radiant and the oscillatory phases, and compare with a theoretical model.

arXiv:1612.06534OpticaMar 31, 2017178 citations

Quantum phase transitions of light

Andrew D. Greentree, Charles Tahan, Jared H. Cole +1 more

arXiv:cond-mat/0609050Nature PhysicsNov 26, 2006788 citations

Revisiting the phase transitions of the Dicke model

Pragna Das, Auditya Sharma

The Dicke model exhibits a variety of phase transitions. The quantum phase transition from the normal phase to the super-radiant phase is marked by a dramatic change in the scaling of the participation ratio. We find that the ground state in the super-radiant phase exhibits multifractality manifest in the participation ratio scaling as the square root of the full Hilbert-space dimension. The thermal phase transition temperature, for which an exact analytical expression may be obtained using the partition function, is strikingly captured by the mutual information between two spins. In the excited-state quantum phase transition within the super-radiant phase, there are two cutoff energies; the central energy bands between the lower and upper cutoff energies show distinctly different behaviors. While the level statistics of the central band is Wigner-Dyson, the lower and upper bands show mixed behavior that is closer to Poisson than Wigner-Dyson. This finding is corroborated with the aid of several eigenvector properties: von Neumann entanglement entropy between spins and bosons, the mean photon number, concurrence between two spins, and participation ratio.The Dicke model exhibits a variety of phase transitions. The quantum phase transition from the normal phase to the super-radiant phase is marked by a dramatic change in the scaling of the participation ratio. We find that the ground state in the super-radiant phase exhibits multifractality manifest in the participation ratio scaling as the square root of the full Hilbert-space dimension. The thermal phase transition temperature, for which an exact analytical expression may be obtained using the partition function, is strikingly captured by the mutual information between two spins. In the excited-state quantum phase transition within the super-radiant phase, there are two cutoff energies; the central energy bands between the lower and upper cutoff energies show distinctly different behaviors. While the level statistics of the central band is Wigner-Dyson, the lower and upper bands show mixed behavior that is closer to Poisson than Wigner-Dyson. This finding is corroborated with the aid of several eigenvector properties: von Neumann entanglement entropy between spins and bosons, the mean photon number, concurrence between two spins, and participation ratio.

arXiv:2109.06227Physical Review AMar 30, 202216 citations

Quantum phase transitions of light

Charles Tahan, Andrew D. Greentree, Jared H. Cole +1 more

Bulletin of the American Physical SocietyMar 9, 20070 citations

We realize a spin-1 Dicke model using magnetic sub-levels of the lowest F=1 hyperfine level of

^{87}

Rb atoms confined to a high finesse cavity. We study this system under conditions of imbalanced driving, which is predicted to have a rich phase diagram of nonequilibrium phases and phase transitions. We observe both super-radiant and oscillatory phases from the cavity output spectra as predicted by theory. Exploring the system over a wide range of parameters, we obtain the boundaries between the normal, super-radiant and the oscillatory phases, and compare with a theoretical model.