Nota de FísicaPublicado
Functional Methods in the Generalized Dicke Model
M. Aparicio Alcalde; A. L. L. de Lemos
Dados da publicação
- Autores
- M. Aparicio Alcalde; A. L. L. de Lemos
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 04/06/2007
- Descrição
- The Dicke model describes an ensemble of $N$ identical two-level atoms (qubits) coupled to a single quantized mode of a bosonic field. The fermion Dicke model should be obtained by changing the atomic pseudo-spin operators by a linear combination of Fermi operators. The generalized fermion Dicke model is defined introducing different coupling constants between the single mode of the bosonic field and the reservoir, $g_{1}$ and $g_{2}$ for rotating and counter-rotating terms respectively. In the limit $N \rightarrow \infty$, the thermodynamic of the fermion Dicke model can be analyzed using the path integral approach with functional method. The system exhibits a second order phase transition from normal to superradiance at some critical temperature with the presence of a condensate. We evaluate the critical transition temperature and present the spectrum of the collective bosonic excitations for the general case $(g_{1}\neq 0$ and $g_{2}\neq 0)$. There is quantum critical behavior when the coupling constants $g_{1}$ and $g_{2}$ satisfy $g_{1}+g_{2}=(\omega_{0}\,\Omega)^{\frac{1}{2}}$, where $\omega_{0}$ is the frequency of the mode of the field and $\Omega$ is the energy gap between energy eigenstates of the qubits. Two particular situations are analyzed. First, we present the spectrum of the collective bosonic excitations, in the case $g_{1}\neq 0$ and $g_{2}=0$, recovering the well known results. Second, the case $g_{1}=0$ and $g_{2}\neq 0$ is studied. In this last case, it is possible to have a superradiant phase when only virtual processes are introduced in the interaction Hamiltonian. Here also appears a quantum phase transition at the critical coupling $g_{2}=(\omega_{0}\,\Omega)^{\frac{1}{2}}$, and for larger values for the critical coupling, the system enter in this superradiant phase with a Goldstone mode.
- Ano
- 2007
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não