The progressive solutions for the Dicke Hamiltonian
A progressive diagonalization scheme for the Dicke Hamiltonian, which describes the interaction of N two-level atoms with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the ground state of the Dicke Hamiltonian with a finite number of atoms can be solved almost exactly by using a progressive diagonalization scheme that involves a one-variable equation at each step. The scheme is efficient for the lower part of the spectrum. Calculated results for ground-state energies, photon numbers, atomic inversions, fluctuations in the latter two quantities, entanglement measures, and Shanon information entropies at resonance points for some finite j cases as functions of the coupling parameter are given. These outcomes show significant changes in the photon number, atomic inversion, and their fluctuations near the critical point where the entanglement measure reaches its maximum value.