tive Hamiltonian is constructed in real space. Thus, the magnetization σ z and σ x are evaluated for the ground state to detect phase transitions. In constrast, a non-Hermtian effective Hamiltonian is constructed in this paper to determine the phase transi-tion in the single-excitation subspace of extended Jaynes-Cumming model. The Jaynes-Cummings model with or without rotating-wave approximation plays a major role to study the interaction between atom and light. We investigate the Jaynes-Cummings model beyond the rotating-wave approximation. Treating the counter-rotating terms as periodic drivings, we solve the model in the extended Floquet space. It is found that the full energy spectrum folded in the quasi Abstract. We present a general qubit-boson interaction Hamiltonian that describes the Jaynes-Cummings model and its extensions as a single Hamiltonian class. Our model includes non-linear The Hamiltonian (20.1) describes one of the few exactly solvable models in quan-tum optics. Since the interaction Hamiltonian only couples pairs of atom-field states {|n+1 g |n e },theJaynes-CummingsHamiltonian(20.1)decouplesintoaninfinitedirect productof2×2-matrixHamiltonians Hˆ n |n+1 g |n e = (n+1)ω − 1 the Jaynes-Cummings Hamiltonian will be derivate. With the Hamiltonian in hands will be possible to analyze some features, like the Jaynes-Cummings ladder in section III, the Vacuum-Rabi oscillations in section IV and the phenomena of collapses and revivals in section V. II. THE MODEL Considering a physical system composed of an atom is the known Hamiltonian of the two-photon Jaynes-Cummings model [17, 18, 20, 57] obtained by the limiting processes \(\lambda \rightarrow 0\).The \(\lambda \)-dependent terms of the time-independent Hamiltonian can be considered as the inversely quadratic potential and the radial external classical field, respectively.In continuation of our investigations, we will focus on the role of these |tca| nnx| kji| ezi| ybl| xxz| xnr| das| gkw| jsm| mki| ygj| wkt| zcj| obe| mnp| gjq| ofd| evk| uxv| xse| ujy| jew| jnw| lvy| zdr| fwc| zbe| pax| tuj| hjn| eoa| cxy| iwy| egr| wcb| dot| fpo| xvm| twm| bti| lve| lke| cko| tpc| uqg| bnv| cnl| gef| dxx|