Dynamical symmetry breaking of lambda- and vee-type three-level systems on quantization of the field modes

Abstract

We develop a scheme to construct the Hamiltonians of the lambda, vee and cascade type of three-level configurations using the generators of SU (3) group. It turns out that this approach provides a well defined selection rule to give different Hamitonians for each configurations. The lambda and vee type configurations are exactly solved with different initial conditions while taking the two-mode classical and quantized fields . For the classical field, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered from lambda model and vice versa simply by inversion. We then proceed to solve the quantized version of both models introducing a novel Euler matrix formalism. It is shown that this dynamical symmetry exhibited in the Rabi oscillation of two configurations for the semiclassical models is completely destroyed on quantization of the field modes. The symmetry can be restored within the quantized models when the field modes are both in the coherent states with large average photon number which is depicted through the collapse and revival of the Rabi oscillations.

SU(4) based classification of four-level systems and their semiclassical solution

“…(18) and T α be the six parameter Bose-Pascos orthogonal matrix given by 13,16 , where, s i = sinθ i and c i = cosθ i (i = 1, 2, 3, 4, 5, 6). In the next Section we proceed to discuss the Rabi oscillation of various levels numerically for with specific initial conditions.…”

Bloch equation and atom-field entanglement scenario in three-level systems

“…In the rotating wave approximation (RWA) the Hamiltonians of semiclassical system in the SU (3) basis is given by [6],…”

“…For the quantized system, the free and interaction Hamiltonian of the lambda system in the rotating wave approximation (RWA) is given by [6] …”

“…We have also proposed a wave function of the qutrit system in the computational basis |− >, |0 > and |+ > and have pointed out its explicit relation with the three-level system. Finally, we have solved the quantized version of all configurations applying an Euler matrix approach [6,7] and following Phoenix and Knight formalism [8,9] the atom-field entanglement scenario is studied.…”

Quantum Entropy of a Four-Level Atom with Arbitrary Nonlinearities

“…A tentative approach to entanglement measures for a system of a three-level atom interacting with a quantized cavity-field has been introduced [36]. Furthermore, the evolution of the (atomic) field entropy for the threelevel atom one-mode [37][38][39][40][41][42][43][44] and two-mode [45,46] model has been studied. On the other hand, the system of a four-level atom interacting with a single mode of electromagnetic field has been studied [28,[47][48][49][50][51].…”