Quantum Coherence In Four-level System Driven By Two Fields

In this thesis, we studied the nonlinear interaction between a multi-lelve atomic system and muli-fields. There is a coupling optical field and a probing optical field which forms a well-studied L - type three level system and the unique feature of this study is the introduction of double micromave driving fields which drive a hyperfine transition within the ground state. The microwave field driven hyperfine trasition shares a common hyperfine level with the probed transition and hence forms a L - type four-level system. The steady-state solution of the density matrix equation is solved using the Floquet method and the probe absorption profiles are studied as a function of Rabi intensities and detunings of the double microwave driving fields.Firstly, we studied the effect of Rabi intensities of the microwave driving fields on the absorption profiles. One of the driving field is exactly resonant with the hyperfine transition,and the other driving field is off-resonant whose detuning equals the Rabi frequency of the resonant driving field. We concentrated our discusion to the case where the resonant field is stronger than the off-resonant field. It is shown that there are two EIT doublet windows in the probe absorption spectrum. The EIT doublet windows positions are symmetrically located with respect to the resonance frequency of the probe field, and the separation is equal to the Rabi frequency of the resonant microwave driving field. However, within each EIT doublet,the splitting is determined by the strength of detuned microwave driving field and is equal to the half of Rabi frequency of the detuned microwave driving field. The results can be explained by the theory of dressed state formalism. It is shown that Multi-EIT windows is due to the dynamic “Stark” splitting of the level which results from the double microwave driving field.Then, we studied the effect of detunings of the microwave driving fields on the absorption profiles. We considered two cases: in the first case there is a resonant driving field and an off-resonant driving field, the so called single off-resonant case, and in the second case there are two off-resonant fields, the so called double off-resonant case. In single off-resonantcase, we considered a special sitution where the detuning of the off-resonant driving field is adjusted to be the 1/k of the Rabi frequency of the resonant microwave driving field where k is an integer. The result shows that this introduces multiple EIT windows where the number of EIT doublet increases with the increase of k value. In double off-resonant case, we considered a special sitution where the two microwave driving fields are of same intensity and symmetrically detuned and the absorption profiles are studied as a function of both driving field intensity and detunings. When the detunings of the double off-resonant driving fields are fixed, there appear mutliple EIT doublets whose number increases with the increase of the Rabi intensity of the driving field, however the splitting of each doublet remain fixed.Furthermore, there is a periodic variation in the deepth of the EIT feature. On the other hand,when the Rabi intensity of the double off-resonant driving fields are fixed, there is no change in number of EIT doublet while the EIT doublet position can be manupulated by the detunings of the double off-resonant driving fields.