The Generation And Control Of Stationary Light Signals In A Four-level Double- Λ Atomic System

In recent years, the electromagnetically induced transparency has become one of the important research topics of modern optic and the quantum computing. Meanwhile, many ideas that based on the characteristics of EIT has been put forward and implemented. We can effectively change and control the dispersion characteristics of transmission light field rely on EIT, a phenomenon referring to the resonant absorption suppression of a probe field through destructive quantum coherence established in an atomic sample. With the improved relevance between dispersion and absorption, we achieve slow light and stationary light pulses successfully. For example, it has been demonstrated experimentally that the group velocity can be controlled to such an extent that a pulse of light can not only be slowed but completely stopped and then regenerated, which attracted many researchers' attention in 2003. Finally, this phenomenon can be implicated for optical data storage, optical networks, optical information and some related work.In this paper, we consider the generation and control of stationary light signals in a four-level double-Λatomic system (as show in Fig.1). In the case of the specific time modulation of the two counter-propagating coupling beams, we discuss the effect of the system's symmetry and initial phase of coupling fields for the preparation of stationary light pulses, in detail. Simultaneously, we provide some corresponding solutions. Form the semi-classical basic theory of the interaction of light and matter, and in the case of electric-dipole approximation and rotating wave approximation, we obtain the density matrix equations through the interaction Hamiltonian of system. Combine with the Maxwell wave equation and under the (space and time) slowly varying envelope approximation, we numerical simulate the generation and control of stationary light pulses (SLP). (?)Fig.1 Four-level double-Λatomic system driven by two weak fields and two coupling laser fields.Ωc >Ωd, Corresponding to the Rabi frequency of forward and backward coupling beams,Ωp andΩs are corresponding to the Rabi frequency of weak probe field and weaker induced field, respectively.We consider the symmetrical system with the Rabi frequency of two counter-propagating coupling beams and the decay of two higher levels are equal, then we mainly in three different processes to discuss, namely storage of the incident pulse, formation of a SLP, and its subsequent release. In the first step, a forward probe pulse moves slowly in the atomic sample until stored in the spin coherence at a time when the forward coupling field is adiabatically switched off. In the following step II, a little time later, we both switch the two counter-propagating coupling beams on with equal intensity simultaneously, both the forward and the backward probe components are generated from spin coherence and somehow frozen in the atomic sample so as to form a SLP, whereas they are map back again onto spin coherence when the two counter-propagating coupling beams are switched off at the end of step II and the memory of SLPs can be achieved. In the last step, after a little time, the forward (backward) probe can be retrieved by switching on the forward (backward) coupling field. (?) Fig.2. (color online) Nonlinear dynamics of the two probe components propagating along the +Z and -Z directions are scaled to the incident probe.For the previous study of SLPs, it can be mostly achieved in traditional coherent standing wave driven three-level atomic system. Due to the existence of double-color field coupling in this ensemble, when the two strong coupling fields are open at the same time, the higher-order spin coherence and optical coherence will be excited. What's more, they can be raised the sharp dispersion and loss of static light. Our theory of SLPs in a four-level double-Λsystem in a cold atomic sample, there are the monochromatic fields coupling between levels so as to avoid the influence of higher-order spin coherence and optical coherence. The advantage of our system is that the dispersion and the loss of prepared static light are small compared with the previous works.Secondly, we consider the preparation of SLP in asymmetrical system under two conditions: the decay of two higher-levels are equality but the Rabi frequency of two counter-propagating coupling beams are not equality; and the Rabi frequency of two counter-propagating coupling beams are equality but the decay of two higher-levels are different. The preparation of SLP is similar to the symmetrical system. In the second case as an example, the results show difference from symmetrical system is that the light pulses is moved in atomic medium, the direction of light pulses is related to the Rabi frequency of two counter-propagating coupling beams. So we can adjust the intensity of two coupling fields to control the stationary or motion of light pulses, the direction and speed of light pulses in the medium. If we chose the different spontaneous relaxation but symmetrical two counter-propagating coupling fields, there would not be emerged SLPs in medium. In view of this situation, we summarize the proportional relation of coupling field intensity and spontaneous relaxation of the two higher levels——(?) We can prepare the SLPs by adjusting the relationship, and the regenerated SLPs in asymmetrical system are exactly accordance with the prepared SLP in the symmetrical system (as show in Fig2). (?)Fig.3. The moved light pulses in asymmetric system (left), after adjust the parameters, the stationary light pulses generated in asymmetric is exactly accordance with the SLPs prepared in the symmetric system (right).Next, we analyze the effect of coupling fields'initial phase on SLPs. The numerical stimulation results show that the initial phase of coupling fields only has the affect on backward probe field by cyclical, but has no difference to SLPs.In conclusion, our work further optimized the forming process of SLPs, and we comprehensively consider the influence on SLPs of the symmetry of system and the initial phase of coupling fields. The numerical simulation results show that we realized a full optical information processing. What'more, the four-level double-Λ atomic system is simpler and more convenient in the theoretical calculation. In addition, we chose the independent traveling wave fields so as to avoid the rapid relaxation by higher-order spin coherence and optical coherence, and reduce the dispersion and loss during the propagating of probe pulse. Our results have potential in multichannel retrieved of optical information, optical networks and deterministic quantum information science with enhanced nonlinearity.