Formation and propagation of matched and coupled ultraslow optical soliton pairs in a four-level double- system L. Deng, 1 M. G. Payne, 1 Guoxiang Huang, 1,2 and E. W. Hagley 1 1 Electron and Optical Physics Division, NIST, Gaithersburg, Maryland 20899, USA 2 Department of Physics and Institute of Theoretical Physics, East China Normal University, Shanghai 200062, China Received 10 November 2004; published 17 November 2005 We investigate the simultaneous formation and stable propagation of ultraslow optical soliton pairs in a lifetime broadened four-state atomic system under double- excitation with large one- and two-photon detun- ings. We show that detrimental probe field distortions due to strong dispersion effects under weak driving conditions can be well balanced by self- and cross-phase modulation effects, leading to a pair of temporal, group velocity, and amplitude matched ultraslow optical solitons of different frequencies. DOI: 10.1103/PhysRevE.72.055601 PACS numbers: 42.81.Dp, 05.45.Yv, 42.50.Gy, 42.65.Tg Optical solitons 1 describe a class of fascinating shape- preserving propagation phenomena of optical fields in non- linear media. Such a remarkable propagation effect is the consequence of the interplay between nonlinear effects and dispersion properties of the medium under optical excita- tions. In general, the glass phase of a solid-state medium optical fibers, for example used in most optical soliton gen- eration techniques implies that there is no distinctive energy level structure. Therefore, conventional optical soliton gen- eration can be classified as far off-resonance operation. Such a “passive mode” of operation is one of the main reasons that high powered lasers are required for soliton formation. As a consequence of such a strong excitation, optical solitons pro- duced this way generally travel with group velocities very close to the speed of light in vacuum and hence, require extensive propagation distance to generate. In the past few years strong index enhancement tech- niques 2 have been vigorously pursued in the field of non- linear and quantum optics. One of the main achievements of these techniques is the possibility of enhancing nonlinear excitations with low optical loss. There is ample evidence that these techniques can lead to many interesting physics effects 3. Recently, we have applied these techniques to investigate 4 the formation and propagation of ultraslow 5 optical solitons in a highly resonant atomic medium. Contrary to the conventional technique where the key is the high local intensity distribution rather than the resonant structure of the medium, we study shape-preserving ul- traslow propagations where resonance effects are essential. It is this structural difference and the index enhancement with low optical loss that give rise to the possibilities of ultraslow optical soliton formation and stable propagation under weak optical excitation in a short medium. In this paper, we report the results of a generation of well-matched 6 ultraslow optical soliton pairs. Specifically, with a four-state double- configuration 7–9, we show the simultaneous formation and stable propagation of a pair of temporal, group-velocity, and amplitude TAG matched ul- traslow optical solitons in a highly resonant medium under weak excitations. We further show interactions and modula- tions between two paired and matched ultraslow solitons. We show that with suitable detunings and initial conditions it is possible to achieve fast dynamic switching between mem- bers of the pair, which have fundamentally different charac- teristics. We note that such dynamic switching features have no correspondence in conventional optical soliton generation techniques. It is remarkable that such a rich soliton-soliton interaction can be produced in a small propagation distance of less than 1 cm with driving fields of typically less than a hundred MHz. We consider a lifetime broadened four-level double- system shown in Fig. 1. In our model, two pulsed probe fields same pulse length at the entrance of the medium and two continuous wave cw control fields complete the respective excitations. Assuming that the probe lasers are weak so that the ground state |0 is not depleted, we obtain the following equations of motion for the atomic response and probe fields n =1, 2; A n t z = id n A 1 + i cn A 3 + i pn A 0 , 1a A 3 t z = id 3 A 3 + i c1 * A 1 + i c2 * A 2 , 1b FIG. 1. Energy levels and the excitation scheme of a lifetime broadened four-state atomic system that interacts with two pulsed probe lasers Rabi frequency 2 p1, p2 and two continuous wave pump lasers Rabi frequencies 2 c1,c2 . PHYSICAL REVIEW E 72, 055601R2005 RAPID COMMUNICATIONS 1539-3755/2005/725/0556014/$23.00 055601-1