| Recent years, people are of great interest for optical precursors phenonme-nonof quantun opticals, nowadays, the phenonmenon has become one of the importantresearch topics of quantun opticals. In1914, Sommerfeld and Brillouin first studyoptical precursors, precursors are characteristic wave patterns caused by dispersion ofan impulse’s frequency components as it propagates through a medium. So far, opticalprecursors have a lot of important results on both theorical and experimental studies.Moreover, the phenomena of precursors have observed inγ rays, microwaves, andsound waves. And optical precursors have important applications in underwatercommunications, the generation of high peak power optical pulses, and biomedicalimaging, it is one of important reasons for interesting about optical precursors.In this paper, we investigate both the temporal and spatial propagationdynamica of a squaremodulated quantum probe field in a sample of cold atoms toshow how the precursors are generated. We consider a three-level Λ atomic system(see Fig.1). Following the semic-classical theory of interaction of light and matter, inthe rotating wave and electric-dipole approximations, we can first write down theinteraction Hamiltonian describing the Λ–type system and then derive a set ofequations for five density matrix elements. To study the propagation dynamics of theprobe pulse, we derive the Maxwell wave equations under the slowly-varyingenvelope approximation. First, we investigate the dynamic propagation and evolution of asquare-modulated probe field incident upon a cold atomic sample with a simple Λ–type configuration illustrated in Fig.1. We can see successively the opticalprecursors from the rising edge, the main pulse, and the precursor from the fallingedge superposing upon the main pulse. In order to demonstrate the formation processof the optical precursors, we invetigate both the spatial and temporal evolutions ofthese two transmitted optical precursors progagating through the cold atomic sample.Second, in order to separate the precursor at the falling edge from the main field.We increase the length of the atomic medium for that the main field can be observedafter the precursors at the sample exit. However, the atomic sample can not be toolong by taking into account the proper N in a real situation. In the meanwhile, theamplitude of the optical precursors and the main pulse will decrease as the samplelength L increases. To this end, it is favorable to induce the EIT-based light storagetechnology to further separate the optical precursors and the main pulse. The timedelay between the precursor and the main pulse is increased by using light storagetechnology. To understand this process, we numerical simulate the whole process ofboth the spatial and temporal evolution.In addition, we design a special square minus-Gaussian pulse propagatingthrough the medium to turn a dark pulse into a bright one. The pulse has maximumvalue only at the beginning and the final moment but zero value at the middle moment.Which can be called a dark pulse. We input the probe pulse upon the cold atomicsample, we can see that the output pulse has three parts, the former two spikes areoptical precursors and the last Gaussian bright pulse is the main pulse.At last, we design a system to test and verify if the optical precursor can be fasterthan the light speed c in vacuum. We use a three-level Λ-type configuration shownas Fig.2, we bring in the incoherent pump field Γ acting on the unique probetransition to realize superlumninal light. we can confirm that the optical precursor isthe first part of the output pulse, it is that no optical components can travel faster thanoptical precursors. |
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