Pulse propagation through a coherently prepared two-level medium

Yuma Takanashi, N. Tan-no, Kenichi Yokoto

Emmanuel Paspalakis, Niels J. Kylstra, P. L. Knight

We explore the laser-pulse propagation dynamics when one, two, or three pulses resonantly drive a coherently prepared four-level medium in a tripod configuration. If the system is prepared in a coherent superposition of two of the lower levels, we show that two incident resonant pulses can parametrically generate a third pulse in the medium. Over short distances, the propagation of this generated pulse can be partially controlled by varying the Rabi frequency of one of the driving fields. For a medium prepared in a coherent superposition of the three lower levels, we obtain a general expression for a three-photon Beer's length. Under specific conditions, the medium can either become completely opaque or completely transparent to three incident resonant pulses. Moreover, a single incident pulse can be used to parametrically generate two additional pulses. Finally, a general relationship is found that links the amplitudes of the initial superposition of states and the amplitudes of the pulses at large distances in the medium, implying that the initial superposition can be used to engineer the amplitudes of the exiting pulses.

Gautam Vemuri, Kashyap V. Vasavada

Vladimir Evgen'evich Zakharov

Antônio Augusto Soares, Luı́s E. E. de Araujo

We study the effects of propagation through an extended sample of two- and three-level atoms on the coherent accumulation of excitation by an ultrashort pulse train. In the two-level case, previous pulses in the train may prepare the medium such that a later pulse may experience amplification and absorption in different positions inside the sample. For a large number of pulses, the atomic medium may be saturated by the train, and some pulses propagate without experiencing either absorption or amplification. In general, absorption of the resonant pulse frequency during propagation compromises the accumulation efficiency. In the three-level case, the coherent accumulation of excitation leads to electromagnetically induced transparency of the pulse train, and the pulses exit the medium without any distortion in their temporal profile.

B. D. Clader, Joseph H. Eberly

We examine fully coherent two-pulse propagation in a $\ensuremath{\Lambda}$-type medium, under two-photon resonance conditions and including inhomogeneous broadening. We examine the effects of both short pulse preparation and medium preparation. We contrast the cases in which the two pulses have or have not matched envelopes, and media with and without ground state coherence. We find that an extended interpretation of the area theorem for single-pulse self-induced transparency is able to unify two-pulse propagation scenarios, including some aspects of electromagnetically induced transparency and stimulated Raman scattering. We present numerical solutions of both three-level and adiabatically reduced two-level density matrix equations and Maxwell's equations, and show that many features of the solutions are quickly interpreted with the aid of analytical solutions that we also provide for restricted cases of pulse shapes and preparation of the medium. In the limit of large one-photon detuning, we show that the adiabatic two-level equations commonly used to study stimulated Raman scattering are not reliable for pulse areas in the $2\ensuremath{\pi}$ range, which allows puzzling features of previous numerical work to be understood.