Two-pulse propagation in media with quantum-mixed ground states

Abstract

We examine fully coherent two-pulse propagation in a lambda-type medium, under two-photon resonance conditions and including inhomogeneous broadening. We examine both the effects of short pulse preparation and the effects of medium preparation. We contrast cases in which the two pulses have matched envelopes or not, and contrast cases in which ground state coherence is present or not. We find that an extended interpretation of the Area Theorem for single-pulse self-induced transparency (SIT) is able to unify twopulse propagation scenarios, including some aspects of electromagnetically-induced transparency (EIT) and stimulated Raman scattering (SRS). 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 analytic 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 two-level equations commonly used are not reliable for pulse Areas in the 2π range, which allows puzzling features of previous numerical work to be understood. 0

Vector-soliton storage and three-pulse-area theorem

“…(10). This is in alignment with previous results for the Λ and double-Λ systems [28,29] II. THEORETICAL MODEL For the tripodal atom (see Fig.…”

“…The pulse area is a key quantity, not only controlling the reshaping of pulses but also the storage and manipulation of the information stored in the medium. Its importance goes well beyond the two-level atom remaining a constant in pulse dynamics for multi-level systems [28,29]. For non-idealized input pulse shapes, these multi-level systems follow a similar behavior to the predictions of the area theorem for a two-level system [28,29,34] even in the absence of Doppler broadening [26].…”

“…The angles φ and ν define the area of each signal pulse, θ 1 = 2π cos (ν/2) and θ 2 = 2πe iφ sin (ν/2) (the area of the first pulse was taken to be real in order to fix the global phase). Note that the signal pulses are "normalized" by the total two-pulse area (as defined by Clader and Eberly in [28]), that is, |θ 1 | 2 + |θ 2 | 2 = 2π. In this limit, the control pulse tends towards zero.…”

“…The first was done by Tan-no et al [35] but is limitied to highlydetuned fields in two-photon resonance. Clader and Eberly presented a clear comparison of this stimulated Raman scattering (SRS) with the exact Maxwell-Bloch equations [28]. Another famous result is the dark area theorem [36], where the dark area is not defined in the usual manner (it has time derivatives of the Rabi frequencies).…”

Multipulse storage and manipulation via solitonic solutions

“…In the particular case of a Λ system (see Fig. 1), the Maxwell-Bloch equations that define the evolution of the system become integrable when both signal and control fields have equal atom-field coupling parameters and are in two-photon resonance, as has been shown by Park and Shin [21] and Clader and Eberly [22]. This leads to solitonic solutions even in non-ideal media preparation such as "mixonium" [23], a partially coherent medium.…”