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Spatial evolution of short pulses under conditions of coherent population trapping

Vasily G. Arkhipkin, Ivan V. Timofeev

Published Mar 23, 2001• 0 citations
OpenAlex

Abstract

We study the features of spatial and temporal evolution of two powerful short different-wavelength laser pulses interacting with optical dense three-level Lambda-type medium under condition of coherent population trapping for the general case of unequal transition oscillator strengths. The pulses are simultaneously sent into an atom. The durations of probe and coupling pulses $T_{1,2}$ ($T_2>T_1$) are supposed to be shorter than all relaxation times in the medium. We present analytical and numerical solutions of the self-consistent set of coupled Schr\\"{o}dinger equations and reduced wave equations in adiabatic limit with taking into account the first non-adiabatic correction. The adiabaticity criterion with account of pulse propagation is studied. We find that propagation dynamics depends on the relationship between the transition oscillator strengths. It is shown that at the initial stage of propagation the envelopes of the pulses slightly change along the length of the medium. This distance can be large compared to one-photon resonant absorption length of the medium. Also it is possible a regime of complete reemitting of the probe pulse into the coupling one during propagation. A spatial evolution of the atomic Raman coherence is investigated in detail too.

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The spatial and temporal dynamics of two short laser pulses propagating in absorbing three-level medium under conditions of induced transparency is investigated in adiabatic approximation. We analyze two cases of electro-magnetically induced transparency creating--coherent population trapping and adiabatic population transfer. It is shown that in both cases the probe pulse can penetrate into a medium at a distance considerably exceeding the length of linear absorption of a single weak probe pulse in absence of a coupling pulse at adjacent transition. The difference of spatial and temporal evolution of level population in processes of coherent population trapping and adiabatic population transfer is although demonstrated.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 14, 2000•0 citations
We study the features of spatial and temporal evolution of two powerful short different-wavelength laser pulses interacting with optical dense three-level Lambda-type medium under condition of coherent population trapping for the general case of unequal transition oscillator strengths. The pulses are simultaneously sent into an atom. The durations of probe and coupling pulses T1,2T_{1,2}T1,2​ (T2>T1T_2>T_1T2​>T1​) are supposed to be shorter than all relaxation times in the medium. We present analytical and numerical solutions of the self-consistent set of coupled Schr\"{o}dinger equations and reduced wave equations in adiabatic limit with taking into account the first non-adiabatic correction. The adiabaticity criterion with account of pulse propagation is studied. We find that propagation dynamics depends on the relationship between the transition oscillator strengths. It is shown that at the initial stage of propagation the envelopes of the pulses slightly change along the length of the medium. This distance can be large compared to one-photon resonant absorption length of the medium. Also it is possible a regime of complete reemitting of the probe pulse into the coupling one during propagation. A spatial evolution of the atomic Raman coherence is investigated in detail too.
The spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level \ensuremath{\Lambda}-type optical medium under coherent population trapping. The general case of unequal oscillator strengths of the transitions is considered. The durations of the probe pulse and the coupling pulse T1,2(T2>T1){T}_{1,2} {(T}_{2}>{T}_{1})T1,2​(T2​>T1​) are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schr\"odinger equations and reduced wave equations in the adiabatic limit taking account of the first nonadiabatic correction. The adiabaticity criterion is also discussed taking account of pulse propagation. The dynamics of propagation is found to be strongly dependent on the ratio of the transition oscillator strengths. It is shown that the envelopes of the pulses slightly change throughout the medium length in the initial stage of propagation. This distance can be large compared to the one-photon resonant absorption length. Eventually, the probe pulse is completely reemitted into the coupling pulse during propagation. An effect of localization of the atomic coherence was observed similar to the one predicted by Fleischhauer and Lukin [Phys. Rev. Lett. 84, 5094 (2000)].
The spatial and temporal dynamics of two short pulses propagating in an optically dense medium of resonant three-level Λ-atoms is investigated numerically and analytically. The maximum coherence for the Raman transition due to coherent population trapping. It is shown that, at the initial stage of propagation, the waveforms of such pulses only slightly change along the length of the medium, which may considerably exceed the length of linear absorption for a single weak pulse. As the length of the absorbing medium increases, the energy of the probe (first) pulse is completely transferred into the second (control) pulse.
The features of spatial and temporal evolution of two short laser pulses propagating in three-level medium under conditions of coherent population trapping and adiabatic population transfer is investigated in adiabatic approximation. It is shown that in both cases pulses can penetrate into a medium at a distance considerably exceeding the length of linear absorption of a single weak probe pulse in absence of a coupling pulse at adjacent transition. The difference of spatial and temporal evolution of level populations in processes of coherent population trapping and adiabatic population transfer is demonstrated. Also we show that the concept of dressed-field pulses is consequence of Manley-Raw relation.
Features of the adiabatic population transfer are studied with the spatial evolution of interacting pulses propagating in an optically dense medium of three-level Λ-atoms taken into account. A self-consistent analytical solution describing the spatial-temporal dynamics of interacting short pulses under the conditions of adiabatic population transfer is constructed in the adiabatic approximation with consideration for the first nonadiabatic correction. Practically complete inversion on a forbidden transition determined by coherent (adiabatic) population transfer is shown to take place over a length of the medium, which may exceed the absorption length of a weak probing pulse in the absence of control radiation on the adjacent transition by several orders of magnitude.
Spatio-temporal dynamics of two short laser pulses propagating in an absorbing medium, which consists of one- and two-photon resonant (Lambda) -atoms, is investigated in the adiabatic approximation. We give an analytical solution and compare it with numerical simulations. It is shown that pulses may propagate in a medium, whose thickness is considerably greater than the length of the linear absorption of a single weak probe wave. Finally, full transfer of the probe pulse energy into the coupling pulse takes place. A vector model of the adiabatic interaction of two pulses with three-level atom is proposed.
The spatial and temporal dynamics of two short laser pulses propagating in absorbing three-level medium under conditions of induced transparency is investigated in adiabatic approximation. We analyze two cases of electro-magnetically induced transparency creating--coherent population trapping and adiabatic population transfer. It is shown that in both cases the probe pulse can penetrate into a medium at a distance considerably exceeding the length of linear absorption of a single weak probe pulse in absence of a coupling pulse at adjacent transition. The difference of spatial and temporal evolution of level population in processes of coherent population trapping and adiabatic population transfer is although demonstrated.