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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Adiabatic following condition for pulse propagation in three-level medium

Grigorii G Grigoryan, Y. Pashayan-Leroy

Published Dec 28, 1999• 1 citation
Publisher

Abstract

The adiabatic following condition for the propagation of pulses in a three-level medium has been obtained. It is shown that the adiabatic criterion depends not only on the total Rabi frequency and pulse duration, but on the relationship between oscillator strengths of electric dipole transitions in an atom too. In particular, for (Lambda) - system if the oscillator strength for the pump transition is less or equal to that for the Stokes transition, the adiabatic following condition is preserved at arbitrary penetration depths. Otherwise it breaks down rather quickly with the distance of propagation.

DOI
10.1117/12.375298

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The adiabatic following condition for the propagation of pulses in a three-level medium has been obtained. It is shown that the adiabatic criterion depends not only on the total Rabi frequency and pulse duration, but on the relationship between oscillator strengths of electric dipole transitions in an atom too. In particular, for (Lambda) - system if the oscillator strength for the pump transition is less or equal to that for the Stokes transition, the adiabatic following condition is preserved at arbitrary penetration depths. Otherwise it breaks down rather quickly with the distance of propagation.
Propagation of a pulse pair in a nondissipative three-level medium is investigated in the adiabatic-following approximation to a trapped state. The general case of unequal oscillator strengths of two electric dipole transitions in an atom is studied analytically, and the adiabaticity criterion for the matter-field interaction is derived. It is shown that the interaction adiabaticity strongly depends on the relationship between oscillator strengths. A simple expression specifying the critical propagation length at which the stimulated Raman adiabatic passage process is still effective is derived. An estimate of the propagation distance at which a complete energy transfer from the pump pulse into the Stokes pulse occurs is made.
The propagation of a weak-field pulse through a medium of three-level atoms is considered. Each atom has a $\ensuremath{\Lambda}$-type level scheme in which the two lower levels are stable. A strong control field drives one of the electronic transitions while the signal field drives the coupled transition under conditions where EIT (electromagnetically induced transparency) is usually operative. The input pulse is slowed and compressed as it enters the medium, adiabatically following the EIT solution. However, if the control field is changed suddenly when the pulse is in the medium, the signal field is transformed into two pulses, one of which propagates as a normal EIT pulse and the other with a different speed and an amplitude that oscillates in time. The temporal oscillations are transformed into both spatial and temporal oscillations as the pulse exits the medium. An analytic expression is derived for the pulse intensity which provides a good approximation to the exact result at all times. It is shown that the oscillating component of the exiting pulse can be spatially compressed in comparison with the input pulse.
We investigate the problem of propagation of three-component resonant light pulses with adiabatically varying amplitudes through a medium consisting of atoms with the tripod level configuration. By means of both analytic and numerical methods we find the two modes of shape-preserving pulse propagation. The pulse propagation velocity of the fast mode is equal to the speed of light in vacuum, whereas the group velocity of the other (slow) mode is significantly slowed down. These two modes represent a general asymptotic solution of the problem of adiabatic pulse propagation, i.e., a pulse of any shape, which is consistent with the adiabaticity conditions, and a finite duration evolves at large propagation distances (and, correspondingly, at large times of interaction with the medium) to a well-separated pair of fast and slow pulses. The experimental requirements for adiabatic pulse propagation in a tripod medium are similar to that needed for observation of slow light propagation in a medium with the $\ensuremath{\Lambda}$ configuration of levels. However, the tripod scheme offers a different possibility, which is absent in the $\ensuremath{\Lambda}$-medium case: collisions of fast and slow pulses. It is found numerically that after such a collision the shapes of the pulses change, so these pulses do not match the classical definition of a soliton.
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.
We consider a medium of multilevel atomic systems interacting with radiation pulses. A relatively simple technique of analytic calculations is proposed, which allows revealing all necessary conditions (with sufficient conditions to be checked separately) imposed on the interaction parameters, for which the mean dipole moment of a multilevel atomic medium vanishes, i.e., the medium becomes transparent via adiabatic interaction. The proposed technique is based on the method of quasienergies and illustrated for three- and five-level atomic systems. The necessary conditions for the propagation length where the interaction adiabaticity is preserved in the medium are obtained.