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arXiv:quant-ph/0001104

Pulse propagation in three-level medium

Y. Pashayan-Leroy, G. G. Grigoryan

Published Jan 28, 2000• 0 citations
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Abstract

We investigate propagation of a pulse pair in a three-level medium under the adiabatic following condition for the general case of unequal oscillator strengths. Exact analytical solutions to the propagation equations have been obtained. It is shown that propagation dynamics strongly depends on the relationship between oscillator strengths. The adiabaticity criterion for the interaction of pulses with three-level media has been derived and analyzed in detail.

DOI
10.48550/arxiv.quant-ph/0001104

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We investigate propagation of a pulse pair in a three-level medium under the adiabatic following condition for the general case of unequal oscillator strengths. Exact analytical solutions to the propagation equations have been obtained. It is shown that propagation dynamics strongly depends on the relationship between oscillator strengths. The adiabaticity criterion for the interaction of pulses with three-level media has been derived and analyzed in detail.
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 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 four laser pulses in the five-level ladder system in the case of arbitrary intensities and the different strengths of oscillators is investigated, when one of the eigenstates of the interaction Hamiltonian is formed in the whole volume of the medium. Taking into account the first non-adiabatic correction, the equations of propagation are obtained. An analytical solution of these equations is obtained. The conditions for an effective excitation of the fifth level in the whole volume of medium and the limitations on the interaction parameters are obtained as well.
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.