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arXiv:quant-ph/0407173 · Physical Review A

Adiabatic pulse propagation in coherent atomic media with the tripod level configuration

I. E. Mazets

Published Feb 10, 2005• 39 citations

Abstract

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.

DOI: 10.1103/physreva.71.023806

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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.

We consider adiabatic propagation of a pair of quantized light pulses in a coherently prepared atomic medium with the tripod level configuration. We find that under conditions of electromagnetically induced transparency, two distinct polariton modes are simultaneously formed in the medium. These polaritons, represented by certain coherent superpositions of the quantized fields, have different group velocities; the fast one propagates at essentially the speed of light, while the group velocity of the slow polariton can be dynamically reduced to zero. The state mapping between the electromagnetic field and atomic ensemble is also demonstrated.

Optical adiabatons are specific shape-invariant pulse pairs propagating at the reduced group velocity and without optical absorption in the medium. The purpose of this study is to analyze and demonstrate adiabaton formation in many level atomic systems. Here we focus on the analysis of five level M-type and double tripod systems. It is found that M-type atomic systems are prone to intensity dependent group velocity and pulse front steepening which prevents the formation of long range optical adiabatons. In contrast, the double tripod atomic system is quite favorable for the formation of optical adiabatons leading to two different optical field configurations propagating with invariant shape.

Optical adiabatons are specific shape-invariant pulse pairs propagating at the reduced group velocity and without optical absorption in the medium. The purpose of this study is to analyze the possibility of adiabaton formation in multilevel atomic systems with the focus on M-type and double tripod (DT) systems having five energy levels and different interaction configurations. Findings show that the M-type atomic system is prone to intensity dependent group velocity and pulse front steepening which prevents the formation of long range optical adiabatons. In contrast, the DT atomic system is quite favorable for the formation of optical adiabatons exhibiting two different optical field configurations propagating with invariant shape.

Optical adiabatons are specific shape-invariant pulse pairs propagating at the reduced group velocity and without optical absorption in the medium. The purpose of this study is to analyze and demonstrate adiabaton formation in many level atomic systems. Here we focus on the analysis of five level M-type and double tripod systems. It is found that M-type atomic systems are prone to intensity dependent group velocity and pulse front steepening which prevents the formation of long range optical adiabatons. In contrast, the double tripod atomic system is quite favorable for the formation of optical adiabatons leading to two different optical field configurations propagating with invariant shape.

The physics of slow-light propagation in atomic Lambda systems is described by the theory of integrable systems, which allows the existence of solitons. Slow-light solitons are stable polarization structures that propagate through the atomic medium at a controllable speed. They represent generalizations of the experimentally demonstrated slow-light pulses in atomic media where one light polarization dominates the other, the probe, and controls its group velocity. In the general case, the overall intensity controls the speed of the entire polarization structure. For zero detuning between light and atoms, even more general shape-preserving pulses exist. Quantum fluctuations of slow-light pulses can be stored in atomic media. In the case of solitons, these are fluctuations of the soliton parameters.