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Physical Review Letters

Coherent Control of the Effective Susceptibility through Wave Mixing in a Duplicated Two-Level System

F. A. Hashmi, M. A. Bouchène

Published Nov 20, 2008• 20 citations

Abstract

We theoretically demonstrate the coherent control of the effective susceptibility of a duplicated two-level system. The control is obtained for a linearly polarized weak field in the presence of a much stronger orthogonally polarized field. For small optical depths, the effective susceptibility ${\ensuremath{\chi}}_{\mathrm{eff}}$ behaves as ${\ensuremath{\chi}}_{\mathrm{lin}}{e}^{2i\ensuremath{\phi}}$ (${\ensuremath{\chi}}_{\mathrm{lin}}$ is the linear susceptibility, $\ensuremath{\phi}$ the phase shift) allowing coherent control of the optical response. For large optical depths, ${\ensuremath{\chi}}_{\mathrm{eff}}\ensuremath{\approx}{\ensuremath{\chi}}_{\mathrm{lin}}^{*}$, turning an absorber into an amplifier without affecting the dispersion.

DOI: 10.1103/physrevlett.101.213601

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We theoretically demonstrate the coherent control of the effective susceptibility of a duplicated two-level system. The control is obtained for a linearly polarized weak field in the presence of a much stronger orthogonally polarized field. For small optical depths, the effective susceptibility

{\ensuremath{\chi}}_{\mathrm{eff}}

behaves as

{\ensuremath{\chi}}_{\mathrm{lin}}{e}^{2i\ensuremath{\phi}}

(

{\ensuremath{\chi}}_{\mathrm{lin}}

is the linear susceptibility,

\ensuremath{\phi}

the phase shift) allowing coherent control of the optical response. For large optical depths,

{\ensuremath{\chi}}_{\mathrm{eff}}\ensuremath{\approx}{\ensuremath{\chi}}_{\mathrm{lin}}^{*}

, turning an absorber into an amplifier without affecting the dispersion.

In this article, we investigate the optical response of a duplicated two-level atomic medium submitted to a stationnary control field and a weak co-propagating probe field, orthogonally polarized to each other. We show that both reflected and transmitted components of the probe may be absorbed and amplified. Moreover, for moderate optical depths, reflection and transmission factors are controlled by the relative phase between control and probe fields, which makes the configuration we present here promising for the development of optical devices. Moreover, we determine the exact conditions where reflection and transmission factors can be controlled by the relative phase between control and probe fields.

We consider a duplicated two-level system where each two-level subsystem is driven by a strong resonant femtosecond pulse and a weak resonant femtosecond pulse connects cross transitions. Strong interference effects are induced in such a configuration leading to a modulation of the medium gain as a function of the relative phase between the pulses []. We study here the influence of the temporal overlap between the pulses on the dynamics of the system and the medium gain. We show that the dynamics is dominated by two competing phenomena: Light shifts (LS) induced by the driving pulse that prevails for small delays and free induction decay (FID) that prevails for large delays. LS enhance the medium gain for and reduce it for , whereas FID always leads to a decrease of the medium gain.

We report the phase control of spatial interference of resonance fluorescence from two duplicated two-level atoms driven by two orthogonally polarized fields. We find that in the strongly driven situation, adjusting the relative phase leads to a redistribution of the atoms and a significant change of the atomic coherences so that the pattern could survive. In order to improve the experimental realizability, we therefore propose a scheme to recover the visibility with fixed relative phase by adjusting the relative intensity between the two driving fields or, alternatively, by using a standing-wave field.