We present a theoretical study of the effects of mismatching wavelengths for the coupling and probe fields in Doppler-broadened media for the three basic energy level configurations commonly used to realize electromagnetically induced transparency (EIT). Three wavelength regimes are considered: mismatched wavelengths for which the coupling frequency is greater than the probe frequency, matched wavelengths for which the coupling and probe frequencies are equal, and mismatched wavelengths for which the probe frequency is greater than the coupling frequency. The transparency that may be induced in these regimes is compared for the cascade-, \ensuremath{\Lambda}-, and Vee-type systems. We show that in the first mismatched regime $({\ensuremath{\lambda}}_{c}<{\ensuremath{\lambda}}_{p})$ EIT is possible in all schemes and is in fact stronger than in the matched case. It is also demonstrated that for the second mismatched regime $({\ensuremath{\lambda}}_{c}>{\ensuremath{\lambda}}_{p})$ EIT can be realized most readily in the Vee-type configuration in the presence of Doppler broadening. These predictions are explained by considering the absorption as a function of both the probe field detuning and the atomic velocity.
Abstract For multi-level systems in hot atomic vapors the interplay between the Doppler shift due to atomic motion and the wavenumber mismatch between driving laser fields strongly influences transmission and absorption properties of the atomic medium. In a three-level atomic ladder-system, Doppler broadening limits the visibility of electromagnetically-induced transparency (EIT) when the probe and control fields are co-propagating, while EIT is recovered under the opposite condition of counter-propagating geometry and k p < k c , with k p and k c being the wavenumbers of the probe and control fields, respectively. This effect has been studied and experimentally demonstrated as an efficient mechanism to realize non-reciprocal probe light transmission, which may enable applications as magnetic-field free optical isolators. Here, we describe the basics of this effect and discuss a simple picture for the underlying mechanism. We illustrate how the non-reciprocity scales with wavelength mismatch and show how to experimentally demonstrate the effect in a simple Rydberg-EIT system using thermal Rubidium atoms.
We study electromagnetically induced transparency (EIT) of a probe field in a four-level Y-type atomic system driven by two strong laser (coupling) fields. Both homogeneously (radiative) and Doppler broadened systems are considered. The effect of residual Doppler broadening on EIT is demonstrated for various wave-vector mismatches occurring when the frequency of coupling fields is equal (
kc = kp), higher (
kc>kp), or lesser (
kc<kp) than that of the probe field frequency. Contrary to usual belief it is found that for the
kc>kp wave-vector mismatch case, the probe absorption profile displays very wide and almost complete single or double EIT windows whose width, depth, and location depend upon the wave-vector mismatch, Rabi frequencies, and atom field detuning of the coupling fields. Analytical results are also obtained to explain these interesting features.