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Physical Review A

Comparison of wavelength dependence in cascade-, Λ-, and Vee-type schemes for electromagnetically induced transparency

J. R. Boon, Evangelini Zekou, David McGloin, Malcolm H. Dunn

Published Jun 1, 1999• 64 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.59.4675

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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 (\ensuremathλc<\ensuremathλp)({\ensuremath{\lambda}}_{c}<{\ensuremath{\lambda}}_{p})(\ensuremathλc​<\ensuremathλp​) 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 (\ensuremathλc>\ensuremathλp)({\ensuremath{\lambda}}_{c}>{\ensuremath{\lambda}}_{p})(\ensuremathλc​>\ensuremathλp​) 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.
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{k}_{c}kc​ === kp{k}_{p}kp​), higher (kc>kp{k}_{c}>{k}_{p}kc​>kp​), or lesser (kc<kp{k}_{c}<{k}_{p}kc​<kp​) than that of the probe field frequency. Contrary to usual belief it is found that for the kc>kp{k}_{c}>{k}_{p}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.
We discuss the electromagnetically induced transparency (EIT) in lambda, cascade and vee type three-level systems where the Hamiltonian and the Lindblad term of each configuration are expressed in the SU(3) representation. At steady state, the Optical Bloch Equations of each configuration are solved to obtain the dispersion and absorption profiles of the probe field along with their group velocities. When the EIT condition is achieved at resonance, the population oscillation shows which of the bare states are contributing to form the dark state. Our study reveals that the dark state for the lambda and cascade system effectively coincides with the lowest bare state of that system, while for the vee system, it is a maximally superposed state of the middle and upper bare states.
Abstract We present the theoretical study of the wavelength dependence of electromagnetically induced transparency (EIT) in a five-level X-type atomic system using dressed state approach. Our numerical calculations reveal that the EIT response of the composite X-type system is more intricate than its constituent Λ and two Ξ subsystems. We derive an analytical solution for probe coherence using the perturbation technique. In the case of stationary atoms, EIT control is possible by varying the strengths and/or the detunings of strong electromagnetic fields. The dressed state picture is employed to describe the position and strength of each peak in probe absorption profile. We also explore in-depth the effect of Doppler broadening on EIT for perfect ( λ p = λ c 1 ≈ λ c 2 = λ c 3 ) and various partial wavelength mismatching schemes ( λ p = λ c 1 > λ c 2 , λ c 3 and λ p = λ c 1 < λ c 2 , λ c 3 ). Our results manifest that when λ p = λ c 1
The effect of changing the coupling laser transition, and hence the wavelength, on the coherently induced transparency seen by a probe beam in a Doppler-broadened cascade electromagnetically induced transparency (EIT) configuration is studied experimentally and theoretically. The transparency of the vapor is shown to be an effect not just of EIT, but of the varying Autler-Townes splitting for each velocity group within the vapor. Consequently, the best overall transparency for Rabi splittings less than the Doppler width is not at the position of matched coupling and probe wavelengths, but for coupling wavelengths less than that of the probe. \textcopyright{} 1996 The American Physical Society.
Continuous inversionless gain is studied in a Doppler-broadened Λ scheme. The inversionless gain is realizable in Doppler-broadened media for a coupling field wavelength well in excess of probe field wavelength when the laser power is significantly less than the Doppler width, and stronger than that of media for the coupling field wavelength equal to the probe field wavelength. In another scheme for the probe field wavelength well in excess of coupling field wavelength, the inversionless gain doesn't exist. The predictions are explained form the point of electromagneticaly-induced transparency.
The propagation of a probe field through a four-level Y-type atomic system is described in the presence of two additional coherent radiation fields, namely, the control field and the coupling field. An expression for the probe response is derived analytically from the optical Bloch equations under steady state condition to study the absorptive properties of the system under probe field propagation through an ensemble of stationary atoms as well as in a Doppler broadened atomic vapor medium. The most striking result is the conversion of electromagnetically induced transparency (EIT) into electromagnetically induced absorption (EIA) as we start switching from weak probe regime to strong probe regime. The dependence of this conversion on residual Doppler averaging due to wavelength mismatch is also shown by choosing the coupling transition as a Rydberg transition.