We analyze the electromagnetically induced transparency (EIT) in $V$-, $\ensuremath{\Lambda}$-, and cascade-type schemes in a time-dependent way via the Schr\"odinger-Maxwell formalism. We derive explicitly the analytical expressions of the space-time dependent probe field, the corresponding phase shift, absorption or amplification, group velocity, and group velocity dispersion for all the three schemes. These simple analytical expressions not only demonstrate explicitly the similarities and essential differences of the three schemes but also provide a convenient basis for investigating how the many-body effects in solids modify the magnitude, spectral shape, and space and time dependence of EIT and EIT-related quantum coherence phenomena.

Electromagnetically induced transparency in V -, Λ -, and cascade-type schemes beyond steady-state analysis

This review paper is devoted to amplification and lasing without population inversion involving atomic transitions in gas media. We start by discussing the main motivation in inversionless lasing research, namely, the generation of short-wavelength laser light. Then, we review the basic physics of inversionless lasing in two-level and, eventually, in three- and multilevel atomic configurations. Finally, we summarize the current state of the art of LWI experiments and indicate the main difficulties with respect to short-wavelength laser generation.

https://iopscience.iop.org/article/10.1088/1464-4266/2/3/201/pdf

Lasing without inversion

In the initial part of the paper, the principles of the electromagnetically induced transparency (EIT) in basic three-level schemes are sketched, and some applications of this phenomenon are described. Next a presentation follows of a five-level EIT model of Bloch equations, which was developed to reconstruct multipeak cascade-EIT spectra registered in a sample of cold 85 Rb atoms in MOT. The respective experiment is also described. The achieved good agreement between theory and performed experiment is documented and discussed.

/pdf/electromagnetically-induced-transparency-1j0ro66k7e.pdf

Electromagnetically Induced Transparency

We have analysed the properties of an electromagnetically induced grating formed in a Ξ-type three-level atomic system in the presence of a standing wave pump and travelling wave probe fields at resonant and off-resonant two-photon absorption. We have also shown the validity of this grating in an inhomogeneously broadened regime.

https://iopscience.iop.org/article/10.1088/0953-4075/39/5/013/pdf

Electromagnetically induced grating in a three-level Ξ-type system driven by a strong standing wave pump and weak probe fields

Four-wave mixing via electron spin coherence in a quantum well waveguide

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 $({\ensuremath{\lambda}}_{c}l{\ensuremath{\lambda}}_{p})$ 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 $({\ensuremath{\lambda}}_{c}g{\ensuremath{\lambda}}_{p})$ 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.

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

An experimental observation of transparency on a transition in the blue spectral region, induced by a continuous-wave (cw) infrared coupling field in a Doppler-broadened medium, is presented. This experimental result is supported by extensive theoretical modeling of the system, a V-type scheme in atomic rubidium vapor. Transparency is observed by a 422-nm probe field on the transition between the hyperfine split ground state ${5S}_{1/2}$ and the excited state ${6P}_{1/2}.$ The coupling laser is employed on the linked transition ${5S}_{1/2}{\ensuremath{-}5P}_{3/2},$ inducing significant levels of transparency $(g70%)$ nondissipatively and in the absence of optical pumping effects.

Experimental observation of a coherently induced transparency on a blue probe in a doppler-broadened mismatched v-type system

Inversionless gain is predicted in a Doppler-broadened $V$ scheme for which the probe laser frequency is approximately twice that of the coupling laser. A comparison is made of inversionless gain achieved via electromagnetically induced transparency in Doppler-broadened matched and mismatched wavelength systems. We show that the presence of Doppler broadening does not preclude inversionless lasing for mismatched wavelengths; importantly, this is shown to hold even for Rabi splittings significantly less than the Doppler width. Our analysis demonstrates that inversionless gain is realizable in Doppler-broadened media, at modest continuous wave laser powers, for a probe frequency well in excess of the coupling field frequency. The presented theory is related to a practical mismatched system in atomic rubidium vapor. Approximately 8% gain is predicted in a 422 nm probe field coherently driven by a 780 nm coupling field, in the presence of a modest level of incoherent excitation.

J. R. Boon

Papers

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

Experimental observation of a coherently induced transparency on a blue probe in a doppler-broadened mismatched v-type system

Prediction of inversionless gain in a mismatched Doppler-broadened medium