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Physical Review A

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

Ying Wu, Xiaoxue Yang

Published May 12, 2005• 574 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.71.053806

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Chinese Journal of Lasers•Jan 1, 2004•0 citations
We analyze the electromagnetically induced transparency (EIT) in VVV-, \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-, 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.
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.
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.
The appearance of quantum interference in the microscopic world is one of the deepest mysteries at the very root of quantum mechanics. When light interacts with atoms, it can induce transitions by way of distinct but indistinguishable pathways and yield unexpected and often counter-intuitive results. Electromagnetically Induced Transparency (EIT), Coherent Population Trapping (CPT), and Lasing Without Inversion (LWI) are modern examples of phenomena where the traditional rules that govern absorption and dispersion undergo major revisions. Spectacular consequences of this new state of affairs include the ability of a light beam to propagate through a normally absorbing medium with little or no absorption, or to undergo amplification even if the active medium is not prepared in a state of population inversion. Light signals have been shown to travel with strongly subluminal group velocities of only a handful of meters per second and, even, to propagate at speed greater than the ordinary speed of light, but without violation of causality or of the established rules that control the transfer of optical information through space. Three-level atoms can interact with two coherent electromagnetic fields according to three different systems, known as Cascade, Lambda and Vee systems. The propagation of a weak probe field can be deeply affected by the presence of a second stronger beam, the so-called coupling field. Transparency windows, splitting of emission and absorption lines and enormously enhanced dispersion have been documented in numerous experiments. In this thesis we explore the physical origin of the transparency induced in these systems by the simultaneous interplay of the coupling and probe fields. We focus our attention on the Cascade system and study its two configurations, Cascade-EIT and Cascade-AT. We develop a variety of complementary approaches for the description of these two configurations, some semiclassical and others fully quantum mechanical. We prove the existence of quantum interference in Electromagnetically Induced Transparency and also the surprising absence of interference in a closely related phenomenon, known as the Autler-Townes effect. Finally we complement the traditional machinery of theoretical quantum optics with techniques borrowed from quantum scattering theory, and offer what we believe is the most convincing physical evidence for the appearance, or for the absence, of quantum interference effects.
We theoretically investigate a double-Λ electromagnetically induced transparency (EIT) system. The property of the double-Λ medium with a closed-loop configuration depends on the relative phase of the applied laser fields. This phase-dependent mechanism differentiates the double-Λ medium from the conventional Kerr-based nonlinear medium, e.g., EIT-based nonlinear medium discussed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)], which depends only on the intensities of the applied laser fields. Steady-state analytical solutions for the phase-dependent system are obtained by solving the Maxwell-Bloch equations. In addition, we discuss efficient all-optical phase modulation and coherent light amplification based on the proposed double-Λ EIT scheme.
Electromagnetically induced transparency (EIT) in a molecular three-level Λ system with permanent dipole moments and undergoing m- and n-photon transitions by pump and probe lasers is investigated. Analytical expressions are derived for probe absorption spectrum and dispersion for a medium of stationary as well as thermal molecules. Contrary to the earlier study by Zhou et al. [J. Chem. Phys. 131, 034105 (2009)], we observe no amplification in 2 + 2 photon process when the sign of the difference of the permanent moments of the excited and the ground levels is reversed. Reasons for these contrasting observations are discussed. Our study shows that the permanent moments essentially damp the laser-molecule Rabi frequency to result in narrower EIT line width and larger group velocity index. These effects are further enhanced when the order of the multi-photon process is increased. The importance of the virtual mechanism is discussed by considering the special case of 2 + 1 photon EIT.
The transient properties of electromagnetically induced transparency (EIT) with different pump laser energies in a Λ-type three-level system are studied by solving the time-dependent matrix equation. The time evolution of the probe laser absorption, the population of the three levels and the coherent term ρ 23 are analyzed. It is shown that transient amplification without inversion can be realized with high pump laser energy and that transient EIT would reduce and transient amplification without inversion would disappear with the decrease of the pump laser energy. Since the probe absorption depends on the product of Rabi frequency of the pump laser and the coherent term ρ 23, the nonzero damping coherent term ρ 23 results in the transient absorption and amplification without inversion at high pump laser energy, and the decrease of the coherence with the decrease of the pump laser energy leads to the disappearance of the amplification and enhancement of absorption.