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arXiv:1305.5056 · Journal of Modern Optics

Comparison of electromagnetically induced transparency in lambda, cascade and vee three-level systems

Surajit Sen, Tushar Kanti Dey, Mihir Ranjan Nath, Gautam Gangopadhyay

Published Sep 30, 2014• 21 citations
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Abstract

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.

DOI
10.1080/09500340.2014.960019

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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.
A theoretical model using density matrix approach has been presented to show the polarization dependence of Electromagnetically Induced Transparency (EIT) in cascade multilevel atomic system. EIT has already been investigated both theoretically and experimentally by using three-level system in lambda (Λ), vee (V), and cascade (Ξ) configurations. However there is asymmetry in absorption measurement. To understand this asymmetry we introduce hyperfine levels in EIT cascade system. We present a five-level atomic system, which is a simple case of87Rb. This study has been extended to investigate the polarization dependence of probe and control lasers on EIT. It has been observed that there is significant change in transparency window for different laser polarizations.
We analyze the electromagnetically induced transparency (EIT) in VVV-, $\ensuremath{\Lambda}$-, 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.
Summary form only given. The field of quantum optics was greatly enriched with the discovery of dark states and electromagnetically induced transparency (EIT). Although these two processes give similar effects, they are distinctly different. Dark states (Gray et al, 1978) are quantum states created in a three-level lambda system that is decoupled from the excited state. Some of the main features are zero linear absorption, no population in the excited state and no spontaneous emission. One limiting factor of a dark state system is that self-phase modulation disappears together with absorption. EIT is a nonlinear effect that can provide transparency to a probe field in a variety of systems. Much work has been done on two-level, cascaded-three-level and even four-level systems. It has also been shown that a large third-order nonlinear susceptibility is present in the absence of absorption. However, spontaneous emission cannot be eliminated in such system, thereby limiting their applications, particularly, to squeezed light generation. Here, we combine the effects of both dark state and EIT to create a system that is suitable for squeezed light generation via self phase modulation.
Electromagnetically induced transparency (EIT) resonance is obtained in a well-studied lambda three level system where an optical coupling field and a probing field interact with two optical transitions. However, both electromagnetically induced absorption (EIA) and EIT can be obtained in a modified quasi-lambda four level system consisting of an optical-radio two-photon coupling field and a probing field. By solving the density matrix equation of motion, a physical account of EIA and EIT is given in terms of a dressed state picture. It can be seen that the optical coupling field in this quasi-lambda four level system has a crucial effect on the forming of EIA and EIT. An EIA is observed under a resonant optical coupling and it evolves into an EIT when there is a detuning. Furthermore, the width of EIA or EIT increases as the optical coupling Rabi frequency increases.
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.