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arXiv:quant-ph/0107061 · American Journal of Physics

Classical analog of electromagnetically induced transparency

Carlos L. Garrido Alzar, M. A. G. Martinez, P. Nussenzveig

Published Jan 1, 2002• 578 citations
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Abstract

We present a classical analog of electromagnetically induced transparency (EIT). In a system of just two coupled harmonic oscillators subject to a harmonic driving force, we reproduce the phenomenology observed in EIT. We also describe a simple experiment with two linearly coupled RLC circuits which can be incorporated into an undergraduate laboratory.

DOI
10.1119/1.1412644

Related papers

Classical Analog of Electromagnetically Induced Transparency

Carlos L. Garrido Alzar, Martínez, M A G, Nussenzveig, P

We present a classical analog for Electromagnetically Induced Transparency (EIT). In a system of just two coupled harmonic oscillators subject to a harmonic driving force we can reproduce the phenomenology observed in EIT. We describe a simple experiment performed with two linearly coupled RLC circuits which can be taught in an undergraduate laboratory class.

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Systems of interacting classical harmonic oscillators have received considerable attention in the past years as analog models for describing electromagnetically induced transparency (EIT) and associated phenomena. We review these models and investigate their validity for a variety of physical systems using two and three coupled harmonic oscillators. From the simplest EIT-$\mathrm{\ensuremath{\Lambda}}$ configuration and two coupled single cavity modes we show that each atomic dipole-allowed transition and a single cavity mode can be represented by a damped harmonic oscillator. Thus, we have established a one-to-one correspondence between the classical and quantum dynamical variables. We show the limiting conditions and the equivalent for the EIT dark state in the mechanical system. This correspondence is extended to other systems that present EIT-related phenomena. Examples of such systems are two- and three-level (cavity EIT) atoms interacting with a single mode of an optical cavity and four-level atoms in a inverted-Y and tripod configurations. The established equivalence between the mechanical and the cavity EIT systems has been corroborated by experimental data. The analysis of the probe response of all these systems also brings to light a physical interpretation for the expectation value of the photon annihilation operator $\ensuremath{\langle}a\ensuremath{\rangle}$. We show that it can be directly related to the electric susceptibility of systems, the composition of which includes a driven cavity-field mode.

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RLC circuits may used to simulate the phenomenon of Electromagnetically Induced Transparency(EIT) in atomic vapors.The EIT-like effect is observed in capacitor coupled RLC circuits due to the classical destructive interference,which is studied by examining the frequency dependence of the power transferred from the external generator to the resonant first loop.We investigated the effect of coupling strength and frequency detuning on EIT-like effect in two mesh circuits which used to analog three-level atom in the Λ configuration and in three mesh circuits which used to analog four-level atom in the inverted-Y and N configuration.

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The phenomena and essential of electromagnetic induced transparency are introduced, and the phenomenon is simulated using two classic linearly coupled RLC circuits. The conclusion that the small coupling capacitance has the more evident effect is gotten. The experiment helps students to understand quantum coherent phenomenon better.

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Demonstration of double EIT using coupled harmonic oscillators and RLC circuits

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Single and double electromagnetically induced transparencies (EIT) in a medium, consisting of four-level atoms in the inverted-Y configuration, are discussed using mechanical and electrical analogies. A three-coupled spring–mass system subject to damping and driven by an external force is used to represent the four-level atom mechanically. The equations of motion of this system are solved analytically, which revealed single and double EIT. On the other hand, three coupled RLC circuits are used, as the electrical analogue, to explore and experimentally demonstrate single and double EIT. The simplicity of these two models makes this experiment appropriate for undergraduate students and easy to incorporate into a college physics laboratory.

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Since a two-level resonant atomic system can be simulated by a simple circuit, three- and four-level electromagnetically induced transparency (EIT) that occur due to light-atom interaction can find its classical counterpart in circuit analog. As the optical response of an EIT atomic medium (including atomic vapors and semiconductor-quantum-dot dielectrics) can be controlled via tunable quantum interference induced by applied external control fields, in the scheme of circuit analog, such a controllable manipulation is achieved via capacitor coupling, where two loops are coupled by a capacitor that can represent the applied control fields in atomic EIT. Both numerical simulation and experimental demonstration of three- and four-level EIT were performed based on such a scenario of circuit analog. The classical “coherence” relevant to quantum interference among transitions pathways driven by both probe and control fields in EIT atomic systems has been manifested in the present circuit analog of EIT.

Advanced materials research•Dec 1, 2011•2 citations
We present a classical analog of electromagnetically induced transparency (EIT). In a system of just two coupled harmonic oscillators subject to a harmonic driving force, we reproduce the phenomenology observed in EIT. We also describe a simple experiment with two linearly coupled RLC circuits which can be incorporated into an undergraduate laboratory.
Systems of interacting classical harmonic oscillators have received considerable attention in the past years as analog models for describing electromagnetically induced transparency (EIT) and associated phenomena. We review these models and investigate their validity for a variety of physical systems using two and three coupled harmonic oscillators. From the simplest EIT-$\mathrm{\ensuremath{\Lambda}}$ configuration and two coupled single cavity modes we show that each atomic dipole-allowed transition and a single cavity mode can be represented by a damped harmonic oscillator. Thus, we have established a one-to-one correspondence between the classical and quantum dynamical variables. We show the limiting conditions and the equivalent for the EIT dark state in the mechanical system. This correspondence is extended to other systems that present EIT-related phenomena. Examples of such systems are two- and three-level (cavity EIT) atoms interacting with a single mode of an optical cavity and four-level atoms in a inverted-Y and tripod configurations. The established equivalence between the mechanical and the cavity EIT systems has been corroborated by experimental data. The analysis of the probe response of all these systems also brings to light a physical interpretation for the expectation value of the photon annihilation operator $\ensuremath{\langle}a\ensuremath{\rangle}$. We show that it can be directly related to the electric susceptibility of systems, the composition of which includes a driven cavity-field mode.
RLC circuits may used to simulate the phenomenon of Electromagnetically Induced Transparency(EIT) in atomic vapors.The EIT-like effect is observed in capacitor coupled RLC circuits due to the classical destructive interference,which is studied by examining the frequency dependence of the power transferred from the external generator to the resonant first loop.We investigated the effect of coupling strength and frequency detuning on EIT-like effect in two mesh circuits which used to analog three-level atom in the Λ configuration and in three mesh circuits which used to analog four-level atom in the inverted-Y and N configuration.
Single and double electromagnetically induced transparencies (EIT) in a medium, consisting of four-level atoms in the inverted-Y configuration, are discussed using mechanical and electrical analogies. A three-coupled spring–mass system subject to damping and driven by an external force is used to represent the four-level atom mechanically. The equations of motion of this system are solved analytically, which revealed single and double EIT. On the other hand, three coupled RLC circuits are used, as the electrical analogue, to explore and experimentally demonstrate single and double EIT. The simplicity of these two models makes this experiment appropriate for undergraduate students and easy to incorporate into a college physics laboratory.
Since a two-level resonant atomic system can be simulated by a simple circuit, three- and four-level electromagnetically induced transparency (EIT) that occur due to light-atom interaction can find its classical counterpart in circuit analog. As the optical response of an EIT atomic medium (including atomic vapors and semiconductor-quantum-dot dielectrics) can be controlled via tunable quantum interference induced by applied external control fields, in the scheme of circuit analog, such a controllable manipulation is achieved via capacitor coupling, where two loops are coupled by a capacitor that can represent the applied control fields in atomic EIT. Both numerical simulation and experimental demonstration of three- and four-level EIT were performed based on such a scenario of circuit analog. The classical “coherence” relevant to quantum interference among transitions pathways driven by both probe and control fields in EIT atomic systems has been manifested in the present circuit analog of EIT.