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Advanced materials research

Experimental Verification of Circuit Analog of Three- and Four-Level Electromagnetically Induced Transparency

Xi Chen, Xia Min Leng, Jing Xin Li, Yi Tsen Yeh, Teh Chau Liau, Jian Qi Shen, Yao‐Huang Kao, Tzong Jer Yang

Published Dec 1, 2011• 2 citations
Publisher

Abstract

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.

DOI
10.4028/www.scientific.net/amr.415-417.1340

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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.
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.
A large number of novel semiclassical and quantum optical effects and phenomena (e.g., coherent population trapping, electromagnetically induced transparency, spontaneous emission inhibition and lasing without population inversion) caused by atomic multi-level phase coherence can be found in three- and four-level atomic vapor media. Such phase coherence includes destructive and constructive quantum interference among various pathways of transition in the atomic systems. Since a simple RLC electric circuit can be used to simulate some resonant responses of a two-level atomic system (or two-state resonant systems), we will consider an analog of interference effect (phase coherence) in an electric circuit containing three RLC meshes for mimicking three- and four-level atomic systems. If certain magnitudes of capacitance and inductance parameters are chosen (or the capacitance and inductance are tuned), the destructive and constructive interference among currents in the circuit can be switched to each other. Thus, the analog of nearly all the quantum coherent effects relevant to a multi-level atomic system that interacts with optical fields can in principle be realized in the present multi-mesh RLC circuit.
Atomic coherence and interference manifested by electromagentically induced transparency (EIT) and coherent population trapping (CPT) plays an important role in the current studies of atom-photon interactions and has found numerous applications in optical physics. EIT is created in a three-level atomic system by a coupling field and results in destructive interference between two excitation paths of a weak probe laser interacting with the atomic medium. This leads to suppressed linear absorption and rapidly varying atomic dispersion for the probe laser near the atomic resonance, which provides the platform for a variety of applications such as nonlinear optics at low light levels, slow light manipulation, and quantum state engineering for photons and atoms. Here we extend the simple three-level EIT system to more complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced: either constructive or destructive interference can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT configuration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system.
A new scheme is suggested to manipulate the probe transitions (and hence the optical properties of atomic vapors) via double-control destructive and constructive quantum interferences. The influence of phase coherence between the two control transitions on the probe transition is also studied. The most remarkable feature of the present scheme is that the optical properties (absorption, transparency and dispersion) of an atomic system can be manipulated using this double-control multi-pathway interferences (multiple routes to excitation). It is also shown that a four-level system will exhibit a two-level resonant absorption because the two control levels (driven by the two control fields) form a dark state (and hence a destructive quantum interference occurs between the two control transitions). However, the present four-level system will exhibit electromagnetically induced transparency to the probe field when the three lower levels (including the probe level and the two control levels) form a three-level dark state. The present scenario has potential applications in new devices (e.g. logic gates and sensitive optical switches) and new techniques (e.g. quantum coherent information storage).
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.
Summary form only given. Electromagnetically induced transparency (EIT) refers to a phenomenon, whereby the optically resonant transition is rendered nearly transparent by applying a strong coupling laser field. The mechanism of EIT is usually explained in terms of quantum coherence or quantum interference. This EIT has attracted increasing interest because absorption associated with nonlinear optical processes can be removed. In the typical three-level /spl lambda/-system, which includes the ground state and the metastable state, when the atomic population is prepared in the superposition of the states by the coupling fields, the optical response of the media to the probe field is significantly modified. Since this is a coherent control of an electric field by another field via the atomic coherence, several schemes to control light coherently have been suggested. We propose an optical coherent control scheme of the polarization of optical pulses using the EIT quantum coherence, and numerically study its applicability to fast optical switching.