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arXiv:1408.1024 · Physical Review A

Electromagnetically-induced-transparency-related phenomena and their mechanical analogs

James Alves de Souza, Luis A. Cabral, R. R. Oliveira, Celso J. Villas-Bôas

Published Aug 11, 2015• 51 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.92.023818

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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-\ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ 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⟨a\ensuremath⟩\ensuremath{\langle}a\ensuremath{\rangle}\ensuremath⟨a\ensuremath⟩. We show that it can be directly related to the electric susceptibility of systems, the composition of which includes a driven cavity-field mode.
We introduce a simple model for electromagnetically induced transparency in which all fields are treated quantum mechanically. We study a system of three separated atoms at fixed positions in a one-dimensional multimode optical cavity. The first atom serves as the source for a single spontaneously emitted photon; the photon scatters from a three-level Lambda-configuration atom which interacts with a single-mode field coupling two of the atomic levels; the third atom serves as a detector of the total transmitted field. We find an analytical solution for the quantum dynamics. From the quantum amplitude describing the excitation of the detector atom we extract information that provides exact single-photon analogs to wave delays predicted by semi-classical theories. We also find complementary information in the expectation value of the electric field intensity operator.
Abstract We study electromagnetically induced transparency (EIT), which is affected by cavity optomechanics in different atomic configurations ( V and Λ ). The cavity mode is depicted as a probe field, and a classical driving field is applied to the atomic medium as the control laser in each system. Interaction between the cavity mode, atomic media and the oscillating mirror of the cavity can change the susceptibility of the atomic ensemble. Equations of motion demonstrate a system of nonlinear equations for each system. Nonlinearity of equations is a result of interaction between the cavity mode and atomic transitions. The equations are solved via a perturbation method. The results show two different aspects of atom-assisted optomechanics in V -type system: a common transparency window and an amplifying process in a transparency window that does not occur in the Λ configuration, notable as a considerable difference between the proposed systems. It is shown that classical field detuning leads to different changes in the susceptibility of both systems; other values of cavity detuning, except in the resonant case, can guarantee the occurrence of EIT in the system. For the initial value of the cavity field, a negative region appears in absorption spectrum of the V -type atomic ensemble. Meanwhile, the Λ configuration does not show a such process. According to our results, in the appearance of the transparency window, the position of movable mirror changes significantly.
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.
Some optomechanical systems can be transparent to a probe field when a strong driving field is applied. These systems can provide an optomechanical analog of electromagnetically induced transparency (EIT). We study the transmission of a probe field through a hybrid optomechanical system consisting of a cavity and a mechanical resonator with a two-level system (qubit). The qubit might be an intrinsic defect inside the mechanical resonator, a superconducting artificial atom, or another two-level system. The mechanical resonator is coupled to the cavity field via radiation pressure and to the qubit via the Jaynes-Cummings interaction. We find that the dressed two-level system and mechanical phonon can form two sets of three-level systems. Thus, there are two transparency windows in the discussed system. We interpret this effect as an optomechanical analog of two-color EIT (or double EIT). We demonstrate how to switch between one and two EIT windows by changing the transition frequency of the qubit. We show that the absorption and dispersion of the system are mainly affected by the qubit-phonon coupling strength and the transition frequency of the qubit.
Abstract We study the reflected and transmitted output properties of a weak probe field incident upon an optomechanical cavity separated by a membrane oscillator and filled with two-level cold atoms. We find that electromagnetically induced transparency (EIT) and optomechanically induced transparency (OMIT) may simultaneously exist owing to separate cavity–atom coupling and cavity-oscillator coupling, respectively. It is more interesting that the hybrid EIT and OMIT phenomena can be manipulated on demand to exhibit various spectral features on dispersion, transmission, and reflection. In particular, we discover the new hybrid double transparency window (a narrow OMIT dip appearing inside the wide EIT window), analogous to double EIT for a four-level atomic system in inverted-Y configuration. Meanwhile, we can reduce the hybrid EIT–OMIT to a single EIT or OMIT shape by changing the magnitude of the driving field power or the atomic number as desired. Furthermore, by changing the system’s detuning it is possible to change the location and the profile of the EIT, therefore switching the shape of the hybrid EIT–OMIT from symmetric to asymmetric, as well as for the profile to change from a absorption dip-like EIT to dispersion-like EIT in both real and imaginary parts of the output probe field. Also, by modifying system’s detuning we have control over the distribution of the output energy, something difficult to achieve with only one of the sub-systems available.
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.