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Applied Sciences

A Perturbative View from the Master Equation: Electromagnetically Induced Transparency Revisited

Xin Wang

Published Oct 24, 2019• 1 citation
Publisher

Abstract

We show that by treating the weak probe field as a perturbation to the strong coupling fields in the atomic system and using the perturbative method in a master equation, the features of linear response of phenomena of electromagnetically induced transparency (EIT) can be uniformly demonstrated, regardless of the details of atomic energy level configuration. We compare our estimation with both typical and atypical EIT-observed configurations and find that our model indeed provides a description of the sharp transmission window in central area of typical EIT curve. It can also be inferred hereby that for various systems other than atomic gas, as long as the description of the system’s dynamics comes down to the simplified form of master equation, the corresponding EIT analogs and EIT-like phenomena can also be explained in this way.

DOI
10.3390/app9214512

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•Mar 16, 2012•1 citation
We show that by treating the weak probe field as a perturbation to the strong coupling fields in the atomic system and using the perturbative method in a master equation, the features of linear response of phenomena of electromagnetically induced transparency (EIT) can be uniformly demonstrated, regardless of the details of atomic energy level configuration. We compare our estimation with both typical and atypical EIT-observed configurations and find that our model indeed provides a description of the sharp transmission window in central area of typical EIT curve. It can also be inferred hereby that for various systems other than atomic gas, as long as the description of the system’s dynamics comes down to the simplified form of master equation, the corresponding EIT analogs and EIT-like phenomena can also be explained in this way.
We show that by treating the weak probe field as a perturbation to the strong coupling fields in the atomic system and using the perturbative method in a master equation, the features of linear response of phenomena of electromagnetically induced transparency (EIT) can be uniformly demonstrated, regardless of the details of atomic energy level configuration. We compare our estimation with both typical and atypical EIT-observed configurations and find that our model indeed provides a description of the sharp transmission window in central area of typical EIT curve. It can also be inferred hereby that for various systems other than atomic gas, as long as the description of the system’s dynamics comes down to the simplified form of master equation, the corresponding EIT analogs and EIT-like phenomena can also be explained in this way.
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.
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.
The propagation of a probe field through a four-level Y-type atomic system is described in the presence of two additional coherent radiation fields, namely, the control field and the coupling field. An expression for the probe response is derived analytically from the optical Bloch equations under steady state condition to study the absorptive properties of the system under probe field propagation through an ensemble of stationary atoms as well as in a Doppler broadened atomic vapor medium. The most striking result is the conversion of electromagnetically induced transparency (EIT) into electromagnetically induced absorption (EIA) as we start switching from weak probe regime to strong probe regime. The dependence of this conversion on residual Doppler averaging due to wavelength mismatch is also shown by choosing the coupling transition as a Rydberg transition.
Semi-quantum or full-quantum electromagnetically induced transparency has been fully studied for three-level atoms in a weak field approximation method, where probe field is very wea ker than the coupling field. The weak field approximation is no t valid in full-quantum model where the number of coupling photons is not so large. In the present article, the master equations for the interaction of two-mode photons with a three-level Λ -type atom are exactly solved and the exact dispersion and absorption spectra for the probe beam photons are also obtained analytically. The results of the exact scheme are compared with the corresponding results in the weak field approximation method in full-quantum and semi-classi cal models.
Atomic coherence is induced in the multilevel atomic system via strong control field that alters the response of medium to a weak probe laser field. This involves quantum interference in the amplitudes of optical transitions and causes the cancellation of absorption, i.e., electromagnetically induced transparency (EIT). Electromagnetically induced transparency is investigated inside a planar optical waveguide. The eigenvalue equation for the waveguide is solved and used to explore various EIT effects. We show how EIT depends on the incidence angle and allowed mode order of the waveguide and on position of EIT atom inside the structure.