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Physical Review A

Quantification of dissipation in a multilevel electromagnetically-induced-transparency system

ZeHao Shen, Enze Li, Yan Li, Wei Zhang, Hong Lin Gao

Published Sep 22, 2025• 0 citations
Publisher

Abstract

Electromagnetically induced transparency (EIT) in multilevel atomic systems exhibits complex dependencies on optical depth (OD) and polarization configurations, yet their combined effects remain underexplored. Here, we introduce a dissipation factor $\ensuremath{\kappa}$ which quantifies polarization-dependent absorption resulting from the emergence of dissipative channels. Starting from a semiclassical framework, we derive the transmission of a resonant probe as ${T}_{\text{res}}=exp(\ensuremath{-}\ensuremath{\kappa}\ifmmode\cdot\else\textperiodcentered\fi{}d)$, where $d$ denotes the optical depth, demonstrating that $\ensuremath{\kappa}$ and OD jointly govern the transparency. And broadly, $\ensuremath{\kappa}$ is universally applicable across any multilevel system when its value spans a range $\ensuremath{\kappa}\ensuremath{\in}[0,1]$, where $\ensuremath{\kappa}=0$ corresponds to ideal transparency and $\ensuremath{\kappa}=1$ represents pure absorption. Our experimental results in cold $^{87}\mathrm{Rb}$ atomic ensemble across low and high OD regimes confirm the completeness of the theoretical model, with EIT line shapes showing close agreement with simulations. By elucidating the joint effects of OD and polarization-dependent dissipation in EIT, this work is conducive to systemic optimization in multilevel EIT systems such as quantum memory, optical switching, and precision metrology applications.

DOI
10.1103/qby1-jhtm

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Physica Scripta•Sep 17, 2026•0 citations
Electromagnetically induced transparency (EIT) in multilevel atomic systems exhibits complex dependencies on optical depth (OD) and polarization configurations, yet their combined effects remain underexplored. Here, we introduce a dissipation factor \ensuremathκ\ensuremath{\kappa}\ensuremathκ which quantifies polarization-dependent absorption resulting from the emergence of dissipative channels. Starting from a semiclassical framework, we derive the transmission of a resonant probe as Tres=exp(\ensuremath−\ensuremathκ\ifmmode⋅\else\textperiodcentered\fid){T}_{\text{res}}=exp(\ensuremath{-}\ensuremath{\kappa}\ifmmode\cdot\else\textperiodcentered\fi{}d)Tres​=exp(\ensuremath−\ensuremathκ\ifmmode⋅\else\textperiodcentered\fid), where ddd denotes the optical depth, demonstrating that \ensuremathκ\ensuremath{\kappa}\ensuremathκ and OD jointly govern the transparency. And broadly, \ensuremathκ\ensuremath{\kappa}\ensuremathκ is universally applicable across any multilevel system when its value spans a range \ensuremathκ\ensuremath∈[0,1]\ensuremath{\kappa}\ensuremath{\in}[0,1]\ensuremathκ\ensuremath∈[0,1], where \ensuremathκ=0\ensuremath{\kappa}=0\ensuremathκ=0 corresponds to ideal transparency and \ensuremathκ=1\ensuremath{\kappa}=1\ensuremathκ=1 represents pure absorption. Our experimental results in cold 87Rb^{87}\mathrm{Rb}87Rb atomic ensemble across low and high OD regimes confirm the completeness of the theoretical model, with EIT line shapes showing close agreement with simulations. By elucidating the joint effects of OD and polarization-dependent dissipation in EIT, this work is conducive to systemic optimization in multilevel EIT systems such as quantum memory, optical switching, and precision metrology applications.
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.
The behavior of multilevel atomic ensembles (e.g., alkali-metal atoms) can be influenced significantly by the intensity of a driving field (or controlling/coupling field). The phase coherence between two transition pathways driven by a probe light and a driving field can lead to the effect known as electromagnetically induced transparency (EIT). In EIT, the probe light can pass through a three-level alkali-metal atomic vapor without absorption or reflection when two coherent resonances (transition pathways driven by the driving and probe fields) are present and the linewidths of the transparency windows are sufficiently narrow. The optical characteristics of atomic systems can also be affected by the Doppler broadening of the absorption profile in a spectroscope. Our analysis indicates that both broadenings (related to the transitions excited by the driving and probe fields) can be expanded, leading to an increase in the transmittance and reflectance broadenings when a coupling field with adaptive strength is applied; the corresponding temperature would, thus, be implemented and readable. We show that the most suitable preparation for temperature sensing via an EIT vapor is to provide 80 times the spontaneous decay rate (SDR) of the excited atomic levels. This configuration results in reflectance and transmittance values that range between zero and one and cover a temperature range of 0 K to 600 K. As an example, we demonstrate the integration of specialized coating technologies with EIT ensembles for temperature sensing in the range of dozens of kelvins at and above room temperature. A key advantage of this temperature-sensing system is its ability to use adaptive resonant visible light as the probe field. This novel approach may find applications in providing unprecedented levels of precision and control in temperature sensing for coating processes and in the design of other photonic or optical devices. It can also be used to determine the temperature-dependent behavior of the specific heat of alkali-metal solids and gases (including the latent heats of vaporization or sublimation of alkali-metal solids) through the reflection and transmission spectra of the vaporized EIT atomic vapors.
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.
Light propagation through an ensemble of ultracold Rydberg atoms in an electromagnetically-induced-transparency (EIT) configuration is studied. In strongly interacting Rydberg EIT media, nonlinear optical effects lead to a nontrivial dependence of the degree of probe-beam attenuation on the medium density and on its initial intensity. We develop a Monte Carlo rate equation model that self-consistently includes the effect of the probe-beam attenuation to investigate the steady state of the Rydberg medium driven by two laser fields. We compare our results to recent experimental data and to results of other state-of-the-art models for light propagation in Rydberg EIT media. We find that for low probe field intensities, our results match the experimental data best if a density-dependent dephasing rate is included in the model. At higher probe intensities, our model deviates from other theoretical approaches, because it predicts a spectral asymmetry together with line broadening. These are likely due to off-resonant excitation channels, which, however, have not been observed in recent experiments. Atomic motion and coupling to additional Rydberg levels are discussed as possible origins for these deviations.
In the present work, a theoretical and experimental study to enhance electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) signals in an 85 R b atomic vapor medium at room temperature is conducted. Also, switching from EIT to EIA signal at a particular value of the magnetic field is observed. Further, by using circularly polarized coupling light, the dispersion profile of the linearly polarized probe signal is investigated theoretically and experimentally. The nine-level system of 85 R b D2 transition in a ladder-type configuration is fully solved by using the density matrix theory. The simulated results are found in good qualitative agreement with experimental observations. Hence, an experimental setup is developed for (1) achieving enhanced EIT and EIA signal, (2) switching from EIT to EIA, and (3) dispersion measurement. These observations have potential applications towards measurement of the group velocity of light, quantum memory, quantum information, and optical switching.
Abstract Electromagnetically induced transparency (EIT) in five-level atomic systems is theoretically investigated for three representative configurations: M-, inverted-Y, and K-type systems driven by a weak probe field and three control laser fields. The different coupling schemes produce different quantum interference pathways and two-photon resonance conditions, leading to markedly different EIT spectra. The M-type configuration exhibits one, two, and three well-resolved transparency windows as successive control fields are introduced. In contrast, the inverted-Y configuration produces broader transparency windows because of the overlap of multiple interference channels, whereas the K-type configuration exhibits only a single EIT window when all control fields are resonant. Multiple transparency windows in the K-type system appear after introducing appropriate coupling-field detunings. Doppler broadening at room temperature significantly broadens the absorption spectrum and reduces the transparency depth, while preserving the number and positions of the EIT windows. These results demonstrate that the coupling scheme plays an important role in determining the formation and evolution of multi-window EIT spectra and identify the characteristics of the three five-level configurations for multi-channel quantum-optical applications, as well as for the experimental observation of EIT spectra in five-level configurations.