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The European Physical Journal D

Simulating coherent interaction of polarized laser light with multi-level atoms in one-dimensional birefringent media of high optical depth

Sergiy Stryzhenko, Леонід Петрович Яценко, Mark IJspeert

Published Sep 1, 2026• 0 citations
Publisher

Abstract

Abstract We present a numerical approach to simulate the propagation of polarized light through a one-dimensional, optically dense, and strongly birefringent medium. The medium is modeled as a gas of atoms with a complex energy-level structure, exemplified by rubidium-87, confined within a birefringent, nonresonant waveguide such as a hollow fiber. The model is formulated within the rotating wave, slowly varying envelope, and Weisskopf–Wigner approximations and is optimized for computational efficiency through the extensive use of tensor operations. As applications, we reproduce key features of two previously reported experiments: biphoton generation via spontaneous four-wave mixing and Raman superfluorescence in an inhomogeneous medium. We further investigate the influence of Zeeman degeneracy and fiber birefringence on electromagnetically induced transparency (EIT) and show that these effects can significantly distort the extracted values of the ground-state dephasing rate.

DOI
10.1140/epjd/s10053-026-01249-1

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Physical Review A•Mar 7, 2011•8 citations
Abstract We present a numerical approach to simulate the propagation of polarized light through a one-dimensional, optically dense, and strongly birefringent medium. The medium is modeled as a gas of atoms with a complex energy-level structure, exemplified by rubidium-87, confined within a birefringent, nonresonant waveguide such as a hollow fiber. The model is formulated within the rotating wave, slowly varying envelope, and Weisskopf–Wigner approximations and is optimized for computational efficiency through the extensive use of tensor operations. As applications, we reproduce key features of two previously reported experiments: biphoton generation via spontaneous four-wave mixing and Raman superfluorescence in an inhomogeneous medium. We further investigate the influence of Zeeman degeneracy and fiber birefringence on electromagnetically induced transparency (EIT) and show that these effects can significantly distort the extracted values of the ground-state dephasing rate.
Low-light-level optical nonlinearities are of significant interest for performing operations such as single-photon switching and quantum non-demolition measurements on single-photons. To evoke strong nonlinearities from singlephotons, one can enhance the matter-photon interaction using strongly nonlinear materials such as alkali vapors in combination with an appropriate geometry such as a waveguide, which provides a long interaction length while maintaining a small light mode area. We demonstrate for the first time that such a system can be experimentally realized by loading rubidium vapor inside a hollow-core photonic band-gap fiber. Using the technique of light-induced atomic desorption in this geometry, we have generated optical depths greater than 1000. As a proof of principle, we demonstrate electromagnetically induced transparency (EIT) with control powers 1000 times lower than those used for hot vapor cells in a focused beam geometry. Working with such a high aspect ratio geometry requires us to identify and measure the various sources of decoherence via spectroscopy of desorbed atoms in the fiber. Using such techniques, we also estimate the temperature of the desorbing atoms inside the fiber. The desorption mechanism is studied, and we show that pulsed desorption beams of the right amplitude and duration can be used for generating precisely controlled optical depths. Finally, we investigate the use of various buffer gas techniques for increasing the effective transverse path of the atoms as they move across the fiber in order to reduce their ground state decoherence and map this effect as a function of buffer gas pressure.
The evolution of an electromagnetic wave with slowly varying polarization, which interacts resonantly with the medium formed by degenerate two-level atoms, is studied using the wave function approach under the conditions of electromagnetically induced transparency. It is shown that the amplitude of the wave field propagates at the velocity of light in such a medium. The equation obtained for the polarization parameter has a solution in the form of a simple wave. The breaking length is determined. It is shown that the velocity of propagation of polarization waves may be much smaller than the velocity of light. The proposed approach is common for two-level systems with an arbitrary degeneracy. The case of a system with Zeeman degeneracy is analyzed in detail. The dependence of the velocity of propagation of the polarization structure on the amplitude and polarization is determined for an arbitrary level degeneracy. The evolution of the polarization structure in such a medium is discussed.
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.
Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.
People have been paying attention to the role of atoms' complex internal level structures in the research of electromagnetically induced transparency (EIT) for a long time, where the various degenerate Zeeman levels usually generate complex linkage patterns for the atomic transitions. It turns out, with special choices of the atomic states and the atomic transitions' linkage structure, clear signatures of quantum interference induced by the probe and coupling light's polarizations can emerge from a typical EIT phenomena. We propose to study a four-state system with double-V\mathsf{\text{V}}V linkage pattern for the transitions and analyze the polarization-induced interference under the EIT condition. We show that such interference arises naturally under mild conditions on the optical field and atom manipulation techniques. Moreover, we construct a variation form of double-M linkage pattern where the polarization-induced interference enables polarization-dependent cross modulation between incident weak lights that can be effective even at the few-photon level. The theme is to gain more insight into the essential question: how can we build a nontrivial optical medium where incident lights experience polarization-dependent nonlinear optical interactions, valid for a wide range of incidence intensities down to the few-photon level?
Electromagnetic induced transparency (EIT) can be produced in a four-level atomic system in the W scheme using a linearly polarized optical field for simultaneously slowing down two $\ensuremath{\sigma}{}^{+}$ and $\ensuremath{\sigma}{}^{\ensuremath{-}}$ circularly polarized optical fields. This four-level atomic system can be set up with a $|{}^{1}{S}_{0}\ensuremath{\rangle}$ ground state and three Zeeman levels of the $|{}^{1}{P}_{1}\ensuremath{\rangle}$ excited state of any alkali-metal atom placed in a weak magnetic field. We apply our W scheme to ultracold magnesium atoms for neglecting the collisional dephasing. Atomic coherences are reported after solving a density matrix master equation including radiative relaxations from Zeeman states of the $|{}^{1}{P}_{1}\ensuremath{\rangle}$ multiplet to the $|{}^{1}{S}_{0}\ensuremath{\rangle}$ ground state. The EIT feature is analyzed using the transit time between the normal dispersive region and the EIT region. The evolution of the EIT feature with the variation of the coupling field is discussed using an intuitive dressed-state representation. We analyze the sensitivity of an EIT feature to pressure broadening of the excited Zeeman states.