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Journal of Modern Optics

Double cavity induced transparency in a Y-type atomic system based on cavity QED photons

Moteb M. Alqahtani

Published Jan 7, 2025• 2 citations
Publisher

Abstract

We show that a fully quantum-mechanical model consisting of a four-level atom with Y-type atomic structure inside a three-mode cavity can exhibit double cavity induced transparency (CIT). In this model, it is cavity photons that induce the transparency, and there is no need to use external classical fields. As this double-CIT model involves several atomic levels, we adapt the wavefunction approach as a quantum-jump description of dissipation to derive an analytical expression for the steady-state linear susceptibility of a weak cavity field. We then use this analytical expression to investigate the dependence of the CIT transparency windows on the detuning of the coupling fields, intensities of the cavity fields and the cavity linewidths. We also have tested the analytical results by numerically integrating the full set of optical Bloch equations for the atomic density-matrix elements.

DOI
10.1080/09500340.2024.2449571

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We show that a fully quantum-mechanical model consisting of a four-level atom with Y-type atomic structure inside a three-mode cavity can exhibit double cavity induced transparency (CIT). In this model, it is cavity photons that induce the transparency, and there is no need to use external classical fields. As this double-CIT model involves several atomic levels, we adapt the wavefunction approach as a quantum-jump description of dissipation to derive an analytical expression for the steady-state linear susceptibility of a weak cavity field. We then use this analytical expression to investigate the dependence of the CIT transparency windows on the detuning of the coupling fields, intensities of the cavity fields and the cavity linewidths. We also have tested the analytical results by numerically integrating the full set of optical Bloch equations for the atomic density-matrix elements.
A method is presented for creating single- and double-cavity-induced transparency based on a cavity QED framework. Using this method we develop a fully quantized model of a cavity-induced transparency (CIT) scheme previously proposed [P. R. Rice and R. J. Brecha, Opt. Commun. 126, 230 (1996)] adopting the quantum-jump approach. This allows us to analyze the interaction of NNN cavity fields with an (N+1)(N+1)(N+1)-level quantum system where N=2,3N=2,3N=2,3 for the cases of single- and double-cavity-induced transparency, respectively. In the steady-state limit, a general analytic expression for the linear susceptibility of a weak cavity field is obtained and $N\ensuremath{-}1$ transparency windows are observed. In the model we consider, no external fields are required to induce the transparency and the CIT effect is fully generated by cavity QED photons. We also compare the numerical integration of density-matrix equations with the analytical solutions provided by the quantum-jump approach and show that both results are in excellent agreement.
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.
Interference-induced photon antibunching is investigated for a three-level system coupled to a cavity mode, in which the level scheme is of a lambda type. One of the transitions is weakly coupled to the cavity mode while the other is driven by a control field. Without the control field, i.e. , in the conventional cavity quantum electrodynamics (QED) scheme in the weak coupling regime, photon antibunching can be achieved by carefully choosing the coupling strength and the detuning. This condition can be alleviated by tuning the strength and the frequency of the control field. The condition for the optimal control field that yields photon blockade is derived, and the effects of changing various parameters are investigated. For a given a set of dissipation rates, the atom-cavity coupling strength g needs to be higher than a certain threshold value, although the whole system still remains in the weak coupling regime. A numerical method for finding the optimal parameter regime is proposed.
The transmission of a probe field experiencing electromagnetically induced transparency and optical switching in an atomic medium enclosed in an optical cavity is investigated. Using a semiclassical input-output theory for the interaction between an ensemble of four-level atoms and three optical cavity fields coupled to the same spatial cavity mode, we derive the steady-state transmission spectra of the probe field and discuss the dynamics of the intracavity field buildup. The analytical and numerical results are in good agreement with recent experiments with ion Coulomb crystals [M. Albert et al., Nature Photon. 5, 633 (2011)].
We consider a four-level atomic system in inverted-Y system and study the phenomenon of Electromagnetically Induced Transparency (EIT) in this system in interaction with three quantized fields (one probe field and two coupling fields) by full quantum model. The results indicate dependency of the interval between peaks and their altitude in absorption curve of probe field on number of coupling field photons’ that trapped inside the quantum cavity. In this paper a non-demolition photon counting method has been offered for two different kind of photons that belong to coupling fields that interact with an ensemble of four-level Inverted-Y type atoms and a quantize probe field by analytical calculation of density matrix equations.
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.