Optical transparency and nonlinearity for a five-level tripod system involving a Rydberg state
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Optical transparency and nonlinearity for a five‑level tripod system involving a Rydberg state Mehdi Javanmard1 Received: 26 February 2020 / Accepted: 29 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We demonstrate electromagnetically-induced transparency and giant Kerr nonlinearity in a five-level atomic system where the upper level is a Rydberg-state coupled coherently to a four-level tripod subsystem. Since the high Rydberg states exhibit rather long lifetimes, the system evolves into a dark state that is a superposition of all long-lived states resulting in an optical transparency for the probe field. We solve the relevant density matrix equations for the atomic system in steady-state and utilize the perturbation approach to obtain the expressions for the linear and nonlinear susceptibility. It is shown that depending on the system parameters, the system can exhibit triple, double or single, optical transparency. Therefore, there is a resulting change in the sign of linear dispersion for different parametric situations giving, rise to switching in the group velocity of the probe pulse from superluminal to subluminal or vice versa. We also identify the existence of giant third-order Kerr nonlinearities within regions of optical transparency and under the slow light condition. Keywords Rydberg EIT · Five-level tripod system · Giant Kerr nonlinearity
1 Introduction Electromagnetically-induced transparency (EIT) is a quantum interference effect arising in three-level systems in Λ configuration composed of two long-lived states coupled coherently through a short-lived state (Fleischhauer et al. 2005; Harris 1997). Application of a strong laser field makes the resonant absorbing medium completely transparent in a narrow spectral window (Boller et al. 1991; Wu and Yang 2005). More complicated EIT configurations are constructed by adding extra energy levels and optical fields to the Λ system, such as the four-level tripod (Paspalakis and Knight 2002a; Beck and Mazets 2017), the double-𝛬 (Korsunsky et al. 1999), the double-tripod (Lee et al. 2014) and the combined tripod and 𝛬 (Hamedi et al. 2017) atom light coupling schemes. The EIT mechanism is responsible for various important phenomena (Asadpour and Soleimani 2014; Sahrai et al. 2004; Paspalakis and Knight 2002; Asadpour et al. 2013; * Mehdi Javanmard [email protected] 1
Department of Computer Engineering and Information Technology, Payam Noor University (PNU), P.O.BOX 19395‑3697, Tehran, Iran
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Li et al. 2011; Solookinejad et al. 2019; Asadpour 2017; Wu et al. 2003; Yang et al. 2005; Wang et al. 2014; Wang and Yu 2014; Javanmard and Refayen 2017; Hamedi 2016; Sedighian and Javanmard 2014; Wu and Yang 2007; Solookinejad et al. 2017; Hang and Huang 2010; Hamedi and Juzeliūnas 2015; Yang et al. 2011; Wu 2008; Wu and Deng 2004; Chen et al. 2014; Wang et al. 2002, 2012; Wu 2005; Si et al. 2010; Wang and Yu 2012; Joshi et al. 2003; Zhang et al. 2012; Hamedi
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