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# Quantum nonlinear cavity quantum electrodynamics with coherently prepared atoms

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We propose a method to study the quantum nonlinearity and observe the multiphoton transitions in a multiatom cavity quantum electrodynamics (CQED) system.We show that by inducing simultaneously destructive quantum interference for the single-photon and two-photon excitations in the CQED system, it is possible to observe the direct three-photon excitation of the higher-order ladder states of the CQED system. We report an experiment with cold Rb atoms confined in an optical cavity and demonstrate such interference control of the multiphoton excitations of the CQED system. The observed nonlinear excitation of the CQED ladder states agrees with a theoretical analysis based on a fully quantized treatment of the CQED system, but disagrees with the semiclassical analysis of the CQED system. Thus it represents a direct observation of the quantum nature of the multiatom CQED system and opens new ways to explore quantum nonlinearity and its applications in quantum optical systems in which multiple absorbers or emitters are coupled with photons in confined cavity structures.
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... This scheme is motivated by work on the atom-driven system and cavity-EIT configuration, where the nonclassicality of cavity photons can be controlled using EIT technique [14,25]. However, differently from early works on the cavity-EIT system [25,46], we consider the atom-driven case, and the frequency of the control field is tuned to be resonant with the one-photon excitation state rather than the cavity. We show that our scheme not only can be used to control the nonclassicality of cavity photons but also exhibits many advantages that the cavity-EIT system does not have. ...
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