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arXiv:quant-ph/0310170 · Physical Review A

Field correlations and effective two-level atom-cavity systems

S. Rebić, A. S. Parkins, S. M. Tan

Published Mar 19, 2004• 13 citations
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Abstract

We analyze the properties of the second-order correlation functions of the electromagnetic field in atom-cavity systems that approximate two-level systems. It is shown that a recently developed polariton formalism can be used to account for all the properties of the correlations, if the analysis is extended to include two manifolds---corresponding to the ground state and the states excited by a single photon---rather than just two levels.

DOI
10.1103/physreva.69.035804

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We present a time-dependent quantum calculations of the first order and second order photon correlation functions for the scattering of a single-photon pulse on a two-level atom (qubit) embedded in a one-dimensional open waveguide. Within Markov approximation we find the analytic expression for the quantum operator of positive frequency electric field. We restricted Hilbert space of initial states by the states with one and two excitations and show that the photon probability amplitudes are given by the off-diagonal matrix elements of the electric field operator between these states. For two-excitation initial state where the atom is excited and there exists a single photon in a waveguide we calculate the second order correlation function which describes the measurements by two detectors at two different space-time points. The second order correlation function exhibits the interference term showing that the measurements of two detectors are correlated. This interference is similar to that found in the Hanbury Brown and Twiss correlation experiment with two indistinguishable photons.
We present a complete analytical solution for a single four-level atom strongly coupled to a cavity field mode and driven by external coherent laser fields. The four-level atomic system consists of a three-level subsystem in an electromagnetically induced transparency configuration, plus an additional atomic level; this system has been predicted to exhibit a photon blockade effect. The solution is presented in terms of polaritons. An effective Hamiltonian obtained by this procedure is analyzed from the viewpoint of an effective two-level system, and the dynamic Stark splitting of dressed states is discussed. The fluorescence spectrum of light exiting the cavity mode is analyzed and relevant transitions identified.
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Nowadays the light-matter interaction phenomena in spatially periodic structure have been studied extensive, i.e. photonic crystals, cavity array. In this thesis, we consider coherent properties of coupled atom-field systems with adding the interaction between atoms and discuss the quantum phase transition and envelope function method for this system. We further show that beyond widely used low excitation density limit and Holstein-Primakoff transformation. We have shown that the phase transition diagram of the normal to superfluid (BEC) state of low branch polaritons in the critical temperature domain. Finally, a multiple-scale technique has been used to analyze the electromagnetic properties of the nonlinear dielectric periodic thin-film stacks. We have found a solitary–wave equation behavior in the array which includes the atom-atom interaction.