Quantum-optical properties of polariton waves

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Abstract
We develop a quantum-mechanical Hamiltonian formulation to treat the polariton in the framework of quantum optics. We exploit two specific Hamiltonians: the conventional Hopfield model, and a more general Hamiltonian. For both of these, exciton-polariton quantum states are found to be squeezed (intrinsic polariton squeezing) with respect to states of an intrinsic, nonpolaritonic, mixed photon-exciton boson. The amount and duration of intrinsic squeezing during the polariton period are calculated for exciton polaritons in typical I-VII and III-V semiconductors. Among the noteworthy features is the possibility of tuning the amount of intrinsic squeezing by varying the frequency–wave-vector dispersion of the polariton mode. We further analyze the photon statistics of the electromagnetic component of the polariton. Tunable non-Poissonian photon statistics and squeezing (optical polariton squeezing) are found in the radiative component of the exciton polariton. This entails the reduction of the fluctuations of the polariton electromagnetic field component below the limit set by the vacuum fluctuations. The Mandel Q factor for the number distribution of photons in a polariton coherent state has been evaluated. Although small, for I-VII and III-V materials in the range of modes analyzed, the Q factor could be enhanced for phonon polaritons as well as for other materials. Interpretations of the origin of squeezing in polariton states are presented.