Quantum optical properties of polariton waves

The polariton, the normal mode of the coupled matter-radiation system, has been well known for at least 40 years. Certain properties of the polaritons have been extensively studied by a variety of spectroscopic methods. In particular, resonant Brillouin scattering techniques and delicate steady-state optical reflection and transmission studies using polarized light have permitted careful and quantitative mapping of the frequency-wavenumber dispersion {dollar}omega(k)equivomegasb{lcub}k{rcub}{dollar} for exciton-polaritons. Phonon polaritons have been studied by related methods, which in many cases antedate the work on exciton-polaritons. Despite this extensive literature the investigations of the quantum-optical properties of these crystal mixed modes has lagged. By contrast the study of the quantum optical properties of the single and multimode cavity electromagnetic radiation, either in isolation or in interaction with one or more atoms has been extensively developed. Part of this impetus has been the expectation that low noise radiation ("squeezed light") can be used e.g. for gravity wave detectors or in communication. Of course the study of the basic statistical properties of light is itself a major stimulus for such investigations. These effects found in optics have a certain generality and they may have analogs in the condensed media.; 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, non-polariton, mixed photon-exciton boson. The amount and duration of intrinsic squeezing during the polariton period are studied for exciton-polaritons in typical I-VII and III-V semiconductors. Among the new features is the possibility of tuning the amount of intrinsic squeezing by varying the frequency-wavevector of the polariton mode. We further analyse the photon statistics of the electromagnetic component of the polariton. Squeezing and tunable non-poissonian photon statistics are found in the electromagnetic component (optical polariton squeezing) 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 photon in a polariton coherent state has been evaluated. Although small for I-VII and III-V materials in the range of modes analysed, the Q-factor could be enhanced for phonon-polaritons and for other materials. Interpretations of the origin of squeezing in polariton states are presented.