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arXiv:quant-ph/0110172 · Optics Communications

Quantum entanglement and the two-photon Stokes parameters

Ayman F. Abouraddy, Alexander V. Sergienko, Bahaa E. A. Saleh, Malvin Carl Teich

Published Jan 1, 2002• 55 citations
arXivHTMLPDF
DOI
10.1016/s0030-4018(01)01645-5

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The correlations of the linear and circular polarizations in the system of two photons have been theoretically investigated. The polarization of a two-photon state is described by the one-photon Stokes parameters and by the components of the correlation “tensor” in the Stokes space. It is shown that in the case of two-photon decays π0 → 2γ, η → 2γ, K 0 → 2γ, K 0 → 2γ and the cascade process |0〉 → |1〉 + γ → |0〉 + 2γ(|0〉 and |1〉 are states with the spin 0 and 1, respectively) the final two-photon state represents a characteristic example of the entangled (nonfactorizable) state, and the correlations between the Stokes parameters in all these decays have the purely quantum character: the incoherence inequalities of the Bell type for the components of the correlation “tensor”, established previously for the case of classical “mixtures”, are violated. The general analysis of the registration procedure for two correlated photons by two one-photon detectors is performed.
Abstract We present a new approach to Stokes parameters, which enables one to see better non-classical properties of bright quantum light, and of undefined overall photon numbers. The crucial difference is as follows. The standard quantum optical Stokes parameters are averages of differences of intensities of light registered at the two exits of polarization analyzers, and one gets their normalized version by dividing them by the average total intensity. The new ones are averages of the registered normalized Stokes parameters, for the duration of the experiment. That is, we redefine each Stokes observable as the difference of photon number operators at the two exits of a polarizing beam splitter multiplied by the inverse of their sum. The vacuum eigenvalue of the operator is defined a zero. We show that with such an approach one can obtain more sensitive entanglement indicators based on polarization measurements.
Stokes parameters are a standard tool in quantum optics. They involve averaged intensities at exits of polarizers. If the overall measured intensity fluctuates, as, e.g., for states with undefined photon numbers, the instances of its increased value contribute more to the parameters. One can introduce normalized quantum Stokes operators. Operationally, for a given single run of the experiment, their values are differences of measured intensities (or photon numbers) at the two exits of a polarizer divided by their sum. Effects of intensity fluctuations are removed. Switching to normalized Stokes operators results in more sensitive entanglement conditions. We also show a general method of deriving an entanglement indicator for optical fields which use polarization correlations, which starts with any two-qubit entanglement witness. This allows one to vastly expand the family of such indicators.