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arXiv:1801.00596 · Journal of the Optical Society of America B

Evaluation of two-photon polarization density matrix of polarization-entangled photon pairs generated through biexciton resonant hyper-parametric scattering

Yasuo Yamamoto, Goro Oohata, Kohji Mizoguchi

Published May 22, 2019• 0 citations

Abstract

We have investigated the excitation-power dependence of polarization-entangled photon pairs generated from a CuCl single crystal using biexciton resonant hyper-parametric scattering. The two-photon polarization density matrix of photon pairs generated from a CuCl single crystal maintained at 10 K was measured under different excitation powers. The measured two-photon polarization density matrix, which corresponds to the two-photon polarization state, changes with an increase in the excitation power. The evaluations of the tangle and the linear entropy obtained from the measured density matrix indicate that the two-photon polarization density matrix can be expressed as the mixed state of an ideal state and a totally mixed state, and the mixture ratio of the totally mixed state increases as the excitation density increases. The variations of the density matrix and the mixture ratio with the excitation power originate from the generation of the multiple photon pairs. Furthermore, a numerical calculation considering simultaneous detection efficiency was able to reproduce the experimental results.

DOI: 10.1364/josab.36.001581

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We have investigated the excitation-power dependence of polarization-entangled photon pairs generated from a CuCl single crystal using biexciton resonant hyper-parametric scattering. The two-photon polarization density matrix of photon pairs generated from a CuCl single crystal maintained at 10 K was measured under different excitation powers. The measured two-photon polarization density matrix, which corresponds to the two-photon polarization state, changes with an increase in the excitation power. The evaluations of the tangle and the linear entropy obtained from the measured density matrix indicate that the two-photon polarization density matrix can be expressed as the mixed state of an ideal state and a totally mixed state, and the mixture ratio of the totally mixed state increases as the excitation density increases. The variations of the density matrix and the mixture ratio with the excitation power originate from the generation of the multiple photon pairs. Furthermore, a numerical calculation considering simultaneous detection efficiency was able to reproduce the experimental results.

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Quantum entanglement is one of the most intriguing features of quantum mechanics. To investigate the entanglement between two excitons in a biexciton, an experimental technique called density matrix spectroscopy (DMS) has recently been developed. DMS combines stimulated emission tomography and pump-probe techniques to obtain a time-resolved density matrix of the polarization state of a photon pair emitted from the biexciton. The reconstructed density matrix is expected to encode information about the biexciton state and its entanglement dynamics, but the precise nature of this connection has remained unclear. In this paper, we derive an analytical relationship between the density matrix obtained by DMS and the biexciton state. In addition, we perform numerical simulations to compare the entanglement dynamics obtained by DMS with the biexciton's entanglement dynamics in a two-dimensional electron-hole system using an extended ionic Hubbard model. We find that DMS can partially capture the entanglement in the biexciton, in particular, the dynamics of the difference

S_{\mathrm{bi}} - S_k

, where

S_{\mathrm{bi}}

is the entanglement entropy of the biexciton and

S_k

is the entanglement in terms of the wavevectors of the excitons that constitute the biexciton. These results demonstrate the validity of DMS for obtaining information about the entanglement dynamics of the biexciton.