Xuanying Lai

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to https://www.mdpi.com/openaccess.

Abstract We report the observation of symmetry protected two-photon coherence time of biphotons generated from backward spontaneous four-wave mixing in laser-cooled Rb87 atoms. When biphotons are nondegenerate, nonsymmetric photonic absorption loss results in exponential decay of the temporal waveform of the two-photon joint probability amplitude, leading to shortened coherence time.

1 Introduction Marius Sophus Lie introduced the concept of infinitesimal transformations as early as 1870s, which allowed classification and manipulation of complex matrices based on simple sets of Lie brackets, known as commutation relationships by physicists [1–6]. Lie algebra is especially powerful for applications in quantum mechanics, since the commutation relationships are essential to understanding fundamental properties of elementary particles [5–9].