Violation of the Cauchy-Schwarz Inequality in Collective Raman Scattering

Nikolay N. Bogolubov, A.S. Shumovsky, Tran Quang

S. V. Lawande, B. N. Jagatap

Yongqing Li, Paul J Edwards, Xu Guang Huang +1 more

A Cauchy-Schwarz inequality in photon noise spectra is derived and discussed for macroscopic fields of light. Violation of this Cauchy-Schwarz inequality is demonstrated experimentally in quantum noise-correlated light beams radiated from a pair of electrically coupled light-emitting diodes. Our measurements directly demonstrate that the violation of this Cauchy-Schwarz inequality can be observed in the absence of sub-shot noise fluctuations in either the single-beam intensity or the dual-beam intensity difference. Therefore, the dual-beam quantum correlation condition required for the violation of this Cauchy-Schwarz inequality is not associated with sub-shot noise fluctuations.

Nikolay N. Bogolubov, A.S. Shumovsky, Tran Quang

Tran Quang, A.S. Shumovsky

Yunxia Ping, Lie Liu, Chaomin Zhang +1 more

Violations of Bell inequality, Cauchy—Schwarz inequality and entanglement in a two-mode three-level atomic system are investigated. It is shown that there are some states, which are entangled but do not violate Bell inequality in this system. Moreover, the relations of violations of Bell inequality, Cauchy—Schwarz inequality, and entanglement are discussed in detail.