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Journal of Mathematical Chemistry

Some features of the nonlocal correlation and geometric phase of the quantum system in two-mode nondegenerate entangled states

Sadah Abdullah Alkhateeb, S. Abdel‐Khalek

Published Aug 17, 2019• 0 citations
Publisher
DOI
10.1007/s10910-019-01057-6

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An important kind of interaction between two moving two-level atoms and a field mode, where the coupling parameter is taken to be time-dependent, is presented in this paper. Nonlocal correlations between the atoms and the field have been investigated by means of concurrence and von Neumann entropy in terms of the involved parameters of the system. The results show that the atomic motion plays an essential role in the evolution of system dynamics, its nonlocal correlations and geometric phase. Moreover, an interesting correlation between the entanglement and the geometric phase during the evolution was observed. The presented system can be very useful for generating and maintaining high amount of entanglement by means of controlling the parameters of atomic motion.
We introduce the entanglement gauge describing the combined effects of local operations and nonlocal unitary transformations on bipartite quantum systems. The entanglement gauge exploits the invariance of nonlocal properties for bipartite systems under local (gauge) transformations. This new formalism yields observable effects arising from the gauge geometry of the bipartite system. In particular, we propose a non-Abelian gauge theory realized via two separated spatial modes of the quantized electromagnetic field manipulated by linear optics. In this linear optical realization, a bipartite state of two separated spatial modes can acquire a non-Abelian geometric phase.
Experimental demonstration of quantum entanglement among more than two quantum systems with continuous spectra is summarized in the paper. The tripartite entangled state, named also GHZ-like state, is produced by distributing a two-mode squeezed state light to three parties using beamsplitter. A nondegenerate optical parameter amplifier (NOPA) operating at deamplification serves as the initial bipartite entanglement source. The output optical modes from the NOPA are a pair of bright EPR entangled beams with orthogonal polarizations, anticorrelated amplitude quadratures and correlated phase quadratures. The results confirm the existence of the quantum correlation among three amplitude quadratures of modes.