Geometric phase and entanglement of Raman photon pairs in the presence of photonic band gap
Abstract
Robustness of the geometric phase (GP) with respect to different noise effects is a basic condition for an effective quantum computation. Here, we propose a useful quantum system with real physical parameters by studying the GP of a pair of Stokes and antiStokes photons, involving Raman emission processes with and without photonic band gap (PBG) effect. We show that the properties of GP are very sensitive to the change of the Rabi frequency and time, exhibiting collapse phenomenon as the time becomes significantly large. The system allows us to obtain a state which remains with zero GP for longer times. This result plays a significant role to enhance the stabilization and control of the system dynamics. Finally, we investigate the nonlocal correlation (entanglement) between the pair photons by taking into account the effect of different parameters. An interesting correlation between the GP and entanglement is observed showing that the PBG stabilizes the fluctuations in the system and makes the entanglement more robust against the change of time and frequency.
 Authors:
 Al Imam Mohammad Ibn Saud Islamic University (IMSIU), College of Science, Department of Physics, Riyadh (Saudi Arabia)
 (Italy)
 Department of Physics, University of Malaya, 50603 Kuala Lumpur (Malaysia)
 Mathematics Department, Faculty of Science, Sohag University, 82524 Sohag (Egypt)
 Publication Date:
 OSTI Identifier:
 22399350
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Applied Physics; Journal Volume: 117; Journal Issue: 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONTROL; CORRELATIONS; FLUCTUATIONS; GEOMETRY; NOISE; PHOTON EMISSION; PHOTONS; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUANTUM SYSTEMS; RAMAN EFFECT; STABILIZATION
Citation Formats
Berrada, K., Email: kberrada@ictp.it, The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, MiramareTrieste, Ooi, C. H. Raymond, and AbdelKhalek, S. Geometric phase and entanglement of Raman photon pairs in the presence of photonic band gap. United States: N. p., 2015.
Web. doi:10.1063/1.4916333.
Berrada, K., Email: kberrada@ictp.it, The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, MiramareTrieste, Ooi, C. H. Raymond, & AbdelKhalek, S. Geometric phase and entanglement of Raman photon pairs in the presence of photonic band gap. United States. doi:10.1063/1.4916333.
Berrada, K., Email: kberrada@ictp.it, The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, MiramareTrieste, Ooi, C. H. Raymond, and AbdelKhalek, S. 2015.
"Geometric phase and entanglement of Raman photon pairs in the presence of photonic band gap". United States.
doi:10.1063/1.4916333.
@article{osti_22399350,
title = {Geometric phase and entanglement of Raman photon pairs in the presence of photonic band gap},
author = {Berrada, K., Email: kberrada@ictp.it and The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, MiramareTrieste and Ooi, C. H. Raymond and AbdelKhalek, S.},
abstractNote = {Robustness of the geometric phase (GP) with respect to different noise effects is a basic condition for an effective quantum computation. Here, we propose a useful quantum system with real physical parameters by studying the GP of a pair of Stokes and antiStokes photons, involving Raman emission processes with and without photonic band gap (PBG) effect. We show that the properties of GP are very sensitive to the change of the Rabi frequency and time, exhibiting collapse phenomenon as the time becomes significantly large. The system allows us to obtain a state which remains with zero GP for longer times. This result plays a significant role to enhance the stabilization and control of the system dynamics. Finally, we investigate the nonlocal correlation (entanglement) between the pair photons by taking into account the effect of different parameters. An interesting correlation between the GP and entanglement is observed showing that the PBG stabilizes the fluctuations in the system and makes the entanglement more robust against the change of time and frequency.},
doi = {10.1063/1.4916333},
journal = {Journal of Applied Physics},
number = 12,
volume = 117,
place = {United States},
year = 2015,
month = 3
}

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 nonAbelian 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 nonAbelian geometric phase.

Properties of entangled photon pairs generated in onedimensional nonlinear photonicbandgap structures
We have developed a rigorous quantum model of spontaneous parametric downconversion in a nonlinear 1D photonicbandgap structure based upon expansion of the field into monochromatic plane waves. The model provides a twophoton amplitude of a created photon pair. The spectra of the signal and idler fields, their intensity profiles in the time domain, as well as the coincidencecount interference pattern in a HongOuMandel interferometer are determined both for cw and pulsed pumping regimes in terms of the twophoton amplitude. A broad range of parameters characterizing the emitted downconverted fields can be used. As an example, a structure composed of 49more » 
Auxiliary Entanglement in Photon Pairs for MultiPhoton Entanglement
A growing number of experiments make use of multiple pairs of photons generated in the process of spontaneous parametric downconversion. We show that entanglement in unwanted degrees of freedom can adversely affect the results of these experiments. We also discuss techniques to reduce or eliminate spectral and spatial entanglement, and we present results from twophoton polarizationentangled source with almost no entanglement in these degrees of freedom. Finally, we present two methods for the generation of fourphoton polarization entangled states. In one of these methods, fourphoton can be generated without the need for intermediate twophoton entanglement. 
Highphotonnumber path entanglement in the interference of spontaneously downconverted photon pairs with coherent laser light
We show that the quantum interference between downconverted photon pairs and photons from coherent laser light can produce a maximally path entangled Nphoton output component with a fidelity greater than 90% for arbitrarily high photon numbers. A simple beam splitter operation can thus transform the twophoton coherence of downconverted light into an almost optimal Nphoton coherence. 
Photon pairs with tailormade entanglement obtained from the twophoton decay of atomic hydrogen
From the work by W. Perrie et al. [Phys. Rev. Lett. 54, 1790 (1985)], it is known that the photon pairs that are emitted in the 2s{sub 1/2}{yields}1s{sub 1/2} (twophoton) decay of atomic hydrogen are quantum mechanically correlated, i.e., entangled. However, less information is available about the degree of polarization entanglement between the two photons if an arbitrary geometry is considered for collecting the photons. In this paper, we study the effect of the decay geometry on the degree of polarization entanglement between the two emitted photons. Results are shown for the 2s{sub 1/2}{yields}1s{sub 1/2} and 3d{sub 5/2}{yields}1s{sub 1/2} twophotonmore »