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Qualitative aspects of the entanglement in the three-level model with
photonic crystals
Mahmoud Abdel-Aty
abstract: This communication is an enquiry into the circumstances under which
concurrence and phase entropy methods can give an answer to the question of
quantum entanglement in the composite state when the photonic band gap is
exhibited by the presence of photonic crystals in a three-level system. An
analytic approach is proposed for any three-level system in the presence of
photonic band gap. Using this analytic solution, we conclusively calculate the
concurrence and phase entropy, focusing particularly on the entanglement
phenomena. Specifically, we use concurrence as a measure of entanglement for
dipole emitters situated in the thin slab region between two semi-infinite
one-dimensionally periodic photonic crystals, a situation reminiscent of planar
cavity laser structures. One feature of the regime considered here is that
closed-form evaluation of the time evolution may be carried out in the presence
of the detuning and the photonic band gap, which provides insight into the
difference in the nature of the concurrence function for atom-field coupling,
mode frequency and different cavity parameters. We demonstrate how fluctuations
in the phase and number entropies effected by the presence of the
photonic-band-gap. The outcomes are illustrated with numerical simulations
applied to GaAs. Finally, we relate the obtained results to instances of any
three-level system for which the entanglement cost can be calculated. Potential
experimental observations in solid-state systems are discussed and found to be
promising.
- oai_identifier:
- oai:arXiv.org:quant-ph/0506226
- categories:
- quant-ph
- comments:
- 28 pages, 10 figures: Accepted in Applied Physics B: Laser and Optics
- doi:
- 10.1007/s00340-005-1838-x
- arxiv_id:
- quant-ph/0506226
- created:
- 2005-06-27
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