Entanglement of three-level atomic system and spontaneous emission fields in a vacuum and near the 1D photonic crystal band gap

Abstract

The time evolution of the quantum entropy in a GaAs/AlAs one-dimensional photonic crystal (1DPC) with an atomic system defect layer is investigated in this work. The entanglement between atomic system and their spontaneous emission fields near the edge of the photonic band gap (PBG) is coherently controlled by the coupling field. Comparison between the atom-photon entanglement of the atomic system in the vacuum surrounding and that near the PBG of the 1DPC shows that the degree of entanglement strongly depends on the PBG. We find that degree of entanglement is strongly dependent on the intensity and detuning of the coupling and probe fields. Furthermore, the effect of the phase difference between applied fields on the atom-photon entanglement is studied. The potentially possible technological applications can be provided by the proposed model in the quantum optics and quantum communications based on photonic crystal.

References

[1] ShiriJ, ShahiF, MehmannavazM R, et al.. Phase control of transient optical properties of double coupled quantum-dot nanostructure via Gaussian laser beams[J]. Chinese physics letters, 2018, 35(02):024204

[2] Al-AmeriH H, AbdullahM, Al-KhursanA H. Entanglement in ladder-plus-Y double quantum dot structure via entropy[J]. Applied optics, 2019, 58: 369

[3] HuX M, HuangC X, ShengY B, et al.. Long-distance entanglement purification for quantum communication[J]. Physical review letters, 2021, 126: 010503

[4] StuteA, CasaboneB, SchindlerP, et al.. Tunable ion-photon entanglement in an optical cavity[J]. Nature, 2012, 485: 482-485

[5] KuangL M, ZhouL. Generation of atom-photon entangled states in atomic Bose-Einstein condensate via electromagnetically induced transparency[J]. Physical review A, 2003, 68: 043606

[6] EntezarS R. Entanglement of a two-level atom and its spontaneous emission near the edge of a photonic band gap[J]. Physical review A, 2009, 373(38):3413-3418

[7] SahraiM, BoroojerdiV T A. Dynamical behavior of atom-photon entanglement for a four-level atom near the band edge of a 3D-anisotropic photonic crystal[J]. Quantum information processing, 2017, 16: 145

[8] SangshekanB, SaghavazN E, GharamalekiA H, et al.. Maximal atom-photon entanglement by the incoherent pumping fields[J]. European physical journal plus, 2019, 134: 274

[9] GarrawayB M, KnightP L. Cavity modified quantum beats[J]. Physical review A, 1996, 54: 3592-3602

[10] ZhangH Z, TangS H, DongP, et al.. Quantum interference in spontaneous emission of an atom embedded in a double-band photonic crystal[J]. Physical review A, 2002, 65: 063802

[11] AbdallaM S, Abdel-AtyM, ObadaA S F. Entropy and entanglement of time dependent two-mode Jaynes-Cummings model[J]. Physica A: statistical mechanics and its applications, 2003, 326(1–2):203-219

[12] ShiriJ, KhalilzadehJ, AsadpourS. Optical properties of 87 Rb atomic vapor near the 1D photonic crystal bandgap and all-optical switching of transmitted light[J]. Physica scripta, 2022, 97: 035503

[13] YablonovitchE. Inhibited spontaneous emission in solid-state physics and electronics[J]. Physical review letters, 1987, 58: 2059-2062

[14] EntezarS R, TajalliH. Probe absorption-dispersion spectra of a driven three-level atom in a double-band photonic crystal[J]. Journal of physics B-atomic molecular and optical physics, 2006, 39: 2959-2967

[15] AdachiS. GaAs, AlAs, and Al_xGa_1−xAs: material parameters for use in research and device applications[J]. Journal of applied physics, 1985, 58: R1-R29

[16] RupasovV I, SinghM. Two-atom problem and polariton-impurity band in dispersive media and photonic-band-gap materials[J]. Physical review A, 1997, 56: 898-904

[17] ArakiH, LiebE H. Entropy inequalities[M], 2002, Berlin, Heidelberg, Springer: 47-57

[18] PhoenixS J D, KnightP L. Establishment of an entangled atom-field state in the Jaynes-Cummings model[J]. Physical review A, 1991, 44: 6023-6029

[19] KittelC. Introduction to solid state physics[M], 2005, 8th editionNew York, John Wiley & Sons