Abstract
This work examines how the real part (dispersion) and imaginary part (absorption or gain) of susceptibility control the entropy in the ladder-plus-Y double quantum dot structure under spontaneously generated coherence (SGC). The results show that the higher real part of susceptibility is related to the higher SGC factor and the structure transfer between the normal and anomalous dispersion but, in a way, depends on the strength of the probe field. At a very weak probe, the system transfers from the gain case under no SGC to an absorption case with increasing SGC and returns to gain under a complete SGC. High entropy is associated with high SGC. When the probe field grows, the system pinned the gain case, but the gain and dispersion are reduced depending on probe increment, reducing the entropy. In a few words, high entropy is associated with high dispersion and gain resulting from a weak probe.
Similar content being viewed by others
Availability of data and material
The data used are placed in the text of this work.
References
M.K. Elsaid, E. Hijaz, Magnetic susceptibility of coupled double GaAs quantum dot in magnetic fields. Acta Phys. Pol. A 131(6), 1491 (2017)
B.O. Al-Nashy, B.T.S. Al-Mosawi, M.O. Oleiwi, A.H. Al-Khursan, Gain of TlBr/BrCl quantum dot semiconductor optical amplifier. J. Electr. Comput. Eng. 2023, 1941232 (2023)
M.O. Oleiwi, B.O. Al-Nashy, SKh. Ajeel, A.H. Al-Khursan, InGaAsSb/GaAsSb quantum dot structures. Micro Nano Lett. 18, e12159 (2023)
B. Al-Nashy, S. Razzaghi, M.A. Al-Musawi, H.R. Saghai, A.H. Al-Khursan, Giant gain from spontaneously generated coherence in Y-type double quantum dot structure. Results Phys. 7, 2411–2416 (2017)
J. Li, R. Yu, J. Liu, P. Huang, X. Yang, Voltage-controlled optical bistability of a tunable three-level system in a quantum-dot molecule. Phys. E 41(1), 70–73 (2008)
M. Sahrai, M.R. Mehmannavaz, H. Sattari, Optically controllable switch for light propagation based on triple coupled quantum dots. Appl. Opt. 53(11), 2375–2383 (2014)
F.K. Hachim, B.O. Al-Nashy, A.H. Al-Khursan, Slow light in a double quantum dot system. Opt. Quant. Electron. 55, 831 (2023)
X. Hao, J. Wu, Y. Wang, Steady-state absorption–dispersion properties and four wave mixing process in a quantum dot nanostructure. J. Opt. Soc. Am. B 29(3), 420–428 (2012)
G.G. Tarasov, Z.Y. Zhuchenko, M.P. Lisitsa, Y.I. Mazur, Z.M. Wang, G.J. Salamo, T. Warming, D. Bimberg, H. Kissel, Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures. Semiconductors 40, 79–83 (2006)
A. Vafafard, S. Goharshenasan, N. Nozari, A. Mortezapour, M. Mahmoudi, Phase-dependent optical bistability in the quantum dot nanostructure molecules via inter-dot tunneling. J. Lumin. 134, 900–905 (2013)
Y. She, X. Zheng, D. Wang, W. Zhang, Controllable double tunneling induced transparency and solitons formation in a quantum dot molecule. Opt. Express 21(14), 17392–17403 (2013)
D. Yan, Y. Liu, Q. Bao, C. Fu, J. Wu, Electromagnetically induced transparency in an inverted-Y system of interacting cold atoms. Phys. Rev. A 86(2), 023828 (2012)
S. Kuang, H. Yang, Blazed gain grating in a four-level atomic system. J. Opt. Soc. Am. B 30(1), 136–139 (2013)
Y. Zhang, M. Xiao, Enhancement of six-wave mixing by atomic coherence in a four-level inverted Y system. Appl. Phys. Lett. 90, 111104 (2007)
S. Michael, W.W. Chow, H.C. Schneider, Group-velocity slowdown in quantum-dots and quantum-dot molecules. Proc. SPIE 8980, 89801I (2014)
J. Kim, S.L. Chuang, Theoretical and experimental study of optical gain, refractive index change, and line width enhancement factor of p-doped quantum-dot lasers. IEEE J. Quantum Electron. 42(9), 942–952 (2006)
H. Al-Husaini, A.H. Al-Khursan, S.Y. Al-Dabagh, III-N QD lasers. Open Nanosci. J. 3, 1–11 (2009)
T. Dakhil, S.M. Abdulalmuhsin, A.H. AL-Khursan, Tunable mechanisms of quantum efficiencies in CdSe and TiO2 quantum dot solar. Appl. Opt. 57(4), 612–619 (2018)
T. Dakhil, S.M. Abdulalmuhsin, A.H. AL-Khursan, Quantum efficiency of CdS quantum dot photodetectors. Micro Nano Lett. 13(8), 1185–1187 (2018)
J.N. Jabir, S.M.M. Ameen, A.H. Al-Khursan, Plasmonic quantum dot nanolaser: effect of waveguide fermi energy. Plasmonics 14, 1881–1891 (2019)
H.H. Al-Ameri, M. Abdullah, A.H. Al-Khursan, Quantum entropy in ladder-plus-Y double quantum dot system using spontaneously generated coherence. Int. J. Theor. Phys. 60(1), 10–25 (2021)
B. Al-Nashy, S.M.M. Amin, A.H. Al-Khursan, Kerr effect in Y-configuration double quantum dot System. JOSA B 31(8), 1991–1996 (2014)
B. Al-Nashy, S.M.M. Ameen, A.H. Al-Khursan, Kerr dispersion in Y-configuration double quantum dot System. J. Opt. 16(10), 105205 (2014)
H.H. Al-Ameri, M. Abdullah, A.H. Al-Khursan, Entanglement in ladder-plus-Y-double quantum dot structure via entropy. Appl. Opt. 58(2), 369–382 (2019)
F.K. Hachim, F.H. Hanoon, A.H. Al-Khursan, Quantum holography in ladder-plus-Y double quantum dot system. Opt. Quantum Electron. 53, 18 (2021)
S. Jasim, A.M. Chkheam, B. Al-Nashy, A.H. Al-Khursan, Kerr effect in ladder-plus-Y-configuration in double quantum dot structure. J. Korean Phys. Soc. 78, 1084–1088 (2021)
B. Al-Nashy, S. Jasim, A.G. Al-Shatravi, A.H. Al-Khursan, Spontaneously generated coherence in ladder-plus-Y double quantum dot system. J Nanomater. Nanoeng. Nanosyst. 233(2–4), 65–71 (2019)
H. Akram, A.H. Al-Khursan, Second-order nonlinearity in ladder plus-Y configuration in double quantum dot structure. Appl. Opt. 55(34), 9866–9874 (2016)
M. Abdullah, F.T.M. Noori, A.H. Al-Khursan, Terahertz emission in ladder plus Y-configurations in double quantum dot structure. Appl. Opt. 54(16), 5186–5192 (2015)
P. Calabrese, J. Cardy, Evolution of entanglement entropy in one-dimensional systems. J. Stat. Mech.: Theory Exp. 2005(04), P04010 (2005)
S.J.D. Phoenix, P.L. Knight, Fluctuations and entropy in models of quantum optical resonance. Ann. Phys. 186(2), 381–407 (1988)
M. Asada, A. Kameyama, Y. Suematsu, Gain and intervalence bans absorption in quantum-well lasers. IEEE Quantum Electron. 20(7), 745–753 (1984)
L. Mandel, E. Wolf, Optical coherence and quantum optics, Cambridge University Press (1995)
A.H. Flayyih, A.H. Al-Khursan, Integral gain in quantum dot semiconductor optical amplifiers. Superlatt. Microstruct. 62, 81–87 (2013)
A.H. Al-Khursan, M.K. Al-Khakani, K.H. Al-Mossawi, Third-order non-linear susceptibility in a three-level QD system. Photon. Nanostruct. Fundam. Appl. 7(3), 153–160 (2009)
M. Mahmoudi, M. Sahrai, Absorption-free superluminal light propagation in a quantum-dot molecule. Phys. E 41, 1772–1778 (2009)
Funding
The authors declare no funding.
Author information
Authors and Affiliations
Contributions
The authors contributed equally.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflicts of interest.
Ethics approval
The work is not sent to any other site.
Consent to participate
All the Authors Consent to participate.
Consent for publication
All the Authors Consent for publication.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Abdullah, M., Al-Ameri, H.H., Kadhim, K.A. et al. The relation between susceptibility and quantum entropy in the ladder-plus-Y double quantum dot system under spontaneously generated coherence. J Opt (2023). https://doi.org/10.1007/s12596-023-01500-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12596-023-01500-7