Geodesic
On the Dimension of the Space of Dark States in the Tavis--Cummings Model
Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 433-442.

Voir la notice de l'article provenant de la source Math-Net.Ru

The space of minimal energy of a qubit system is the dark subspace of quantum states of a system of two-level atoms in the finite-dimensional Tavis–Cummings (TC) model of quantum electrodynamics. The two-level atoms in the dark state do not interact with the electromagnetic field, which makes this subspace free from decoherence. An exact expression is obtained for the dimension of the dark subspace in the exact TC model and for the rotating wave approximation (RWA).
Keywords: Tavis–Cummings model, dark states. 
@article{MZM_2022_111_3_a9,
     author = {Yu. I. Ozhigov},
     title = {On the {Dimension} of the {Space} of {Dark} {States} in the {Tavis--Cummings} {Model}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {433--442},
     publisher = {mathdoc},
     volume = {111},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a9/}
}
TY  - JOUR
AU  - Yu. I. Ozhigov
TI  - On the Dimension of the Space of Dark States in the Tavis--Cummings Model
JO  - Matematičeskie zametki
PY  - 2022
SP  - 433
EP  - 442
VL  - 111
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a9/
LA  - ru
ID  - MZM_2022_111_3_a9
ER  - 
%0 Journal Article
%A Yu. I. Ozhigov
%T On the Dimension of the Space of Dark States in the Tavis--Cummings Model
%J Matematičeskie zametki
%D 2022
%P 433-442
%V 111
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a9/
%G ru
%F MZM_2022_111_3_a9
Yu. I. Ozhigov. On the Dimension of the Space of Dark States in the Tavis--Cummings Model. Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 433-442. http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a9/

[1] E. T. Jaynes, F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser”, Proc. IEEE, 51:1 (1963), 89–109 | DOI

[2] M. Th. Tavis, A Study of an N Molecule Quantized-Radiation-Field Hamiltonian, Dissertation, arXiv: 1206.0078

[3] J. Q. Quach, W. J. Munro, “Using dark states to charge and stabilise open quantum batteries”, Phys. Rev. Applied, 14 (2020), 024092 | DOI

[4] A. André, L. M. Duan, M. D. Lukin, “Coherent atom interactions mediated by dark-state polaritons”, Phys. Rev. Lett., 88:24 (2002), 243602 | DOI

[5] J. Hansom, C. Schulte, C. Le Gall, C. Matthiesen, E. Clarke, M. Hugues, J. M. Taylor, M. Atatüre, “Environment-assisted quantum control of a solid-state spin via coherent dark states”, Nature Physics, 10 (2014), 725–730 | DOI

[6] E. S. Lee, C. Geckeler, J. Heurich, A. Gupta, Kit-Iu Cheong, S. Secrest, P. Meystre, “Dark states of dressed Bose–Einstein condensates”, Phys. Rev. A, 60 (1999), 4006 | DOI

[7] M. Ferretti, R. Hendrikx, E. Romero, J. Southall, R. J. Cogdell, V. I. Novoderezhkin, G. D. Scholes, R. van Grondelle, “Dark States in the Light-Harvesting complex 2 Revealed by Two-dimensional Electronic Spectroscopy”, Scientific Reports, 6 (2016), 20834 | DOI

[8] C. Pöltl, C. Emary, T. Brandes, “Spin entangled two-particle dark state in quantum transport through coupled quantum dots”, Phys. Rev. B, 87 (2013), 045416 | DOI

[9] T. Tanamoto, K. Ono, F. Nori, “Steady-state solution for dark states using a three-level system in coupled quantum dots”, Jpn. J. Appl. Phys., 51:2S (2012), 02BJ07 | DOI

[10] H. Rose, D. V. Popolitova, O. V. Tikhonova, T. Meier, P. R. Sharapova, “Dark-state and loss-induced phenomena in the quantum-optical regime of Lambda-type three-level systems”, Phys. Rev. A, 103 (2021), 013702 | DOI