Master equation averaged over stochastic process realizations for the description of a three-level atom relaxation
V.A. Mikhailov, N.V. Troshkin

 

Image Processing Systems Institute оf RAS, – Branch of the FSRC “Crystallography and Photonics” RAS, Samara, Russia,
Samara National Research University, Samara, Russia

Full text of article: English language.

 PDF

Abstract:
The relaxation of a three-level atom interacting with a photon heat bath and an external stochastic field is investigated. For the reduced density matrix, a master equation averaged over stochastic process realizations is derived. An exact solution is obtained and the radiation line shapes are calculated.

Keywords:
three-level atom, quantum kinetic equations, radiation line shape.

Citation:
Mikhailov VA, Troshkin NV. Master equation averaged over stochastic process realizations for the description of a three-level atom relaxation. Computer Optics 2016; 40(5): 649-653. DOI: 10.18287/2412-6179-2016-40-5-649-653.

References:

  1. Scully M, Zubairy M. Quantum Optics. Cambridge: Cambridge University Press; 1997. ISBN: 978-0524235959.
  2. Agarwal GS. Quantum statistical theories of spontaneous emission and their relation to other approaches. Springer Tracts in Modern Physics 1974; 70(1): 1-128. ISBN 978-3-540-06630-9. DOI: 10.1007/BFb0042382.
  3. Louisell W. Quantum statistical properties of radiation. N.Y.: Wiley; 1990. ISBN: 978-0471523659.
  4. Walser R, Ritsch H, Zoller P, Cooper J. Laser-noise-induced population fluctuations in two-level systems: Complex and real Gaussian driving fields. Phys Rev A 1992; 45(1): 468-476. DOI: 10.1103/PhysRevA.45.468.
  5. Walser R, Zoller P. Laser-noise-induced polarization fluctuations as a spectroscopic tool. Phys Rev A 1994; 49(6): 5067-5077. DOI: 10.1103/PhysRevA.49.5067.
  6. Osad’ko IS. Blinking fluorescence of single molecules and semiconductor nanocrystals. Physics-Uspekhi 2006; 49: 19-51. DOI: 10.1070/PU2006v049n01ABEH002088.
  7. Bashkirov EK, Litvinova DV. Entanglement between qubits due to the atomic coherence. Computer Optics 2014; 38(4): 663-669.
  8. Bashkirov EK, Stupatskaya MP. Entanglement of two atoms interacting with a thermal electromagnetic field [In Russian]. Computer Optics 2011; 35(2): 243-249.
  9. Mikhailov VA, Troshkin NV, Trunin AM. The Fokker-Planck equation for relaxation of a system of two dipole-dipole interacting atoms. Proc SPIE 2016; 9917: 991732. DOI: 10.1117/12.2229712.
  10. Petrov EG, Teslenko VI. Kinetic equations for a quantum dynamical system interacting with a thermal reservoir and a random field. Theoretical and Mathematical Physics 1990; 84(3): 986-995.
  11. Petrov EG, Teslenko VI, Goychuk IA. Stochastically averaged master equation for a quantum-dynamic system interacting with a thermal bath. Phys Rev E 1994; 49(5): 3894-3902. DOI: 10.1103/PhysRevE.49.3894.
  12. Goychuk IA. Kinetic equations for a dissipative quantum system driven by dichotomous noise: An exact result. Phys. Rev. E 1995; 51(6): 6267-6270. DOI: 10.1103/PhysRevE.51.6267.
  13. Gorokhov AV, Mikhailov VA. Relaxation of two-level system interacting with external stochastic field [In Russian]. Theoretical Physics 2000; 1: 54-62.
  14. Mikhailov VA, Troshkin NV. Relaxation of a three-level atom interacting with a thermostat and an external stochastic field. Proc SPIE 2016; 9917: 991731. DOI: 10.1117/12.2229651.
  15. Mikhailov VA. Solution methods of the Fokker-Planck equation for a two-level atom in a stochastic field [In Russian]. Theoretical Physics 2006; 7: 93-101.
  16. Blum K. Density matrix theory and applications. Berlin: Springer-Verlag Berlin Heidelberg; 2012. ISBN: 978-3-642-20560-6.
  17. Gorokhov AV, Semin VV. Radiation spectrum of the two-level atom with an external electromagnetic field [In Russian]. Theoretical Physics 2008; 9: 164-170.

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: journal@computeroptics.ru; Phones: +7 (846) 332-56-22, Fax: +7 (846) 332-56-20