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We propose a new Ket-Bra entangled state (KBES) method to solve the master equation of finite-level system. The KBES method can convert the master equation into Schrdinger-like equation which is easier to solve than the master equation, and Schrdinger equation in a certain form can also be used to solve the Schrdinger-like equation. Thus the KBES method has a wider application range. In the paper, we mainly study the master equation of the two-level atom. The corresponding master equation is solved by the KBES method, and for the first time we obtain the opera-sum solution of the atom. Furthermore, we compare this result with the well known solution that describes the laser channel. There is much analogousness between both opera-sum solutions, which show that there is some supersymmetry between Bose creation-annihilation operator and upper-down transition operators of atom. Finally, we further analyze the supersymmetry between the bose and atom system, and find that the spin-up and spin-down operator can be represented by the creation and annihilation operator repectively, which can be achieved in infinite ways. It is easy to understand that the bose operator is infinite-level while the spin operator is two-level, thus the creation-annihilation operator is super-complete for the spin operator. Thus the representation is not unique, and all of this directly shows and proves the supersymmetry.
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Keywords:
- KBES Method /
- Atomic Master Equation /
- Kraus Form Solution /
- Supersymmetry
[1] Song J, Fan H Y, Zhou J 2011 Acta Phys. Sin. 60 110302 (in Chinese) [宋军, 范洪义, 周军 2011 物理学报 60 110302]
[2] Mandl L, Wolf E 1985 Optical Coherence and Quantum Optics (Vol. 1) (Cambridge: Cambridge Press) pp55-68
[3] Li H Q, Xu X L, X S M, Fan H Y 2015 Int. J. Theor. Phys. 54 3278
[4] Fan H Y, Hu L Y 2008 Mod. Phys. Lett. B 22 2435
[5] Fan H Y, Li X C 2012 Acta Phys. Sin. 61 200301 (in Chinese) [范洪义, 李学超 2012 物理学报 61 200301]
[6] Fan H Y, Klauder J R 1994 Phys. Rev. A 49 704
[7] Fan H Y 2014 Acta Phys. Sin. 63 020302 (in Chinese) [范洪义 2014 物理学报 63 020302]
[8] Peng J S, Li G X 1996 Introduction to Modern Quantum Optics (Beijing: Higher Education Press) pp115-132 (in Chinese)
[9] Li H Q, Xu X L, Fan H Y 2011 Commun. Theor. Phys. 55 787
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[1] Song J, Fan H Y, Zhou J 2011 Acta Phys. Sin. 60 110302 (in Chinese) [宋军, 范洪义, 周军 2011 物理学报 60 110302]
[2] Mandl L, Wolf E 1985 Optical Coherence and Quantum Optics (Vol. 1) (Cambridge: Cambridge Press) pp55-68
[3] Li H Q, Xu X L, X S M, Fan H Y 2015 Int. J. Theor. Phys. 54 3278
[4] Fan H Y, Hu L Y 2008 Mod. Phys. Lett. B 22 2435
[5] Fan H Y, Li X C 2012 Acta Phys. Sin. 61 200301 (in Chinese) [范洪义, 李学超 2012 物理学报 61 200301]
[6] Fan H Y, Klauder J R 1994 Phys. Rev. A 49 704
[7] Fan H Y 2014 Acta Phys. Sin. 63 020302 (in Chinese) [范洪义 2014 物理学报 63 020302]
[8] Peng J S, Li G X 1996 Introduction to Modern Quantum Optics (Beijing: Higher Education Press) pp115-132 (in Chinese)
[9] Li H Q, Xu X L, Fan H Y 2011 Commun. Theor. Phys. 55 787
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