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Ket–Bra entangled state method for solving master equation of finite-level system

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Abstract

In this paper, we first introduce Ket–Bra entangled state method to solve master equation of finite-level system, which can convert master equation into Schrödinger-like equation and solve it with the mature methodology of Schrödinger equation. Then, several physical models include a radioactivity damped 2-level atom driven by classical field, a J–C model with cavity damping, a V-type qutrit under amplitude damping and N-qubits open Heisenberg chain have been solved with KBES method. Furthermore, the dynamic evolution and decoherence process of these models are investigated.

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Notes

  1. TFD investigate the dynamic evolution of open quantum system by introducing an extra mode which refers to the environment.

  2. For instance, \(e^{x_{-}\left( t\right) L_{-}}\rho =\sum \nolimits _{n=0}^{\infty }\frac{x_{-}^{n}\left( t\right) L_{-}^{n}}{n!}\rho =\sum \nolimits _{n=0}^{\infty }\frac{x_{-}^{n}\left( t\right) }{n!}\left( \sigma ^{-}\right) ^{n}\rho \left( \sigma ^{+}\right) ^{n}=\rho +\sigma ^{-}\rho \sigma ^{+}\).

  3. Mathematica is a symbolic mathematical computation program, used in many scientific, engineering, mathematical and computing fields. MatrixExp is the order to compute the exponent of matrix.

  4. The comparison may quite trivial because the expression of \(x_{\pm ,z}\left( t\right) \) is complicated; however, this process can be simplified by setting \(n=0\); besides, the comparison between c-number method in Ref. [23] and KBES method is quite simple.

  5. For instance, the Mathematica order MatrixExp[\(\mathscr {F}\)] can immediately obtain the expression of \(e^{\mathscr {F}}\) where \(\mathscr {F}\) is arbitrary-order matrix.

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Authors and Affiliations

  1. Key Laboratory of Atmospheric Composition and Optical Radiation, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei City, China

    Yi-Chong Ren & Shu Wang

  2. University of Science and Technology of China, Hefei City, China

    Shu Wang & Hong-Yi Fan

  3. Hefei University, Hefei, Anhui, China

    Feng Chen

Authors
  1. Yi-Chong Ren
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  2. Shu Wang
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  3. Hong-Yi Fan
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  4. Feng Chen
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Correspondence to Yi-Chong Ren.

Additional information

Granted by National Natural Science Foundation of China (No. 11574295) and Natural Science Fund of Education Department of Anhui province (No. KJ2016A590).

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Ren, YC., Wang, S., Fan, HY. et al. Ket–Bra entangled state method for solving master equation of finite-level system. Quantum Inf Process 16, 270 (2017). https://doi.org/10.1007/s11128-017-1710-z

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