Effect of bath temperature on the decoherence of quantum dissipative systems

Wei Wu and Hai-Qing Lin

Phys. Rev. A 94, 062116 – Published 20 December 2016

Abstract

We report an anomalous decoherence phenomenon of a quantum dissipative system in the framework of a stochastic decoupling scheme along with a hierarchical equations-of-motion formalism without the usual Born-Markov or weak-coupling approximations. It is found that the decoherence of a two-qubit spin-boson model can be reduced by increasing the bath temperature in strong-coupling regimes. For the weak-coupling situation, we find that the bath temperature may enhance the decoherence. This result is contrary to the common recognition that a higher bath temperature always induces a more severe decoherence and suggests that a decoherence dynamical transition occurs in this two-qubit spin-boson model. We also demonstrate that the critical transition point can be characterized by the behavior of the frequency spectrum of the quantum coherence indicator.

Received 27 October 2016

DOI:https://doi.org/10.1103/PhysRevA.94.062116

Physics Subject Headings (PhySH)

Quantum information with atoms & light

Quantum Information, Science & Technology

Authors & Affiliations

Wei Wu^1,2,* and Hai-Qing Lin¹

¹Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
²Zhejiang Institute of Modern Physics and Physics Department, Zhejiang University, Hangzhou 310027, China

^*weiwu@csrc.ac.cn

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Issue

Vol. 94, Iss. 6 — December 2016

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Images

Figure 1
(a) The quantum coherence indicator $〈 {\hat{σ}}_{x} (t) 〉$ versus $t$ at zero temperature with different coupling parameters: $λ = 0.01 ω_{0}$ (numerical results, purple dashed line; analytical results, orange rectangles), $λ = 0.05 ω_{0}$ (numerical results, blue dot-dashed line; analytical results, green triangles), and $λ = 0.1 ω_{0}$ (numerical results, red solid line; analytical results, yellow circles). Other parameters are chosen as $γ = 0.5 ω_{0}$ and $ω_{0} = 1$ . (b) The quantum coherence indicator $〈 {\hat{σ}}_{x} (t) 〉$ versus $t$ at different temperatures: $T^{- 1} = 0.01 ω_{0}^{- 1}$ (numerical results, purple dashed line; analytical results, orange rectangles), $T^{- 1} = 0.03 ω_{0}^{- 1}$ (numerical results, blue dot-dashed line; analytical results, green triangles), and $T^{- 1} = 0.05 ω_{0}^{- 1}$ (numerical results, red solid line; analytical results, yellow circles). Other parameters are chosen as $η = 5 \times 10^{- 4} ω_{0}$ , $ω_{c} = 3 ω_{0}$ , and $ω_{0} = 1$ .
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Figure 2
The quantum coherence indicator $〈 {\hat{σ}}_{x} (t) 〉$ of qubit $A$ versus $t$ at different temperatures in the strong-coupling regime $η = 0.05 ω_{0}$ : (a) $T^{- 1} = 0.05 ω_{0}^{- 1}$ (numerical results, left red solid line; Born-Markov results, left yellow circles), (c) $T^{- 1} = 0.10 ω_{0}^{- 1}$ (numerical results, left blue dot-dashed line; Born-Markov results, left green triangles), and (e) $T^{- 1} = 0.20 ω_{0}^{- 1}$ (numerical results, left purple dashed line; Born-Markov results, left orange rectangles). The $〈 {\hat{σ}}_{x} (t) 〉$ of qubit $A$ versus $t$ at different temperatures in the weak-coupling regime $η = 0.001 ω_{0}$ : (b) $T^{- 1} = 0.05 ω_{0}^{- 1}$ (numerical results, right red solid line; Born-Markov results, right yellow circles), (d) $T^{- 1} = 0.10 ω_{0}^{- 1}$ (numerical results, right blue dot-dashed line; Born-Markov results, right green triangles), and (f) $T^{- 1} = 0.20 ω_{0}^{- 1}$ (numerical results, left purple dashed line; Born-Markov results, left orange rectangles). Other parameters are chosen as $ω_{c} = 5 ω_{0}$ , $g_{0} = 0.1 ω_{0}$ , and $ω_{0} = 1$ .
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Figure 3
The frequency spectrum $〈 {\hat{σ}}_{x} (ω) 〉$ of qubit $A$ versus $ω$ in (a) strong-coupling regime $η = 0.05 ω_{0}$ and (c) weak-coupling regime $η = 0.001 ω_{0}$ with different bath temperatures: $T^{- 1} = 0.05 ω_{0}^{- 1}$ (red dashed line), $T^{- 1} = 0.10 ω_{0}^{- 1}$ (blue dot-dashed line), and $T^{- 1} = 0.20 ω_{0}^{- 1}$ (purple solid line). The effective bath spectral density function $J_{eff} (ω)$ in (b) strong-coupling regime $η = 0.05 ω_{0}$ and (d) weak-coupling regime $η = 0.001 ω_{0}$ with different bath temperatures: $T^{- 1} = 0.05 ω_{0}^{- 1}$ (red dashed line), $T^{- 1} = 0.10 ω_{0}^{- 1}$ (blue dot-dashed line), and $T^{- 1} = 0.20 ω_{0}^{- 1}$ (purple solid line). Other parameters are chosen as $ω_{c} = 5 ω_{0}$ , $g_{0} = 0.1 ω_{0}$ , and $ω_{0} = 1$ .
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Figure 4
The frequency spectrum $〈 {\hat{σ}}_{x} (ω) 〉$ of qubit $A$ versus $ω$ with different coupling strengths: $η = 0.001 ω_{0}$ (purple line with solid rectangles), $η = 0.002 ω_{0}$ (blue line with solid diamonds), $η = 0.003 ω_{0}$ (green line with solid down triangles), $η = 0.004 ω_{0}$ (cyan line with solid squares), $η = 0.005 ω_{0}$ (brown line with solid up triangles), $η = 0.006 ω_{0}$ (yellow line with solid circles), $η = 0.007 ω_{0}$ (pink line with open squares), $η = 0.008 ω_{0}$ (orange line with open down triangles), $η = 0.009 ω_{0}$ (magenta line with open diamonds), and $η = 0.010 ω_{0}$ (red line with solid stars). Other parameters are chosen as $T^{- 1} = 0.03 ω_{0}^{- 1}$ , $ω_{c} = 5 ω_{0}$ , $g_{0} = 0.1 ω_{0}$ , and $ω_{0} = 1$ .
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