Decoherence induced by electron accumulation in a quantum measurement of charge qubits

Ming-Tsung Lee and Wei-Min Zhang

Phys. Rev. B 74, 085325 – Published 30 August 2006

Abstract

In this paper, we study the quantum decoherence induced by accumulation of electron tunnelings during the quantum measurement of a charge qubit. The charge qubit is a single electron confined in coupled quantum dots. The measurement of the qubit states is performed using a quantum point contact. A set of master equations for qubit states is derived within a nonequilibrium perturbation to the equilibrium reservoir due to the electron accumulation between the source and drain of the quantum point contact. The quantum decoherence of the qubit states arose from the electron accumulation during the measurement is explored in this framework, and several interesting results on charge qubit decoherence are obtained.

Received 8 November 2005

DOI:https://doi.org/10.1103/PhysRevB.74.085325

Authors & Affiliations

Ming-Tsung Lee¹ and Wei-Min Zhang^1,2

¹Physics Division, National Center for Theoretical Sciences, Tainan, Taiwan 70101, Republic of China
²Department of Physics and Center for Quantum Information Science, National Cheng Kung University, Tainan, Taiwan 70101, Republic of China

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Vol. 74, Iss. 8 — 15 August 2006

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Images

Figure 1
(Color online) (a) Schematic plot of a single electron in a coupled quantum dots measured by the QPC. (b) Schematic diagram of the electron accumulation in reservoir, the first figure shows the forward tunneling processes (FTP) of electrons from the source to the drain which causes electrons accumulating in the drain, and induces a variation of the Fermi energy. The second one shows the backward tunneling processes (BTP) of electrons from the drain to the source and a corresponding variation of the Fermi energy.Reuse & Permissions
Figure 2
(Color online) (a) The decay rate $Γ_{0, r}^{θ}$ of the measured qubit in the equilibrium state. The solid curves are for symmetric CQD $(γ = 2 Ω_{0})$ and the dash curves for asymmetric CQD $(γ = 10 Ω_{0})$ . (b) The asymptotic reduced density matrix $ρ_{0, r}^{θ} (\infty)$ of the measured qubit. Two branches corresponds to the symmetric CQD (solid curves) and the asymmetric CQD with $γ = 10 Ω_{0}$ (dashed curves), respectively.Reuse & Permissions
Figure 3
(Color online) (a) The dephasing rate $Γ_{0, p}^{+}$ of the fast mode of the measured qubit in the equilibrium state. (b) The dephasing rate $Γ_{0, p}^{-}$ of the slow mode for the measured qubit. The figures are plotted with the fixed parameter $γ ∕ ℏ η_{d} = Ω_{0}$ .Reuse & Permissions
Figure 4
The EA current $I_{1} (t)$ in the QPC. The qubit is initially in the $∣ L ⟩$ state without energy-level offset. The following measurement parameters are used to plot figures: $Ω = Ω_{0}$ , $δ Ω = 0.1 Ω_{0}$ , $β = 1 ∕ Ω_{0}$ , $μ_{L} = 100 Ω_{0}$ , $(V_{d} = 10 Ω_{0})$ , and $g_{L, R} = 2 ∕ Ω_{0}$ . The initial input number of electrons in the source is set to be 100. There is no electron accumulation at initial time. Two cases with different ER decay rate are plotted.Reuse & Permissions
Figure 5
(Color online) The time evolution of the reduced density matrix of the first order perturbation. The symmetric CQD is simulated. The qubit is initially in $∣ L ⟩$ state with $ξ Tr [{\hat{ρ}}_{1} (t = 0)] = 0.01$ . The input initial electron number is 100. The following measurement parameters are used: $Ω = Ω_{0}$ , $δ Ω = 0.1 Ω_{0}$ , $β = 1 ∕ Ω_{0}$ , $μ_{L} = 100 Ω_{0}$ , $g_{L, R} = 2 ∕ Ω_{0}$ , $ω_{d} = 0$ , and $μ_{R} = μ_{L} - V_{d}$ with $V_{d} = 0$ and $Γ_{L, R} = 0.15 Ω_{0}$ for the red curve, $V_{d} = 10 Ω_{0}$ and $Γ_{L, R} = 0.15 Ω_{0}$ for the black curve, $V_{d} = 10 Ω_{0}$ and $Γ_{L, R} = 0.3 Ω_{0}$ for the green curve, and $V_{d} = 10 Ω_{0}$ and $Γ_{L, R} = 0$ for the cyan curve, respectively. (a) The qubit relaxation. The time evolution of the matrix elements $ρ_{1 g} (ρ_{1 e})$ for the qubit in the ground (excited) state are plotted by solid (dashed) curves, respectively. (b) The qubit relaxation under the pure EA effect $(Γ_{L, R} = 0)$ . (c) and (d) The qubit dephasing. The time evolution of the matrix element $ρ_{1 d}$ and $ρ_{1 p}$ are plotted, respectively.Reuse & Permissions
Figure 6
(Color online) The EA induced relaxation rate. The curves are plotted with different temperatures.Reuse & Permissions

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