Non-Markovian dynamics and phonon decoherence of a double quantum dot charge qubit

In this paper we investigate decoherence times of a double quantum dot (DQD) charge qubit due to it coupling with acoustic phonon baths. We individually consider the acoustic piezoelectric as well as deformation coupling phonon baths in the qubit environment. The decoherence times are calculated with two kinds of methods. One of them is based on the qusiadiabatic propagator path integral (QUAPI) and the other is based on Bloch equations, and two kinds of results are compared. It is shown that the theoretical decoherence times of the DQD charge qubit are shorter than the experimental reported results. It implies that the phonon couplings to the qubit play a subordinate role, resulting in the decoherence of the qubit.

Figure 1

Real (line) and imaginary (short lines) parts of the response function of the piezoelectric coupling phonon bath (PCPB). Here, we set the temperature $T=30\mathrm{mK}$, and ${\omega }_d=0.02{\left(\mathrm{ps}\right)}^{-1}$, ${\omega }_l=0.5{\left(\mathrm{ps}\right)}^{-1}$, $g^{pz}=0.035{\left(\mathrm{ps}\right)}^{-2}$.

Figure 2

Real (line) and imaginary (short lines) parts of the response function of the deformation coupling phonon bath (DCPB). Here, we set $g^{df}=0.029{\left(\mathrm{ps}\right)}^{-2}$, and other parameters are same as those in Fig. 1.

Figure 3

The evolutions of the off-diagonal elements of the reduced density matrix for the DQD charge qubit in PCPB when ${\omega }_l=0.5{\left(\mathrm{ps}\right)}^{-1}$ (line) and ${\omega }_l=0.7{\left(\mathrm{ps}\right)}^{-1}$ (short lines). Here, the cutoff frequency is ${\omega }_c=5{\left(\mathrm{ps}\right)}^{-1}$; other parameters are same as those in Fig. 1. The initial state of the qubit and environment are described in the text.

Figure 4

The evolutions of the off-diagonal elements of the reduced density matrix for the DQD charge qubit in DCPB when ${\omega }_l=0.5{\left(\mathrm{ps}\right)}^{-1}$ (line) and ${\omega }_l=0.7{\left(\mathrm{ps}\right)}^{-1}$ (short lines). Here, the parameters are same as those in Figs. 2, 3.