Charge decoherence in laterally coupled quantum dots due to electron-phonon interactions

We investigate electron charge decoherence in a laterally coupled single-electron semiconductor double quantum dot through electron-phonon interaction. We analytically and numerically evaluate the relaxation and dephasing rates due to electron coupling to both acoustic and optical phonons, and explore the system parameter space in terms of interdot distance, strength of single-dot confinement, and interdot coupling strength. Our numerical results show that the electron scattering rates are strongly dependent on the strength of the electron confinement and the size of the system. In addition, although the most dominant factor that determines the charge decoherence rate is the energy splitting between the charge qubit states, the details of the double dot configuration are also very important.

Figure 1

Relaxation rates of an electron in the first excited state through acoustic phonon emission as a function of the half interdot distance $\alpha$. The relaxation rates due to deformation potential interaction, piezoelectric interaction, and the total relaxation rates are presented by dashed, dotted, and straight lines, respectively. The strength of the lateral confinement is $\hslash {\omega }_0=3\mathrm{meV}$.

Figure 2

The relaxation rates versus the strength of the confinement. The scattering rates due to deformation potential, piezoelectric phonons and total relaxation rates are presented by dashed, dotted, and straight lines, respectively. The interdot distance is $2\alpha =60\mathrm{nm}$.

Figure 3

Electron relaxation rates as a function of the energy splitting between the first excited state and the ground state in a double quantum dot. Again, rates due to deformation potential, piezoelectric interaction, and the total relaxation rates are represented by dashed, dotted, and straight lines, respectively. The energy splitting versus the confinement strength is given in the inset. The interdot distance is $2\alpha =60\mathrm{nm}$.

Figure 4

The relaxation rates for the second excited state as a function of the half interdot distance $\alpha$. The total scattering rates include contributions from both the deformation potential and the piezoelectric interaction. The straight line gives relaxation rates to the ground state, while the dashed line is the relaxation rates to the first excited state. The strength of the confinement is $\hslash {\omega }_0=3\mathrm{meV}$.

Figure 5

Dephasing factor $B^2\left(t\right)$ as a function of time $t$. The dashed, dotted, and straight lines represent dephasing rates due to deformation potential, piezoelectric interaction, and the total, respectively. The strength of the confinement $\hslash {\omega }_0=3\mathrm{meV}$, the interdot distance is $2\alpha =60\mathrm{nm}$, and there is no interdot bias: $V_R=0\mathrm{meV}$.

Figure 6

Dephasing factor $B^2\left(t\right)$ as a function of the half interdot distance $\alpha$. No bias is applied across the two quantum dots, and time $t$ is chosen to be 60 ps. The dephasing rates due to deformation potential, piezoelectric interaction, and total dephasing rates are represented by dashed, dotted, and straight lines, respectively. The strength of the confinement is $\hslash {\omega }_0=3\mathrm{meV}$.

Figure 7

Dephasing factor $B^2\left(t\right)$ as a function of time $t$ in the presence of interdot bias. Again, the dephasing rates due to deformation potential, piezoelectric interaction, and the total rates are represented by dashed, dotted, and straight lines, respectively. The strength of the confinement is $\hslash {\omega }_0=3\mathrm{meV}$, the interdot distance is $2\alpha =60\mathrm{nm}$, and the interdot bias voltage is $V_R=1.5\mathrm{meV}$.

Figure 8

Dephasing factor $B^2\left(t\right)$ as a function of time of the interdot bias voltage $V_R$. The solid line represents dephasing rates due to electron-acoustic-phonon interaction through both the deformation potential and piezoelectric interaction. The dashed and dotted lines represent the deformation potential and piezoelectric contributions separately. The dot-dashed line represents the dephasing effects from polar interaction with optical phonons. Here the strength of the confinement is $\hslash {\omega }_0=3\mathrm{meV}$, the interdot distance is $2\alpha =60\mathrm{nm}$, and the time of observation for the dephasing effect is $t=60\mathrm{ps}$.