Charge qubit dynamics in a double quantum dot coupled to phonons

The dynamics of charge qubit in a double quantum dot coupled to phonons is investigated theoretically in terms of a perturbation treatment based on a unitary transformation. The dynamical tunneling current is obtained explicitly. The decoherence induced by acoustic phonons is analyzed in detail after a derivation of spectral density. It is shown that the contribution from deformation potential coupling is comparable to that from piezoelectric coupling in small dots and large tunneling rates. A possible decoupling mechanism is predicted.

Figure 1

Spectral functions of double quantum dot due to piezoelectric coupling (labeled by pz) and deformation potential coupling (labeled by df) with ${\omega }_d=0.02$ and ${\omega }_d=0.05{\left(\mathrm{ps}\right)}^{-1}$. (a) ${\omega }_l=1{\left(\mathrm{ps}\right)}^{-1}$. (b) ${\omega }_l=0.5{\left(\mathrm{ps}\right)}^{-1}$.

Figure 2

The tunneling electron population in the right dot as a function of ${\omega }_{l}t$ for GaAs double quantum dot with $T_c=0.1{\omega }_l$ and ${\omega }_d=0.02{\omega }_l$.

Figure 3

Decoherence rates ${\gamma }_{\mathrm{pz}}$ (solid line) and ${\gamma }_{\mathrm{df}}$ (dashed line) as functions of cutoff frequency ${\omega }_l$ when ${\omega }_d=0.02{\left(\mathrm{ps}\right)}^{-1}$. The tunneling rates in (a) and (b) are $0.05{\left(\mathrm{ps}\right)}^{-1}$ and $0.5{\left(\mathrm{ps}\right)}^{-1}$, respectively.

Figure 4

Decoherence rate $\gamma$ as a function of tunneling rate $T_c$ and distance $d$ between two dots. The dot size is chosen to be $100\mathrm{nm}$.