Counting statistics and decoherence in coupled quantum dots

We theoretically consider charge transport through two quantum dots coupled in series. The corresponding full counting statistics for noninteracting electrons is investigated in the limits of sequential and coherent tunneling by means of a master equation approach and a density matrix formalism, respectively. We clearly demonstrate the effect of quantum coherence on the zero-frequency cumulants of the transport process, focusing on noise and skewness. Moreover, we establish the continuous transition from the coherent to the incoherent tunneling limit in all cumulants of the transport process and compare this with decoherence described by a dephasing voltage probe model.

Figure 1

(Color online) Current statistics for $\Omega ∕\Gamma =0.5$ and for various dephasing rates ${\Gamma }_{\phi }∕\Gamma =0$, 5, 20; dashed lines: master equation (ME) approach; solid lines: density matrix (DM) formalism; on-resonance $\Delta \epsilon =0$; symmetric contact coupling: $\Gamma ={\Gamma }_{\mathrm{e}}={\Gamma }_{\mathrm{c}}$. ${\Gamma }_0\equiv \left(2\Gamma {\Omega }^2\right)∕[4{\Omega }^2+\Gamma (\Gamma +{\Gamma }_{\phi })]$. Inset: Setup of the coupled QD system with (e)mitter and (c)ollector contact and mutual coupling $\Omega$.

Figure 2

(Color online) Average current $C_1$, noise $C_2$ in units of $t_0\Gamma$, Fano factor $C_2∕C_1$, normalized skewness $C_3∕C_1$ vs coupling $\Omega$ for various dephasing rates ${\Gamma }_{\phi }∕\Gamma =0$, 5, 20; master equation approach (ME): dashed lines; density matrix formalism (DM): solid lines; on-resonance: $\Delta \epsilon =0$; symmetric contact coupling: $\Gamma ={\Gamma }_{\mathrm{e}}={\Gamma }_{\mathrm{c}}$.

Figure 3

Fano factor vs inter-QD coupling $\Omega$ for various dephasing rates ${\Gamma }_{\phi }$. (a) elastic voltage probe, (b) inelastic voltage probe in scattering formalism (solid curves); dashed curves: master equation (ME) Fano factor for ${\Gamma }_{\phi }∕\Gamma =20$; on-resonance: $\Delta \epsilon =0$; symmetric coupling: $\Gamma ={\Gamma }_{\mathrm{e}}={\Gamma }_{\mathrm{c}}$.