Counting Statistics for Mesoscopic Conductors with Internal Degrees Of Freedom

We consider the transport of electrons passing through a mesoscopic device possessing internal dynamical quantum degrees of freedom. The mutual interaction between the system and the conduction electrons contributes to the current fluctuations, which we describe in terms of full counting statistics. We identify conditions where this discriminates coherent from incoherent internal dynamics and also identify and illustrate conditions under which the device acts to dynamically bunch transmitted or reflected electrons, thereby generating super-Poissonian noise.

Figure 1

(a) Sketch of a mesoscopic device with internal degrees of freedom, attached to leads contacted by electronic reservoirs. (b) Realization of such a system in terms of a coherent which-path interferometer, consisting of an excess electron in a double quantum dot (states $|\uparrow ⟩$ and $|\downarrow ⟩$ and tunnel splitting $\Delta$), which interacts via a state-dependent potential $V_{\uparrow ,\downarrow }$ with charge carriers passing through an Aharonov-Bohm ring.

Figure 2

Fano factor for the coherent which-path interferometer sketched in Fig. 1b, where (a) shows results as a function of the magnetic flux $\Phi$ penetrating the Aharonov-Bohm ring, for fixed tunnel splitting $\Delta =0.01E_F$, and (b) shows results as a function of $\Delta$, for fixed $\Phi =h/2e$. Solid (dashed) lines: Coherent (incoherent) internal dynamics. Insets in (a): Dimensionless conductance (top) and ratio of incoherent and coherent Fano factors (bottom). The results are obtained by propagation of minimal-uncertainty wave packets with energy spread $\Delta E=0.007E_F$. The interaction $V_{\uparrow ,\downarrow }$ is modeled by an effectively impenetrable barrier of height $20E_F$, which blocks one of the two arms (of length $L$, with ${\hslash }^2/2m{L}^2=0.061E_F$) depending on the occupation of the double dot.