Time-resolved noise of adiabatic quantum pumps

We investigate quantum-statistical correlation properties of a periodically driven mesoscopic scatterer on a time scale shorter than the period of a drive. In this limit the intrinsic quantum fluctuations in the system of fermions are the main source of a noise. Nevertheless the effect of a slow periodic drive is clearly visible in a two-time current-current correlation function as a specific periodic in time modulation. In the limit of a strong drive such a modulation can change the sign of a current correlation function.

Figure 1

The correlation function $P_{\alpha \beta }(\omega ,{\omega }^{\prime })$, Eq. (7b), for currents generated by the pump is nonzero along the straight lines in the plane ($\omega$,${\omega }^{\prime }$). The lines corresponding to $l=0,\pm 1,\pm 2,\pm 3$ are shown. The width of lines shows schematically a noise intensity decreasing with increasing number $\mid l\mid$. The area bounded by the dashed circle with radius ${\tau }_0^{-1}$ contributes to the two-time current correlation function $P_{\alpha \beta }(t_1,t_2;{\tau }_0)$, Eq. (20b). Here ${\tau }_0$ is a measurement time period. The small solid circle bounds the area contributing to the zero-frequency noise power, Eq. (29).

Figure 2

The normalized function $\eta \left(\xi \right)∕\eta \left(0\right)$ [see Eq. (21)] at $k_{B}T∕h∕{\tau }_0$ = 0 (solid line), 0.05 (dot-dashed line), and $\infty$ (dashed line). ${\tau }_0$ is a measurement time interval.

Figure 3

The currents $I_1$ (in the left lead) and $I_2$ (in the right lead) generated by the pump are given in units of $e\Omega ∕\left(2\pi \right)$ as a function of time. The parameters are ${\phi }_2=\pi ∕2$, ${\phi }_1=0$, $L=100\pi$, $V_{01}=V_{02}=20$, $V_{11}=V_{12}=10$, and $\mu =1.018624$.

Figure 4

The correlation coefficient $\mathcal{R}(t_1^{\left(\max \right)},t)$ as a function of time for ${\phi }_2=\pi ∕2$ and ${\phi }_1=0$. $t_1^{\left(\max \right)}=0.615\mathcal{T}$ is a time moment when the current $I_1\left(t\right)$ peaks. Other parameters are the same as in Fig. 3.

Figure 5

The transmission coefficient through the pump as a function of time for ${\phi }_2=\pi ∕2$ and ${\phi }_1=0$. Other parameters are the same as in Fig. 3.

Figure 6

The correlation coefficient $\mathcal{R}(t_1,t)$ as a function of time for ${\phi }_2=\pi ∕2$ and ${\phi }_1=0$. The time moment $t_1=0.8\mathcal{T}$ is taken away from the time interval during which the current $I_1\left(t\right)$ peaks. Other parameters are the same as in Fig. 3.

Figure 7

The currents [in units of $e\Omega ∕\left(2\pi \right)$] generated by the pump as a function of time for ${\phi }_2=\pi$ and ${\phi }_1=0$. Two electron-hole pairs are generated in each cycle. Each lead receives an electron and a hole and the net pumped current is zero. Other parameters are the same as in Fig. 3.

Figure 8

The correlation coefficient $\mathcal{R}(t_1^{\left(\max \right)},t)$ (solid line) and the transmission coefficient $T\left(t\right)$ (dashed line) as functions of time for ${\phi }_2=\pi$ and ${\phi }_1=0$. $t_1^{\left(\max \right)}=0.615\mathcal{T}$ is a time moment when the current $I_1\left(t\right)$ peaks. Other parameters are the same as in Fig. 3.

Figure 9

The currents [in units of $e\Omega ∕\left(2\pi \right)$] generated by the pump as a function of time for ${\phi }_2=0$ and ${\phi }_1=0$. Other parameters are the same as in Fig. 3.

Figure 10

The correlation coefficient $\mathcal{R}(t_1^{\left(\max \right)},t)$ (solid line) and the transmission coefficient $T\left(t\right)$ (dashed line) as functions of time for ${\phi }_2=0$ and ${\phi }_1=0$. The current $I_1\left(t\right)$ peaks at $t_1^{\left(\max \right)}=0.655\mathcal{T}$. Other parameters are the same as in Fig. 3.