Single quasiparticle and electron emitter in the fractional quantum Hall regime

We propose a device consisting of an antidot periodically driven in time by a magnetic field as a fractional quantum Hall counterpart of the celebrated mesoscopic capacitor-based single-electron source. We fully characterize the setup as an ideal emitter of individual quasiparticles and electrons into fractional quantum Hall edge channels of the Laughlin sequence. Our treatment relies on a master equation approach and identifies the optimal regime of operation for both types of sources. The quasiparticle/quasihole emission regime involves in practice only two charge states of the antidot, allowing for an analytic treatment. We show the precise quantization of the emitted charge, we determine its optimal working regime, and we compute the phase-noise/shot-noise crossover as a function of the escape time from the emitter. The emission of electrons, which calls for a larger amplitude of the drive, requires a full numerical treatment of the master equations as more quasiparticle charge states are involved. Nevertheless, in this case the emission of one electron charge followed by one hole per period can also be achieved, and the overall shape of the noise spectrum is similar to that of the quasiparticle source, but the presence of additional quasiparticle processes enhances the noise amplitude.

Figure 1

View of a (strongly asymmetric) antidot embedded into an Hall fluid and coupled with edge channels through tunneling amplitudes $t_L$ and $t_R$ respectively ($|t_L|\gg |t_R|$. Dark area represents the Hall fluid while the bright ones are in correspondence of the edges of the Hall bar (black arrows) and of the antidot (with black circles indicating the its energy levels). Blue dots indicated quasiparticles. The antidot is also pierced by a time-dependent magnetic flux $\Phi$.

Figure 2

Occupation of the antidot over time as a function of the drive amplitude $\delta$ for the SQS (top) and the SES (bottom) regime. Other parameters are: $\nu =1/3,E_c/{\omega }_c=0.01,\beta E_c=20$, and ${\gamma }_{0}T=100$.

Figure 3

Occupation probability of the two relevant levels of the antidot (${\widehat{\mathcal{P}}}_0$ and ${\widehat{\mathcal{P}}}_1$) for the optimal regime of the SQS $\left(\delta =-0.2\right)$. Other parameters are: $\nu =1/3,E_c/{\omega }_c=0.01,\beta E_c=20$, and ${\gamma }_{0}T=100$. The relevant scale entering the master equation is then $\gamma \simeq 17.4512T^{-1}$.

Figure 4

Occupation of the antidot (top) and current flowing between the source and the edge in units of $\frac{e^{*}}{T}$ (bottom), in the optimal regime of SQS $\left(\delta =-0.2\right)$ for different values of ${\gamma }_{0}T$. Other parameters are: $\nu =1/3,E_c/{\omega }_c=0.01$, and $\beta E_c=20$.

Figure 5

Time-averaged charge correlation $\overline{{\mathcal{C}}_Q(t,t^{\prime })}$ in units of ${e^{*}}^2$, for the optimal regime of the SQS $\left(\delta =-0.2\right)$ and different values of ${\gamma }_{0}T$. Other parameters are: $\nu =1/3,E_c/{\omega }_c=0.01$, and $\beta E_c=20$.

Figure 6

Frequency-dependent current noise ${\mathcal{S}}_I$ in units of $\frac{{e^{*}}^2}{T}$, computed at the frequency $\Omega$ of the external drive as a function of the escape time $\tau$ from the antidot, for the optimal regime of the SQS $\left(\delta =-0.2\right)$. The result is compared to the analytical expectation transposed from the known results of the SES in the IQH case, assuming a fractional charge $e^{*}=\nu e$. Other parameters are: $\nu =1/3,E_c/{\omega }_c=0.01$, and $\beta E_c=20$.

Figure 7

Occupation probability of the relevant levels for the optimal regime of the SES $\left(\delta =-1.2\right)$, with ${\gamma }_{0}T=100$. Other parameters are: $\nu =1/3,E_c/{\omega }_c=0.01$, and $\beta E_c=20$.

Figure 8

Occupation of the antidot (top) and current flowing between the source and the edge in units of $\frac{e^{*}}{T}$ (bottom), in the optimal regime of SES $\left(\delta =-1.2\right)$ for different values of ${\gamma }_{0}T$. Other parameters are: $\nu =1/3,E_c/{\omega }_c=0.01$, and $\beta E_c=20$.

Figure 9

Average charge $\overline{Q}$ transferred during one half period, in units of $e^{*}$, as a function of the escape time (corresponding to different values of ${\tau }_{\text{dot}},{\tau }_2$, and ${\tau }_{\Omega }$) and for the optimal regime of the SES $\left(\delta =-1.2\right)$. Other parameters are: $\nu =1/3,E_c/{\omega }_c=0.01$, and $\beta E_c=20$.

Figure 10

Time-averaged charge correlation $\overline{{\mathcal{C}}_Q(t,t^{\prime })}$ in units of ${e^{*}}^2$, for the optimal regime of the SES $\left(\delta =-1.2\right)$ and different values of ${\gamma }_{0}T$. Other parameters are: $\nu =1/3,E_c/{\omega }_c=0.01$, and $\beta E_c=20$.

Figure 11

Frequency-dependent current noise ${\mathcal{S}}_I$ in units of $\frac{{e^{*}}^2}{T}$ computed at the frequency $\Omega$ of the external drive as a function of the escape time $\tau$ from the antidot, for the optimal regime of the SES $\left(\delta =-1.2\right)$. Other parameters are: $\nu =1/3,E_c/{\omega }_c=0.01$, and $\beta E_c=20$. The results are compared to the analytical expectation transposed from the SQS regime, Eq. (32), multiplied by 9 to account for the fact that the emitted charge now corresponds to one electron (three QPs).