Fermi-sea correlations and a single-electron time-bin qubit

A new principle of manipulation of an electron phase is proposed. The phase is added not directly to an electron but to a finite-length portion of the Fermi sea associated with it, which I name a phase carrier. This phase can be read out with the help of an imbalanced interferometer, where the phase carrier interferes with the reference Fermi sea. As a result of such interference, the same value but opposite sign charge appears at the interferometer's outputs. A phase carrier can be created, for instance, with the help of an on-demand single-electron source able to produce excitations with multiple-peak density profiles.

Figure 1

A sketch of a Mach-Zehnder interferometer with the arm difference $\Delta L>0$ made of 1D chiral electronic waveguides (light grey). When a portion of the Fermi sea of a finite length $\ell >\Delta L$ (dark grey) having an extra phase $\chi$ passes through the interferometer, an opposite charge $Q_{\chi }=Q+Q^{\prime }$ (carried by segments of length $\Delta L$ shown in red and blue) is transferred to output leads.

Figure 2

A time-dependent current $I\left(t\right)$ generated by a single-electron source driven by the voltage $U\left(t\right)$. Time $t$ is given in units of the period $\mathcal{T}=2\pi /\Omega$. When the quantum level of the source crosses the Fermi level of the electronic waveguide, an electron $\left(t_e=0.25\right)$ and a hole $\left(t_h=0.75\right)$ are emitted. Upper panel: When the voltage is varied continuously, the emitted particle has a density profile with one peak. Lower panel: When the voltage is frozen for a while at the time of crossing, the emitted particle has a density profile with two peaks separated by the flat part of duration ${\tau }_{\mathrm{delay}}=0.1\mathcal{T}$ in the present case. Importantly this flat part has an extra phase $\pi$ compared to the Fermi sea residing outside the particle.

Figure 3

The maximum value of a dc current, $I_{\mathrm{dc}}$, measured at one of the interferometer's outputs is shown as a function of the imbalance $\Delta \tau =\Delta L/v_{\mu }$ for several values of the duration ${\tau }_{\mathrm{delay}}$ of the sleep stage of a driving potential. The plateau due to zero-energy electron-hole pairs lasts until $\Delta \tau <{\tau }_{\mathrm{delay}}$. $\Gamma$ is the half-width of a single-electron excitation. $I_0=2\gamma e/\mathcal{T}$ with $\mathcal{T}$ the period of the driving potential and the parameter $\gamma$ defined after Eq. (3).