Control of electron-hole pair generation by biharmonic voltage drive of a quantum point contact

A time-dependent electromagnetic field creates electron-hole excitations in a Fermi sea at low temperature. We show that the electron-hole pairs can be generated in a controlled way using harmonic and biharmonic time-dependent voltages applied to a quantum contact, and we obtain the probabilities of the pair creations. For a biharmonic voltage drive, we find that the probability of a pair creation decreases in the presence of an in-phase second harmonic. This accounts for the suppression of the excess noise observed experimentally (Gabelli and Reulet, arXiv:1205.3638), proving that dynamic control and detection of elementary excitations in quantum conductors are within the reach of the present technology.

Figure 1

Probabilities $p_k$ of electron-hole pair creations for harmonic drive $V\left(t\right)=\overline{V}+V_1\cos \left(\omega t\right)$ as a function of the ac amplitude $V_1$ and for different dc voltage offsets $e\overline{V}/\omega =N$: (a) $N=0$, (b) $N=1$, and (c) $N=2$. dc offset $\overline{V}$ sets the number of electrons injected toward the contact while $V_1$ controls the electron-hole pair generation. Symbols denote experimental data for the excess noise $S_{\mathrm{ac}}$ in units $2GF\omega$ taken from Ref. 19 for a quantum contact with $F=1/2$ and ($◯$) $\omega /2\pi =17.32\mathrm{GHz}$, ($\square$) $\omega /2\pi =8.73\mathrm{GHz}$.

Figure 2

(a) Current noise $S$ as a function of dc voltage $\overline{V}$ for biharmonic time-dependent drive $V\left(t\right)=\overline{V}+V_1\cos \left(\omega t\right)+V_2\cos (2\omega t+\phi )$ with $e{V}_1/\omega =5.4$, $e{V}_2/\omega =2.7$, and $\phi =0$ (thick solid line), $\pi /2$ (dash-dotted line), and $\pi$ (thin solid line). The excess noise $S_{\mathrm{ac}}$ is shown as a function of $\overline{V}$ for the same voltage drive with (b) $\phi =0$ and (c) $\phi =\pi /2$. Symbols in (b) and (c) denote experimental data taken from Ref. 8 for a tunnel junction ($F=1$) at low temperature ($T=0.14\omega$).

Figure 3

Decomposition of the excess noise $S_{\mathrm{ac}}$ shown in Fig. 2 into elementary electron-hole pair excitations [see Eq. (2)]. Probabilities $p_k^{\left(N\right)}$ of the pair creations are denoted by stacked bars at dc voltages $e\overline{V}/\omega =N$ with $N$ integer: $k=1$ (blue), $k=2$ (green), and $k=3$ (red bars). The elementary excitations comprise a few (one or two) electron-hole pairs generated with probabilities $p_{1,2}^{\left(N\right)}$ per voltage cycle.

Figure 4

Probabilities $p_k$ of the electron-hole pair creations as a function of the amplitude $V_2$ of the second harmonic for the biharmonic voltage drive with $e\overline{V}/\omega =3$, $e{V}_1/\omega =5.4$, and the phase difference (a) $\phi =0$ and (b) $\phi =\pi /2$. Dashed lines indicate the excess noise $S_{\mathrm{ac}}$ in units $2GF\omega$. The presence of an in-phase second harmonic decreases the probability of the electron-hole pair creation leading to suppression of $S_{\mathrm{ac}}$ observed experimentally.[8]