Crystallization of levitons in the fractional quantum Hall regime

Using a periodic train of Lorentzian voltage pulses, which generates solitonlike electronic excitations called levitons, we investigate the charge density backscattered off a quantum point contact in the fractional quantum Hall regime. We find a regular pattern of peaks and valleys, reminiscent of analogous self-organization recently observed for optical solitons in nonlinear environments. This crystallization phenomenon is confirmed by additional side dips in the Hong-Ou-Mandel noise, a feature that can be observed in present-day electron quantum optics experiments.

Figure 1

Inset: sketch of the setup. The pulses originate from contacts 1 (top edge, $x\le -d$) and 4 (bottom edge, $x\ge +d$) and propagate along the edge states of a FQH system. They may be either reflected or transmitted at $x=0$ due to the presence of a QPC. Main panels: Excess charge density $\mathrm{\Delta }{\rho }_L(-d,t)$ evaluated in terminal 2 (i.e., $x=-d$) in the presence of a single source for $q=5$ and $q=6$, in units of $\frac{e{\left|\mathrm{\Lambda }\right|}^2{\omega }_c}{2\pi v^3}$. Two different filling factors are considered: $\nu =\frac{1}{3}$ (solid lines) and $\nu =\frac{1}{5}$ (dashed lines). The other parameters are $W=0.04\mathcal{T},k_{\mathrm{B}}\theta ={10}^{-3}\omega$, and $\omega =0.01{\omega }_c$.

Figure 2

Ratio $\mathcal{R}$ as a function of the time delay $t_D$ for $q=1,q=4,q=5$, and $q=6$. The integer case (dashed lines) and the fractional case for $\nu =\frac{1}{3}$ (solid lines) are compared. The other parameters are $W=0.04\mathcal{T},k_{\mathrm{B}}\theta ={10}^{-3}\omega$, and $\omega =0.01{\omega }_c$.

Figure 3

Ratio $\mathcal{R}$ as a function of the time delay $t_D$ for $q=3,q=4,q=5$, and $q=6$. The integer case (dashed lines) and the fractional case for $\nu =\frac{1}{3}$ (solid lines) are compared. The other parameters are $W=0.1\mathcal{T}$ and $\omega =0.01{\omega }_c$.

Figure 4

Ratio $\mathcal{R}$ as a function of $W/\mathcal{T}$ for $q=3,q=4,q=5$, and $q=6$. The integer case (dashed lines) and the fractional case for $\nu =\frac{1}{3}$ (solid lines) are compared. The other parameters are $t_D=0.5\mathcal{T}$ and $\omega =0.01{\omega }_c$.