Spatiotemporal imaging of gate-controlled multipath dynamics of fractional quantum Hall edge excitations

Abstract

Quantum Hall edge excitations, whose low-energy behavior admits a chiral conformal-field-theory description, are a promising platform for engineered dynamical experiments, including analog-spacetime proposals. However, establishing their edge dynamics in realistic electrostatic landscapes is essential for controlled dynamical experiments and has remained experimentally challenging. Here we report spatiotemporal imaging of gate-controlled multipath dynamics of edge excitations in a $ν= 1/3$ fractional quantum Hall device using stroboscopic time-resolved photoluminescence microscopy and spectroscopy with $\sim$100-ps resolution. By tuning a control-gate-defined potential landscape, we observe switching between mesa-defined and gate-defined trajectories and identify an intermediate regime in which a single launched excitation accesses multiple pathways. Time-resolved measurements at downstream locations reveal gate-dependent arrival times and pronounced temporal broadening, showing that the propagation dynamics are strongly modified by the local confinement and become increasingly dispersive in a multipath landscape. We further observe a long-range transverse optical response extending tens of micrometers into the bulk and persisting over distances exceeding 200 $μ$m downstream, consistent with the near-field component of an edge magnetoplasmon. These results establish direct experimental access to controllable multipath edge dynamics in the fractional quantum Hall regime and suggest a platform for engineered nonequilibrium and interference-based experiments, as well as future analog-spacetime studies in quantum Hall edge systems.

Figures (6)

• Figure 1: Optical microscope image of the measurement device. An arbitrary waveform generator (AWG) is connected to the upstream excitation gate, located 42 $\mu$m upstream from the edge of the control gate along the mesa. The semi-circular region is covered by the control gate electrode, comprising an opaque Ti/Au area ($\sim$300 nm thick) and a semi-transparent Au area ($\sim$10 nm thick) eytan1998nearyusa2000onset. The semi-transparent area has an optical transmittance of $50\%$. Points 1 and 2 correspond to the measurement positions in Fig. \ref{['fig:time-resolve']}. Scan area 1 is used for mapping in Fig. \ref{['fig:mappings']}, and Scan area 2 corresponds to Fig. \ref{['fig:excitation-gate']}. Lines A--D indicate the measurement paths for Fig. \ref{['fig:microPLspectra']}. Grounded electrodes are part of coplanar waveguide structures france2025electrically.
• Figure 2: $45 \times 24~\mu\mathrm{m}^2$ spatial map of (a) reflectance and (b)--(f) time-resolved snapshots of the singlet PL intensity change. (a) Reflectance map of Scan area 1 acquired with the same optical setup at $40$--$50$ mK; the yellow region indicates the semi-transparent area of the control gate. (b)--(f) Time-resolved snapshots of the singlet PL intensity change plotted as $\log(I_\mathrm{singlet}/I_0)$ (see main text for definitions). A value of 0 indicates no change, whereas positive and negative values indicate increases and decreases induced by the edge excitation, respectively. The rectangular pulse amplitude is $\pm 100$ mV in (b)--(f). The applied control-gate voltages are: (b) $V_\mathrm{c}=-1.0$ V; (c) $-0.2$ V; (d) $0$ V; (e) $0.3$ V; (f) $0.5$ V.
• Figure 3: Evolution of the singlet PL intensity as a function of $t$ (here $t\equiv t_2$; see Supplemental Material) measured at (a) Point 1 and (b) Point 2 (see Fig. \ref{['fig:device']}). A negative-polarity pulse (levels $150~\mathrm{mV}$ to $-350~\mathrm{mV}$) is applied to the excitation gate. Each trace corresponds to a different control-gate voltage $V_\mathrm{c}$, as indicated on the right; traces are vertically offset for clarity. Each trace is collected with an exposure time of 20 s. Insets schematically indicate the measurement locations.
• Figure 4: Triplet intensity maps ($51\times 50~\mu\mathrm{m}^2$) of Scan Area 2 (Fig. \ref{['fig:device']}) measured as snapshots at $t_1 = -3.1$ ns with an exposure time of 10 s. The dark blue region corresponds to the region occluded by the excitation gate. (a) Reference map recorded with no voltage pulse applied to the excitation gate. (b) and (c), Maps obtained when a bipolar negative-polarity rectangular voltage pulse with a width of approximately $2$ ns is applied to the excitation gate. The amplitude of the rectangular pulse is $\pm 50$ mV in panel (b) and $\pm 100$ mV in panel (c).
• Figure 5: (a)--(c) Micro-PL spectra measured as snapshots at positions along the $y$ direction (perpendicular to the mesa boundary defined at $y=0$): $y=-3$, $-10$, $-20$, $-30$, and $-35~\mu$m (the last only in (a) and (b)). Delay times are $t_1=-3.1$ ns for (a) and (b), and $t_3=-2.6$ ns for (c) (see Sec. \ref{['subsec:experimental']} and Supplemental Material). (a) Spectra along Line A at $V_\mathrm{c}=0.0$ V ($17~\mu$m upstream from the center of the excitation gate). (b) Spectra along Line B at $V_\mathrm{c}=0.0$ V ($17~\mu$m downstream from the center of the excitation gate). (c) Spectra along Line C at $V_\mathrm{c}=-0.4$ V (downstream beyond the control-gate region; exposure time 15 s). Dotted curves show spectra measured without the excitation pulse. Insets in (a)--(c) schematically indicate the measurement locations (Lines A--C). (d) Singlet and triplet PL peak intensities and their average as a function of $y$ along Line D at $V_\mathrm{c}=-1.0$ V. Definitions of the $y$ direction and the locations of Lines A--D are provided in Fig. \ref{['fig:device']}. The pulse amplitude is $\pm 100$ mV for (a) and (b), and $\pm 200$ mV for (c) and (d).