Eigenstate control of plasmon wavepackets with electron-channel blockade

TL;DR

Coherent manipulation of propagating plasmon wavepackets in quasi-one-dimensional electron circuits is hindered by charge fractionalisation across multiple conduction channels. The authors implement electron-channel blockade by forming a Fabry-Pérot cavity between local constrictions, enabling selection of the plasmon eigenstate and tuning propagation speed by locally controlling the number of transmitting channels. The blockade operates when the plasmon bandwidth is smaller than the cavity's resonance frequency $f_{FP}$, preventing occupation of confined channels and channeling the plasmon through a single mode; when the bandwidth exceeds $f_{FP}$, standing-wave modes form and fractionalisation persists, limiting control. This approach suppresses plasmon excitation leakage to nearby circuits and is demonstrated in parallel-wire geometries, providing a versatile tool for designing precise plasmonic quantum circuits and flying-electron qubits.

Abstract

Coherent manipulation of plasmon wavepackets in solid-state systems is crucial for advancing nanoscale electronic devices, offering a unique platform for quantum information processing based on propagating quantum bits. Controlling the eigenstate of plasmon wavepackets is essential, as it determines its propagation speed and hence the number of quantum operations that can be performed during its flight-time through a quantum system. When plasmon wavepackets are generated by short voltage pulses and transmitted through nanoscale devices, they distribute among multiple electron conduction channels via Coulomb interactions, a phenomenon known as charge fractionalisation. This spreading complicates plasmon manipulation in quantum circuits and makes precise control of the eigenstates of plasmon wavepackets challenging. Using a cavity, we demonstrate the ability to isolate and select electron conduction channels contributing to plasmon excitation, thus enabling precise control of plasmon eigenstate. Specifically, we observe an electron-channel blockade effect, where charge fractionalisation into cavity-confined channels is suppressed due to the plasmon's narrow energy distribution, enabling more stable and predictable plasmonic circuits. This technique provides a versatile tool for designing plasmonic circuits, offering the ability to tailor plasmon speed through local parameters, minimise unwanted plasmon excitation in adjacent circuits, and enable the precise selection of electron-channel plasmon eigenstates in quantum interferometers.

Figures (12)

• Figure 1: Experimental setup and time-resolved measurement of plasmon wavepackets.a. Schematic of the device and the measurement setup. A 50µ m-long electron waveguide can be formed by polarising gates w2 and its length can be extended to 100µ m by additionally polarising gates w1, and $g_{\rm res}$. QPC1 and QPC2 are used to locally control the number of transmitting electron conduction channels for the 100µ m and 50µ m long waveguide, respectively. QPC3 is used for time-resolved measurements of plasmon wavepackets. A high bandwidth bias tee is connected to the upper QPC3 gate to be able to apply a fast voltage pulse, $V_{\rm det} (t)$ on top of the dc voltage, $V_{\rm QPC3}$. The reservoir gate $g_{\rm res}$ is used to connect the 100µ m-long electron waveguide to the Ohmic contact, $O_{\rm r}$. Plasmon wavepackets are excited by applying a voltage pulse, $V_{\rm in} (t)$, on the Ohmic contact, $O_{\rm i}$. The output current at the Ohmic contact, $O_{\rm o}$, is measured by the voltage, $V_{\rm o}$ across a cold 10kΩ resistor. b. Temporal shape of the voltage pulses generated by the AWG, with pulse widths defined by full width at half maximum (FWHM) ranging from 52ps to 500ps. c. Time-resolved measurement of plasmon wavepackets excited by a 180ps-long voltage pulse, for different wire widths in the 50µ m-long quantum wire. The vertical scale is normalised to one. Each curve is offset vertically for clarity. The voltage applied on the gates w2, $V_{\rm w2}$ is changed from -0.6V at the bottom to -1.2V at the top by -0.1V step. The peak positions are indicated with black points. d. Speed of plasmon wavepackets excited by a 180ps-long voltage pulse as a function of the gate voltage, $V_{\rm w2}$. The speed is calculated from the length of the quantum wire and the delay time at the peak obtained as in c. e. Time-resolved measurements of plasmon wavepackets excited by a 180ps-long voltage pulse with varying pulse amplitudes. The peak voltage at $O_{\rm i}$ is adjusted between 0.24mV and 2.4mV. The dashed line highlights the unchanged peak position despite varying pulse amplitudes. These characterisation measurements were conducted at 4K.
• Figure 1: Scanning electron micrograph of the device. False colours are used to indicate the gates used for the experiment and correspond to the ones employed in Fig. \ref{['fig:device']}a. The inset is the focus around QPC2. The gates without the false colours are not used in this experiment.
• Figure 2: Local control of the number of transmitting electron conduction channels in 100 $\mathbf{\mu m}$ quantum wire.a, b. Time-resolved measurement of plasmon wavepackets excited by 52ps-long voltage pulse (a) and 500ps-long voltage pulse (b) for different voltages on the gates of QPC1. The amplitude is normalised to one. Each curve is offset vertically for clarity. The gate voltage $V_{\rm QPC1}$ was stepped from -0.2V at the bottom to -1.4V at the top. The gate voltage $V_{\rm w1, w2}$ was fixed to -0.7V. The peak position is indicated by the black circles. The shape of the voltage pulse used to excite the plasmon wavepacket is drawn by the black dashed line. c. Speed of the plasmon wavepackets calculated from the peak delay indicated by the black circles in a, b. Here the number $N$ on top of the grey shaded gate voltage indicates the number of transmitting electron channels across QPC1 at the each voltage, which is determined by the observation of the quantised conductance.
• Figure 2: Calibration of RF line delay time using a two dimensional plasmon. A two dimensional plasmon is excited by applying the voltage pulse with different full width at half maximum (FWHM) on the contact, $O_{\rm i}$ without applying any voltage on the gates (w1, w2, QPC1, QPC2, $g_{\rm res}$). The time-resolved measurement is performed by using QPC3 as explained in the main text. The peak position does not change for different pulse lengths and is estimated to be 112(7)ps.
• Figure 3: Fabry-Pérot cavity and speed control with a local constriction.a. The ratio between the frequency quantisation of the Fabry-Pérot cavity, $f_{\rm FP}$, and the bandwidth, $\Delta f$ for the plasmon wavepackets. The dashed line indicates $f_{\rm FP} / \Delta f = 1$. $f_{\rm FP}\ (=\ v_{\rm p}/2L_{\rm FP})$ as a function of $V_{\rm QPC1}$ is calculated from $v_{\rm p}$ in Fig. \ref{['fig:qpc_speed']}c. $\Delta f\ (=\ 1 / t_{\rm FWHM})$ is calculated from $t_{\rm FWHM}$ in Fig. \ref{['fig:device']}b. b, c. Normalised amplitude of fast Fourier transform (FFT) of the voltage pulse in Fig. \ref{['fig:device']}b for 52ps-long voltage pulse (b) and 500ps-long voltage pulse (c). The bandwidth value, $\Delta f$, is indicated by a black solid line. In addition, $f_{\rm FP}$ at $V_{\rm QPC1} =$ -0.2V and its multiples are indicated by the red dashed lines. d. Time-resolved measurement of a plasmon wavepacket excited by 500ps pulse for different gate voltages applied to QPC1 in the 100µ m-long electronic waveguide while it is connected to the Ohmic contact $O_{\rm r}$. The amplitude is normalised to one. Each curve is offset vertically for clarity. The gate voltage $V_{\rm QPC1}$ was stepped from -0.2V (bottom) to -1.4V (top). The peak position is indicated by the black dots. e. Comparison of plasmon speed as a function of $V_{\rm QPC1}$ with and without the FP cavity for the wavepackets excited by 500ps pulse. The data without the FP cavity (new data) and the data with the FP cavity (from Fig. \ref{['fig:qpc_speed']}c) is provided for direct comparison. Here the number $N$ on top of the grey shaded gate voltage indicates the number of transmitting electron channels across QPC1, which is determined by the observation of the quantised conductance.