Generation of a Single-Cycle Acoustic Pulse: A Scalable Solution for Transport in Single-Electron Circuits

The synthesis of single-cycle pulses of compressed light and microwave signals sparked novel areas of fundamental research. In the field of acoustics, however, such a generation has not been introduced yet. For numerous applications, the large spatial extent of surface acoustic waves (SAW) causes unwanted perturbations and limits the accuracy of physical manipulations. Particularly, this restriction applies to SAW-driven quantum experiments with single flying electrons, where extra modulation renders the exact position of the transported electron ambiguous and leads to undesired spin mixing. Here, we address this challenge by demonstrating single-shot chirp synthesis of a strongly compressed acoustic pulse. Employing this solitary SAW pulse to transport a single electron between distant quantum dots with an efficiency exceeding 99%, we show that chirp synthesis is competitive with regular transduction approaches. Performing a time-resolved investigation of the SAW-driven sending process, we outline the potential of the chirped SAW pulse to synchronize single-electron transport from many quantum-dot sources. By superimposing multiple pulses, we further point out the capability of chirp synthesis to generate arbitrary acoustic waveforms tailorable to a variety of (opto)nanomechanical applications. Our results shift the paradigm of compressed pulses to the field of acoustic phonons and pave the way for a SAW-driven platform of single-electron transport that is precise, synchronized, and scalable.

Popular Summary

Sound waves provide a powerful platform to transport a single electron in nanoscale devices. Accordingly, they are highly promising to implement novel quantum-computing approaches where electrons are manipulated on the fly. Since sound waves typically consist of many periods, however, the implementation of such quantum logic is extremely challenging on a large scale. Here, we address this problem by engineering an acoustic wave that has a single surge—resembling a tidal bore at the nanoscale.

We employ a nonuniform transducer to compress many frequencies into an acoustic wave with a single peak. Letting a single electron surf on this acoustic wave front, we successively transport the elementary particle between distant nodes with an efficiency greater than 99%. In addition, we show that our technique enables formation of a solitary acoustic pulse with an arbitrary shape that is tailorable for a vast set of nanomechanical applications.

Since the acoustic pulse can successively pick up single electrons from multiple nodes, it provides a scalable innovation marking a paradigm shift for quantum-computing approaches.

Figure 1

Experimental setup. Schematic of chirp IDT launching a compressed SAW towards a quantum rail and a subsequent broadband SAW detector. We show a perspective view on the sample that is realized via metallic surface gates in a $\mathrm{GaAs}/\mathrm{AlGaAs}$ heterostructure. Inset: comparison between the periodic SAW modulation from regular transduction (dotted gray line) with the ideal SAW profile for electron transport consisting of a single propagating minimum (red line).

Figure 2

SEM images of the chirp IDT with zooms (insets) in the regions of large (left panel) and small (right panel) periodicity of the interlocked electrodes.

Figure 3

Frequency response. Transmission measurement between opposing chirp IDTs (black) with simulation via the delta-function model (gray) and indications of the passband ranging from $f_1\approx 0.5\mathrm{GHz}$ to $f_N\approx 3.0\mathrm{GHz}$. Note that the transmission bandwidth of the radio-frequency lines is not considered in the simulation.

Figure 4

Time-resolved measurements. (a) Trace of detector response for the frequency-modulated input signal applied on the chirp IDT with $t_S\approx 120\mathrm{ns}$. After initial electromagnetic crosstalk ($t=0\mathrm{ns}$), SAW arrives at the expected delay time $t_D$. (b) Zoom-in of the time window around $t_D$, which shows the detected voltage pulse (black) with impulse-response simulation (gray) and the corresponding SAW shape (red; with offset and arbitrary units) derived via deconvolution of the detector response.

Figure 5

Electron shuttling along quantum rail. (a) SEM image of the quantum rail consisting of two surface-gate-defined quantum dots (QD) that are connected via a depleted transport channel. We further show the quantum-point-contact (QPC) electrometers that are placed next to each QD to sense the presence of electrons. (b) Time-dependent measurement of the chirped pulse in the cryogenic setup via the SAW detector (black). The offset red line shows the corresponding SAW profile extracted via deconvolution of the detector’s response function. (c) Histogram of jumps in the electrometer current $\mathrm{\Delta }{I}_{\mathrm{QPC}}$ at the receiver QD from 70 000 single-shot measurements after launching the SAW pulse with (red) and without (gray) precedent loading of an electron in the source QD. (d) Table of transfer and error probabilities with QD-occupation code of the events (source before, source after, receiver before, receiver after). (e) Successful (1001) and failed (1000) transfer probabilities as a function of the trigger delay $\tau$ of the sending process with respect to the SAW emission.

Figure 6

Acousto-electric wave engineering. Time-resolved measurements from the SAW detector for an input signal consisting of two superposed pulses with different time delays $\mathrm{\Delta }t=\mathrm{\Delta }{t}_2-\mathrm{\Delta }{t}_1\in [0,3,6]\mathrm{ns}$.

Figure 7

SAW-dispersion relation for aluminium IDTs on a GaAs substrate. We show the resonance frequency for IDTs having different periodicity—here expressed as wave number $1/{\lambda }_0=k/2\pi$. The points are extracted from Gaussian fits of distinct peaks in the transmission data (reflection data for the case of 8 GHz) from a network analyzer measurement.

Figure 8

Detection bandwidth. Pass band of a regular IDT with $N=1.5$. The shaded area indicates the FWHM of the transmission peak. The vertical double-headed arrow indicates the employed resonance frequency of the detector IDT, $f_0\approx 2.81\mathrm{GHz}$.

Figure 9

Nonideal input signals. Time-resolved measurements of the SAW response for an input signal with duration deviation of $t_S-t_N\in [-10,-5,0,5,10]\mathrm{ns}$. The semitransparent line in the background shows the course expected from an impulse-response model.

Figure 10

Construction of the impulse response of IDTs. We show examples of the response function $h(t)$ (vertical axis) in comparison to the finger positions for (a) a regular IDT and (b) a chirp IDT.

Figure 11

Time-resolved measurements on regular IDT. (a) Trace of detector response for resonant input signal applied for a duration $t_S=40\mathrm{ns}$ on the regular IDT. The SAW arrives with expected delay $t_D$ after initial electromagnetic crosstalk. (b) Zoom in of SAW region at $t_D$.

Figure 12

Effect of design parameters. SAW shapes of impulse-response model for changing IDT parameters. (a) Varying maximal frequency $f_N$ with $f_1=0.5\mathrm{GHz}$ and $t_N=40\mathrm{ns}$. (b) Increasing IDT length $t_N$ with $f_1=0.5\mathrm{GHz}$ and $f_N=3.5\mathrm{GHz}$. (c) Reducing minimum frequency $f_0$ with $f_N=7\mathrm{GHz}$ and $t_N=40\mathrm{ns}$.