Coherent time evolution of a single-electron wave function

Pulse-controlled qubit in semiconductor double quantum dots

We present a numerically-optimized multipulse framework for the quantum control of a single-electron double quantum dot qubit. Our framework defines a set of pulse sequences, necessary for the manipulation of the ideal qubit basis, that avoids errors associated with excitations outside the computational subspace. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation. This basis generates spatially localized logical qubit states, making readout straightforward. We consider experimentally realistic semiconductor qubits with finite pulse rise and fall times and determine the fastest pulse sequence yielding the highest fidelity. We show that our protocol leads to improved control of a qubit. We present simulations of a double quantum dot in a semiconductor device to visualize and verify our protocol. These results can be generalized to other physical systems since they depend only on pulse rise and fall times and the energy gap between the two lowest eigenstates.

Deep Quantum-Dot Arrays in Moiré Superlattices of Non-van der Waals Materials

Recently, moiré superlattices of twisted van der Waals (vdW) materials have attracted substantial interest due to their strongly correlated properties. However, the vdW interlayer interaction is intrinsically weak, such that many desired properties can only exist at low temperature. Here, we theoretically predict some unusual properties stemming from the chemical bonding between twisted PbS nanosheets as an example of non-vdW moiré superlattices. The strong interlayer coupling in such systems results in giant strain vortices and dipole vortices at the interface. The modified electronic structures become a series of dispersionless bands and artificial-atom states. In real space, these states are analogous to arrays of well-positioned quantum dots, which may be promising for use in single-electron devices. In theory, if the materials are doped with a low concentration of electrons, a Wigner crystal will form even without any magnetic field. To confirm the accessibility and stability of non-vdW moiré superlattices in experiment, we synthesized PbS moiré superlattices with different twist angles. Our transmission-electron-microscope observations reveal the resemblance of the small-angle-twisted structures with the square matrices of quantum dots, which is in good accordance with our calculations.

Possible pair-graphene structures govern the thermodynamic properties of arbitrarily stacked few-layer graphene

The thermodynamic properties of few-layer graphene arbitrarily stacked on LiNbO3 crystal were characterized by measuring the parameters of a surface acoustic wave as it passed through the graphene/LiNbO3 interface. The parameters considered included the propagation velocity, frequency, and attenuation. Mono-, bi-, tri-, tetra-, and penta-layer graphene samples were prepared by transferring individual graphene layers onto LiNbO3 crystal surfaces at room temperature. Intra-layer lattice deformation was observed in all five samples. Further inter-layer lattice deformation was confirmed in samples with odd numbers of layers. The inter-layer lattice deformation caused stick-slip friction at the graphene/LiNbO3 interface near the temperature at which the layers were stacked. The thermal expansion coefficient of the deformed few-layer graphene transitioned from positive to negative as the number of layers increased. To explain the experimental results, we proposed a few-layer graphene even-odd layer number stacking order effect. A stable pair-graphene structure formed preferentially in the few-layer graphene. In even-layer graphene, the pair-graphene structure formed directly on the LiNbO3 substrate. Contrasting phenomena were noted with odd-layer graphene. Single-layer graphene was bound to the substrate after the stable pair-graphene structure was formed. The pair-graphene structure affected the stacking order and inter-layer lattice deformation of few-layer graphene substantially.

Piezoacoustics for precision control of electrons floating on helium

Piezoelectric surface acoustic waves (SAWs) are powerful for investigating and controlling elementary and collective excitations in condensed matter. In semiconductor two-dimensional electron systems SAWs have been used to reveal the spatial and temporal structure of electronic states, produce quantized charge pumping, and transfer quantum information. In contrast to semiconductors, electrons trapped above the surface of superfluid helium form an ultra-high mobility, two-dimensional electron system home to strongly-interacting Coulomb liquid and solid states, which exhibit non-trivial spatial structure and temporal dynamics prime for SAW-based experiments. Here we report on the coupling of electrons on helium to an evanescent piezoelectric SAW. We demonstrate precision acoustoelectric transport of as little as ~0.01% of the electrons, opening the door to future quantized charge pumping experiments. We also show SAWs are a route to investigating the high-frequency dynamical response, and relaxational processes, of collective excitations of the electronic liquid and solid phases of electrons on helium.

Hybrid devices based on electrons on helium may find application in quantum devices. Here the authors demonstrate surface acoustic wave driven acoustoelectric transport of electrons on superfluid helium.

Phase-space studies of backscattering diffraction of defective Schrödinger cat states

The coherent superposition of two well separated Gaussian wavepackets, with defects caused by their imperfect preparation, is considered within the phase-space approach based on the Wigner distribution function. This generic state is called the defective Schrödinger cat state due to this imperfection which significantly modifies the interference term. Propagation of this state in the phase space is described by the Moyal equation which is solved for the case of a dispersive medium with a Gaussian barrier in the above-barrier reflection regime. Formally, this regime constitutes conditions for backscattering diffraction phenomena. Dynamical quantumness and the degree of localization in the phase space of the considered state as a function of its imperfection are the subject of the performed analysis. The obtained results allow concluding that backscattering communication based on the defective Schrödinger cat states appears to be feasible with existing experimental capabilities.

Coherent Beam Splitting of Flying Electrons Driven by a Surface Acoustic Wave

We develop a coherent beam splitter for single electrons driven through two tunnel-coupled quantum wires by surface acoustic waves (SAWs). The output current through each wire oscillates with gate voltages to tune the tunnel coupling and potential difference between the wires. This oscillation is assigned to coherent electron tunneling motion that can be used to encode a flying qubit and is well reproduced by numerical calculations of time evolution of the SAW-driven single electrons. The oscillation visibility is currently limited to about 3%, but robust against decoherence, indicating that the SAW electron can serve as a novel platform for a solid-state flying qubit.

Picosecond coherent electron motion in a silicon single-electron source

An advanced understanding of ultrafast coherent electron dynamics is necessary for the application of submicrometre devices under a non-equilibrium drive to quantum technology, including on-demand single-electron sources¹, electron quantum optics^2-4, qubit control^5-7, quantum sensing^8,9 and quantum metrology¹⁰. Although electron dynamics along an extended channel has been studied extensively^2-4,11, it is hard to capture the electron motion inside submicrometre devices. The frequency of the internal, coherent dynamics is typically higher than 100 GHz, beyond the state-of-the-art experimental bandwidth of less than 10 GHz (refs. ^6,12,13). Although the dynamics can be detected by means of a surface-acoustic-wave quantum dot¹⁴, this method does not allow for a time-resolved detection. Here we theoretically and experimentally demonstrate how we can observe the internal dynamics in a silicon single-electron source that comprises a dynamic quantum dot in an effective time-resolved fashion with picosecond resolution using a resonant level as a detector. The experimental observations and the simulations with realistic parameters show that a non-adiabatically excited electron wave packet¹⁵ spatially oscillates quantum coherently at ~250 GHz inside the source at 4.2 K. The developed technique may, in future, enable the detection of fast dynamics in cavities, the control of non-adiabatic excitations¹⁵ or a single-electron source that emits engineered wave packets¹⁶. With such achievements, high-fidelity initialization of flying qubits⁵, high-resolution and high-speed electromagnetic-field sensing⁸ and high-accuracy current sources¹⁷ may become possible.

Sound-driven single-electron transfer in a circuit of coupled quantum rails

Surface acoustic waves (SAWs) strongly modulate the shallow electric potential in piezoelectric materials. In semiconductor heterostructures such as GaAs/AlGaAs, SAWs can thus be employed to transfer individual electrons between distant quantum dots. This transfer mechanism makes SAW technologies a promising candidate to convey quantum information through a circuit of quantum logic gates. Here we present two essential building blocks of such a SAW-driven quantum circuit. First, we implement a directional coupler allowing to partition a flying electron arbitrarily into two paths of transportation. Second, we demonstrate a triggered single-electron source enabling synchronisation of the SAW-driven sending process. Exceeding a single-shot transfer efficiency of 99%, we show that a SAW-driven integrated circuit is feasible with single electrons on a large scale. Our results pave the way to perform quantum logic operations with flying electron qubits.

Coherent control of single electrons: a review of current progress

In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.

Collective spin correlations and entangled state dynamics in coupled quantum dots

Here we demonstrate that the dynamics of few-electron states in a correlated quantum-dot system coupled to an electronic reservoir is governed by the symmetry properties of the total system leading to the collective behavior of all the electrons. Time evolution of two-electron states in a correlated double quantum dot after coupling to the reservoir has been analyzed by means of kinetic equations for pseudoparticle occupation numbers with constraint on possible physical states. It was revealed that the absolute value of the spin correlation function and the degree of entanglement for two-electron states could considerably increase after coupling to the reservoir. The obtained results demonstrate the possibility of a controllable tuning of both the spin correlation function and the concurrence value in a coupled quantum-dot system by changing of the gate voltage applied to the barrier separating the dots.

Dynamics of interacting electrons under effect of a Morse potential

We consider interacting electrons moving in a nonlinear Morse lattice. We set the initial conditions as follows: electrons were initially localized at the center of the chain and a solitonic deformation was produced by an impulse excitation on the center of the chain. By solving quantum and classical equations for this system numerically, we found that a fraction of electronic wave function was trapped by the solitonic excitation, and trapping specificities depend on the degree of interaction among electrons. Also, there is evidence that the effective electron velocity depends on Coulomb interaction and electron-phonon coupling in a nontrivial way. This association is explained in detail along this work. In addition, we briefly discuss the dependence of our results with the type of initial condition we choose for the electrons and lattice.

High-resolution imaging of gigahertz polarization response arising from the interference of reflected surface acoustic waves

The surface polarization caused by traveling SAWs at 1.585 GHz has been imaged using a dynamic homodyne electrostatic force microscope technique. Instead of measuring topographic changes caused by the SAW, the reported technique measures polarization in the piezoelectric substrate arising from mechanical stress caused by the SAW. The polarization associated with this stress field modulates the scanning probe cantilever deflection amplitude, which is extracted using a lock-in-based technique. High-resolution imaging is presented with images of the interference arising from a metal reflector on a SAW device. A mathematical model combining SAW generation and force interactions between the probe and the substrate was used to verify the experimental data. In addition to overcoming the challenge associated with detecting and imaging polarization effects at gigahertz frequencies, this imaging technique will greatly assist the development of SAW-based devices that exploit the reflection and interference of SAWs in areas as diverse as microfluidic mixing, cell sorting, and quantum entanglement.

Validity of the single-particle approach for electron transport in quantum wires assisted by surface acoustic waves

We study by means of time-dependent numerical simulations the quantum entanglement stemming from the Coulomb interaction between two electrons trapped in the minima of the piezoelectric potential generated by surface acoustic waves. We find that for particles captured in low-energy bound states the quantum correlations turn out to be negligible, thus validating a single-particle approach to the dynamics of such systems. At long times, for high-energy electrons, a substantial entanglement appears, which is an indicator of a mostly correlated dynamics.