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arXiv:quant-ph/0409219 · Physical Review B

Surface-acoustic-wave single-electron interferometry

Roberta Rodriquez, Daniel K. L. Oi, M. Kataoka, C. H. W. Barnes, Toshio Ohshima, ARTUR K. EKERT

Published Aug 15, 2005• 28 citations
arXivHTMLPDF

Abstract

We propose an experiment to observe interference of a single electron as it is transported along two parallel quasi-one-dimensional channels trapped in a single minimum of a traveling periodic electric field. The experimental device is a modification of the surface-acoustic-wave-based quantum processor. Interference is achieved by creating a superposition of spatial wave functions between the two channels and inducing a relative phase shift via either a transverse electric field or a magnetic field. The interference can be used to estimate the decoherence time of an electron in this type of solid-state device.

DOI
10.1103/physrevb.72.085329

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We propose an experiment to observe interference of a single electron as it is transported along two parallel quasi-one-dimensional channels trapped in a single minimum of a traveling periodic electric field. The experimental device is a modification of the surface-acoustic-wave-based quantum processor. Interference is achieved by creating a superposition of spatial wave functions between the two channels and inducing a relative phase shift via either a transverse electric field or a magnetic field. The interference can be used to estimate the decoherence time of an electron in this type of solid-state device.
Motivated by recent experimental observations [M. Kataoka et al., Phys. Rev. Lett. 102, 156801 (2009)], we propose here a theoretical approach to implement quantum computation with bound states of electrons in moving quantum dots generated by the driving of surface acoustic waves. Differing from static quantum dots defined by a series of static electrodes above the two-dimensional electron gas (2DEG), here a single electron is captured from a 2DEG reservoir by a surface acoustic wave and then trapped in a moving quantum dot (MQD) transported across a quasi-one-dimensional channel, wherein all the electrons have been excluded by the actions of the surface gates. The flying qubit introduced here is encoded by the two lowest levels of the electron in the MQD, and the Rabi oscillation between these two levels could be implemented by applying finely selected microwave pulses to the surface gates. By using the Coulomb interaction between the electrons in different MQDs, we show that a desirable two-qubit operation, i.e., iswap gate, could be realized. Readouts of the present flying qubits are also feasible with the current single-electron detected technique.
We propose and numerically simulate a semiconductor device based on coupled quantum wires, suitable for deterministic quantum teleportation of electrons trapped in the minima of surface acoustic waves. We exploit a network of interacting semiconductor quantum wires able to provide the universal set of gates for quantum information processing with the qubit defined by the localization of a single electron in one of two coupled channels. The numerical approach is based on a time-dependent solution of the three-particle Schr\"odinger equation. First, a maximally entangled pair of electrons is obtained via Coulomb interaction between carriers in different channels. Then, a complete Bell-state measurement involving one electron from this pair and a third electron is performed. Finally, the teleported state is reconstructed by means of local one-qubit operations. The large estimated fidelity explicitly suggests that an efficient teleportation process could be reached in an experimental setup.
Gallium arsenide is piezoelectric, so it is possible to generate coupled mechanical and electrical surface acoustic waves (SAWs) by applying a high-frequency voltage to a transducer on the surface of GaAs. By combining SAWs with existing low-dimensional nanostructures one can create a series of dynamic quantum dots corresponding to the minima of the travelling electric wave, and each dot carries a single electron at the SAW velocity (∼ 2800 m/s). These devices may be of use in developing future quantum information processors, and also offer an ideal environment for probing the quantum mechanical behaviour of single electrons. This thesis describes a numerical and theoretical study of the dynamics of an electron in a range of geometries. The numerical techniques for solving the time-dependent Schr ̈dinger equation with an arbitrary time-dependent potential will be described in Chapter 2, and then applied in Chapter 3 to calculate the transmission of an electron through an Aharonov-Bohm (AB) ring. It will be seen that an important property of the techniques used in this thesis is that they can be easily adapted to study realistic geometries, and we will see features in the AB oscillations which do not arise in simplified analytic descriptions. In Chapter 4, we will then study a device consisting of two parallel SAW channels separated by a controllable tunnelling barrier. We will use numerical simulations to investigate the effect of electric and magnetic fields upon the electron dynamics, and develop an analytic model to explain the simulation results. From the model, it will be apparent that it is possible to use this device to rotate the state of the electron to an arbitrary superposition of the first two eigenstates. We then introduce coherent and squeezed states in Chapter 5, which are ex- cited states of the quantum harmonic oscillator. Coherent and squeezed electronic states may be of use in quantum information processing, and could also arise due to unwanted perturbations in a SAW device. We will discuss how these states can be controllably generated in a SAW device, and also discuss how they could then be detected. In Chapter 6 we describe how to use the motion of a SAW to create a rapidly- changing potential in the frame of the electron, leading to a nonadiabatic excita- tion. The nonadiabatically-excited state oscillates from side to side within a 1D channel on a few-picosecond timescale, and this motion can be probed by placing a tunnelling barrier at one side of the channel. Numerical simulations will be performed to show how this motion can be controlled, and the simulation results will be seen to be in good agreement with recent experimental work performed by colleagues. Finally, we will show that this device can be used to measure the initial state of an electron which is an arbitrary superposition of the first two eigenstates.
Imaging GHz surface acoustic wave modes in electrostricted LaAlO3_33​/SrTiO3_33​ heterostructures
The LaAlO3_33​/SrTiO3_33​ (LAO/STO) interface hosts a gate-tunable superconducting two-dimensional electron gas (2DEG) which can be programmed to create quantum devices such as ballistic electron waveguides and quantum dots. To fully exploit this platform for quantum transport, a key requirement is the ability to shuttle single electrons, electron pairs, and other exotic states between spatially separated devices with precision. Surface acoustic waves (SAWs), which travel along the surface of a solid, offer a powerful route to achieve this through their moving electrical potential that captures and transfers electrons. %acoustoelectric coupling. In particular, SAWs in the GHz regime enable fast, controlled transport of individual quantum particles. Although this approach is well-explored in GaAs-based 2DEG, SAW generation in STO remains largely unexplored due to the lack of intrinsic piezoelectricity at room temperature. Here, we investigate room-temperature SAWs in LAO/STO and observe SAW modes up to 2.2 GHz with very low propagation loss of the order 10−310^{-3}10−3 dB per wavelength. To directly visualize these modes, we employ Atomic Acoustic Force Microscopy (AAFM), achieving sub-micron resolution imaging of the SAW wave forms, providing insight into the electrostriction-induced SAW generation mechanism. Our measurements indicate a shear horizontal-type mode, which provides the ability to couple to in-plane degrees of freedom for future acoustoelectric and quantum device applications. This work studies the fundamentals of SAW excitation and propagation on STO, a widely used and commercially available substrate, enabling straightforward coupling of SAWs to a broad range of materials that can be grown or transferred onto STO.