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Communications in Theoretical Physics

Coupling Distant Spins of Surface-State Electrons by Manipulating Their Collective Vibrations

Yong Chun Zeng, Miao Zhang, Lian-Fu Wei

Published Jan 1, 2014• 0 citations
Publisher

Abstract

The system of electrons on liquid helium is an interesting candidate to implement quantum computation, due to the long coherence times of the qubits encoded by the electronic spins. In order to implement the quantum logic operations between the spins, we propose here a configuration, similarly to the cooled ions in a trap, to couple the distant electrons via manipulating their center of mass (CM) vibrations. First, we show that the electrons could be confined in a common harmonic oscillator potential by using an electrostatic field. Then, with a single current pulse (applied on the micro-electrode below the liquid helium) the distant electronic spins can be coupled simultaneously to the CM mode. Finally, by adiabatically eliminating the CM mode, effective interaction between the distant spins is induced for implementing the desired quantum computing.

DOI
10.1088/0253-6102/61/1/21

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The system of electrons on liquid helium is an interesting candidate to implement quantum computation, due to the long coherence times of the qubits encoded by the electronic spins. In order to implement the quantum logic operations between the spins, we propose here a configuration, similarly to the cooled ions in a trap, to couple the distant electrons via manipulating their center of mass (CM) vibrations. First, we show that the electrons could be confined in a common harmonic oscillator potential by using an electrostatic field. Then, with a single current pulse (applied on the micro-electrode below the liquid helium) the distant electronic spins can be coupled simultaneously to the CM mode. Finally, by adiabatically eliminating the CM mode, effective interaction between the distant spins is induced for implementing the desired quantum computing.
We propose an approach to entangle spins of electrons floating on liquid helium by coherently manipulating their spin-orbit interactions. The configuration consists of single electrons, confined individually on liquid helium by the microelectrodes, moving along the surface as the harmonic oscillators. It has been known that the spin of an electron could be coupled to its orbit (i.e., the vibrational motion) by properly applying a magnetic field. Based on this single electron spin-orbit coupling, here we show that a Jaynes-Cummings (JC) type interaction between the spin of an electron and the orbit of another electron at a distance could be realized via the strong Coulomb interaction between the electrons. Consequently, the proposed JC interaction could be utilized to realize a strong orbit-mediated spin-spin coupling and implement the desirable quantum information processing between the distant electrons trapped individually on liquid helium.
Abstract Surface-state electrons floating on liquid Helium have been served as one of the great potential experimental platforms to implement quantum computation, wherein the qubits are usually encoded by either the lowest two levels of the vertical vibrations (i.e., Hydrogen-like atoms) or the electronic spins. Given the relevant operations require additional techniques, such as the corresponding millimeter-wave or magnetic field manipulations, here we investigate how to implement the scalable quantum computation with a trapped electron array by alternatively using the usual centimeter-wave manipulating techniques. This is because the eigenfrequency of the present qubit, encoded by the two lowest levels of the lateral vibration of the trapped electron, is limited in the centimeter-wave band. We show that, by biasing the electrodes properly and driving the coplanar waveguide transmission line resonator, the electrons can be individually trapped in a series of anharmonic potentials on liquid Helium. Therefore, the well-developed circuit quantum electrodynamics technique for the implementation of superconducting quantum computation can be conveniently utilized here in the present quantum computing platform (proposed firstly in Phys Rev Lett 105:040503, 2010, to implement the fundamental logic gates, typically such as the single-qubit rotations of the individually addressable trapped electrons, the switchable two-qubit manipulations between the electrons trapped in the distant traps, and also the high-fidelity readouts of the target qubits. The feasibility of the proposal is also discussed by numerical simulations.
Numerous physical systems have been proposed for constructing quantum computers, but formidable obstacles stand in the way of making even modest systems with a few hundred quantum bits (qubits). Several approaches utilize the spin of an electron as the qubit. Here it is suggested that the spin of electrons floating on the surface of liquid helium will make excellent qubits. These electrons can be electrostatically held and manipulated much like electrons in semiconductor heterostructures, but being in a vacuum the spins on helium suffer much less decoherence. In particular, the spin-orbit interaction is reduced so that moving the qubits with voltages applied to gates has little effect on their coherence. Remaining sources of decoherence are considered, and it is found that coherence times for electron spins on helium can be expected to exceed 100s100\phantom{\rule{0.3em}{0ex}}\mathrm{s}100s. It is shown how to obtain a controlled-NOT operation between two qubits using the magnetic dipole-dipole interaction.
An electron inside liquid helium forms a bubble of 17 Åin radius. In an external magnetic field, the two-level system of a spin 1/2 electron is ideal for the implementation of a qubit for quantum computing. The electron spin is well isolated from other thermal reservoirs so that the qubit should have very long coherence time. By confining a chain of single electron bubbles in a linear RF quadrupole trap, a multi-bit quantum register can be implemented. All spins in the register can be initialized to the ground state either by establishing thermal equilibrium at a temperature around 0.1 K and at a magnetic field of 1 T or by sorting the bubbles to be loaded into the trap with magnetic separation. Schemes are designed to address individual spins and to do two-qubit CNOT operations between the neighboring spins. The final readout can be carried out through a measurement similar to the Stern-Gerlach experiment.
A quantum computer based on the manipulation and detection of coherent states of electrons localized above a helium film is described. Each quantum logic element (qubit) is made of a combination of the ground and first excited states of an electron trapped in the image potential well at the surface. Potentials applied to micro-electrodes located beneath each electron confine the lateral motion of the electron and are used to operate gates. Mechanisms for one- and two-qubit logic operations and a readout of the final state are discussed. The principle decay channel for the excited state is via the emission of one phonon into the bulk liquid. Dechoherence times are calculated to be of order of 100 μs and allow greater than 104 serial operations.