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Chinese Physics B

Preparation of cluster states with trapped electrons on a liquid helium surface

Ling-Yan Ai, Yan-Li Shi, Zhi‐Ming Zhang

Published Oct 1, 2011• 2 citations
Publisher

Abstract

We present a scheme for the preparation of one-dimensional (1D) and two-dimensional (2D) cluster states with electrons trapped on a liquid helium surface and driven by a classical laser beam. The two lowest levels of the vertical motion of the electron act as a two-level system, and the quantized vibration of the electron along one of the parallel directions (the x direction) serves as the bosonic mode. The degrees of freedom of the vertical and parallel motions of the trapped electron can be coupled together by a classical laser field. With the proper frequency of the laser field, the cluster states can be realized.

DOI
10.1088/1674-1056/20/10/100303

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We present a scheme for the preparation of one-dimensional (1D) and two-dimensional (2D) cluster states with electrons trapped on a liquid helium surface and driven by a classical laser beam. The two lowest levels of the vertical motion of the electron act as a two-level system, and the quantized vibration of the electron along one of the parallel directions (the x direction) serves as the bosonic mode. The degrees of freedom of the vertical and parallel motions of the trapped electron can be coupled together by a classical laser field. With the proper frequency of the laser field, the cluster states can be realized.
Jaynes-Cummings model is a typical model in quantum optics and has been realized with various physical systems [e.g, cavity quantum electrodynamics (QED), trapped ions, circuit QED, etc.] of two-level atoms interacting with quantized bosonic fields. Here, we propose an implementation of this model by using a single classical laser beam to drive an electron floating on liquid helium. Two lowest levels of the vertical motion of the electron act as a two-level ``atom'' and the quantized vibration of the electron along one of the parallel directions, e.g., xxx direction, serves as the bosonic mode. These two degrees of freedom of the trapped electron can be coupled together by using a classical laser field. If the frequencies of the applied laser fields are properly set, the desirable Jaynes-Cummings models could be effectively realized.
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.
An electron floating on liquid helium is proposed to be trapped (by a microelectrode set below the liquid helium) in a high-finesse terahertz (THz) cavity. The two lowest levels of the vertical motion of the electron act as a two-level "atom," which could resonantly interact with the THz cavity, and thus the famous Jaynes-Cummings model (JCM) and driven JCM could be implemented. The numerical results show that, for the typical parameters of the cavity and electrons on the surface of liquid helium, strong coupling between the artificial atom and the THz cavity could be obtained.