The External Field Bias Of Surface-state Electrons On The Liquid Helium

The electrons on the surface of liquid helium is an ideal platform to investigate various properties of two-dimensional electronic system for electric devices and solid-state quantum computation.The existence of surface electrons on liquid helium was predicted theoretically in the early 1960s and subsequently confirmed experimentally.It was shown that the electrons on liquid helium are very clean with the significantly-high mobility,and thus could generate the desired two-dimensional Wigner crystal.The quantum manipulations of qantum states of the single electrons on liquid Helium can be achieved by applying the external electric fields biased via the microelectrodes at the bottom of the liquid Helium.The longer decoherence times of these quantum states imply that the electronic surface-state system is also an attractive experimental platform for the implementations of Jaynes-Cummings model,electromagnetic radiation and millimeter wave photon detection,which are expected to achieve the desired millimeter wave single-photon sources and single photon detectors.After a brief review on the basic physical properties of two-dimensional electrons floating on liquid helium,such as surface electron formation,electron mobility,thermal excitation,microwave absorption,etc.,we focus on the controls of surface-state electrons through the electrode on the bottom of liquid Helium.Without the external electric field bias,the short-range Hartree-Fock repulsive force between the electrons and Helium atoms generates a barrier of about 1 eV,making the electrons floating on the surface of liquid Helium and becomes an artificial quantum system.The question we are concerned with is,whether the barrier to electrons will be changed by the electric field of about10~4-10~5 V/m biased in the usual experiments for quantum controls.Obviously,the applied electric field bias will change the wave function of the Helium atom and generate a polarization in the direction of the electric field,which may change the barrier of electron.Therefore,the question is,how the electric field change the potential barrier of the electron and the surface-state electron is allowed to tunnel into the liquid Helium?In this thesis we treat this problem by using the pseudopotential method to simplify the wave functions of the electrons.First,we calculate the wave function of the Helium atom in the electric field,and then calculate the pseudopotential between the electron and the helium atom.Finally,the barrier in the electric field is obtained by sum the pseudopotential of the electron with all the Helium atoms.The results show that the electron barrier changed by the external field bias is negligible for the applied electric filed usually in the quantum manipulation experiments.Therefore,electrons floating on the surface of liquid helium is stable for the quantum information processing,even under the bias of the external electric field.Furthermore,we design a preliminary experimental scheme for implementing the quantum manipulations by coupling the surface-state electrons to microwave superconducting resonator at the bottom of the liquid Helium.We discuss how to account the number of the electrons on liquid Helium and read out their quantum information by the microwave transmission measurements.Finally,the summary and prospect are given.