Image-Charge Detection of the Rydberg States of Surface Electrons on Liquid Helium

Abstract

We propose and experimentally demonstrate a new spectroscopic method, image-charge detection, for the Rydberg states of surface electrons on liquid helium. The excitation of the Rydberg states of the electrons induces an image current in the circuit to which the electrons are capacitively coupled. In contrast to the conventional microwave absorption measurement, this method makes it possible to resolve the transitions to high-lying Rydberg states of the surface electrons. We also show that this method can potentially be used to detect quantum states of a single electron, which paves a way to utilize the quantum states of the surface electrons on liquid helium for quantum computing. PACS numbers:Surface electrons (SE) above liquid helium constitute an exquisitely pure quantum system which for a long time served as a unique experimental platform to discover interesting many-electron phenomena [1]. The quantized (Rydberg) states of SE with a hydrogen-like energy spectrum E n = −R e /n 2 , where R e ∼ 10 −3 eV and n is a positive integer number, are formed due to the attractive interaction between an electron and its image charge inside the liquid, as well as a strong repulsive barrier experienced by the electron at the vapor-liquid interface. For typical experimental temperatures below 1 K, electrons occupy the ground state and are localized about 10 nm above the surface. The higher-energy Rydberg states can be excited by millimeter-waves (∼ 100 GHz) radiation. Grimes and Brown first measured the transitions from the ground (n = 1) to the low-lying excited states (n = 2 ∼ 6) by detecting the change in the microwave (MW) absorption caused by the excitation of the Rydberg states of SE using a cryogenic bolometer [2]. A renewed interest in the Rydberg states of SE has emerged from their potential as qubit states [3,4], which was followed by several other proposals to use either orbital or spin states of SE as qubit states [5,6]. A crucial point for successful qubit implementation is the ability to manipulate and detect quantum states of a single electron. For such an application, the conventional MW absorption measurement is inappropriate as a detection of the quantum state because it is applicable only for a sufficiently large number of electrons [2,7,8], and so is the indirect detection of the Rydberg transitions via the measurement of SE conductivity [9,10]. Originally, a destructive readout of the Rydberg states was proposed, in which the electrons leave the liquid surface depending on the occupied Rydberg states [3,11]. An interesting and promising idea is to use the strong coupling of a single electron to a superconducting resonator to realize a nondestructive readout of electron quantum states [6,12]. However, this method is limited to a low transition frequency which should match the frequency of the coplanar resonator (∼ 5 GHz), thus it is not applicable for the de-tection of the excitation of the Rydberg states.Here, we propose and demonstrate a new spectroscopic method, image-charge detection, for the Rydber...

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