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

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 would pave a way to utilize the quantum states of the surface electrons on liquid helium for quantum computing.

Figure 1

Principle diagram of the image-charge detection method (see text for details).

Figure 2

The current signal measured at the bottom (red line) and top (blue line) capacitor plate for SE irradiated with pulse-modulated MW at frequency ${\omega }_0/2\pi =140\mathrm{GHz}$. (Inset) The current signal at the resonance measured for different values of the pulse-modulation frequency ${\omega }_m$.

Figure 3

The current signal measured at the top capacitor plate for SE irradiated with pulse-modulated MW at frequency ${\omega }_0/2\pi =140\mathrm{GHz}$ for different MW power. Inset: The current signal at the resonance vs the normalized MW power.

Figure 4

The current signal measured at the bottom capacitor plate for SE irradiated with pulse-modulated MW at frequency ${\omega }_0/2\pi =200\mathrm{GHz}$ vs bias $V_{\mathrm{dc}}$ applied to the bottom electrode. The dashed lines indicate theoretical predictions for the transitions between the ground state and excited states using the approximate model with infinitely large potential barrier [3]. The deviation from the theoretical model is due to the finiteness of the barrier and decreases with increasing $n$ because an electron occupying high-laying Rydberg states is less sensitive to the potential barrier at the surface.