Relaxation of the Excited Rydberg States of Surface Electrons on Liquid Helium

We report the first direct observation of the decay of the excited-state population in electrons trapped on the surface of liquid helium. The relaxation dynamics, which are governed by inelastic scattering processes in the system, are probed by the real-time response of the electrons to a pulsed microwave excitation. Comparison with theoretical calculations allows us to establish the dominant mechanisms of inelastic scattering for different temperatures. The longest measured relaxation time is around $1\mu \mathrm{s}$ at the lowest temperature of 135 mK, which is determined by the inelastic scattering due to the spontaneous two-ripplon emission process. Furthermore, the image-charge response shortly after applying microwave radiation reveals interesting population dynamics due to the multisubband structure of the system.

Figure 1

Normalized voltage signals due to excitation of SEs by pulsed MW radiation at frequency $\omega /2\pi =110\mathrm{GHz}$ measured for different liquid helium temperatures $T$ in the range from 135 to 660 mK. The radiation is switched on for $0\le t\le 2.5$ $\mu \mathrm{s}$ and is switched off for $2.5\le t\le 5$ $\mu \mathrm{s}$. Each trace is obtained at a fixed value of $T$ by averaging over about ${10}^6$ repetitions. The inset shows a magnified view of the main figure in a region of $t$ shortly after the radiation was switched on. The details of this region are discussed in the text.

Figure 2

(a) Semilog plot of the decaying voltage signals shown in Fig. 1 after MW is switched off. Dashed lines are fits with the exponential decay law $\exp (-t/{\tau }_f)$. (b) The fitting parameter ${\tau }_f$ (open black circles) is plotted as a function of liquid helium temperature $T$. The relaxation times ${\tau }_f$ are also extracted from the simulated decay signals (as in Fig. 3) using the same fitting procedure as in (a) and are plotted for Rabi frequency ${\mathrm{\Omega }}_R/2\pi =30\mathrm{MHz}$ (blue pointing down triangles), 40 MHz (purple unfilled rectangle), and 50 MHz (green pointing up triangles). The lines represent the inverse of the energy relaxation rates $\tilde{\nu }$ calculated according to Ref. [35] for ${\mathrm{\Omega }}_R/2\pi =40\mathrm{MHz}$ (see main text), by taking into account the inelastic vapor-atom scattering (dashed line), the inelastic two-ripplon scattering (dotted line), and both processes simultaneously (solid line).

Figure 3

Normalized image-charge signals due to excitation of SEs by pulsed MW radiation calculated using the state occupancies ${\rho }_{nn}$ obtained by numerically solving the rate and energy-balance equations [28] for Rabi frequency ${\mathrm{\Omega }}_R/2\pi =40\mathrm{MHz}$. The inset shows a magnified view of the main figure in a region of $t$ shortly after the excitation is started.