Studying bubbles in liquid He4 containing single and many electrons

Abstract

Helium is an inert element with fully occupied orbitals and is a super fluid at low temperatures. An electron close to the surface of liquid Helium faces a long range attraction due to the finite polarizability of the bulk Helium, and a close range repulsion of 1 eV potential from the valence electrons due to Pauli's Exclusion Principle. Due to this, electrons get trapped on the surface, forming a two dimensional electron gas (2DES). If the density of this charged surface surpasses a critical value, Electro-Hydrodynamic (EHD) instabilities are formed leading to the formation of Multi Electron Bubbles (MEB). These are micron sized cavities containing a layer of electrons on its inner surface. On the other hand if an energetic electron is injected into bulk Helium, once the electron is thermalized, it repels the Helium atoms and forms a spherical cavity of radius 19 A, known as a Single Electron Bubble (SEB). This system is a textbook example of an electron in a finite spherical potential well with flexible walls. In this thesis we present studies done on MEBs as well as SEBs inside liquid Helium4. So far, there have been limited measurements on MEBs which have been transient in nature. Here we present experiments where we were able to manipulate MEBs in an electromagnetic trap, observe these bubbles for long periods, and image them at high speeds enabling us to measure their properties, like radius, mass and charge in a completely non-destructive way. Some MEBs were observed to shrink and ultimately disappear. This was due to the condensation of vapour inside the MEB into the cooler liquid. Based on this model we developed a theory along with numerical simulations, and compared the results with many MEBs that were observed to collapse. We found good agreement between our observation and the prediction. We also present a simple analytical formula that relates the initial radius of the MEB to the collapse time. Shrinking causes the surface charge density of MEBs to vary widely paving the path to observe various phases and phase transitions in a 2DES. SEBs have been theoretically and experimentally studied over the past many years, but there lies much scope to study them further. Here we describe an experiment to measure the lifetime of the first excited state (1P) of the SEB very close to the lambda transition temperature using a cavitation method. Previous theoretical studies have calculated this to be 40 s from considerations of radiative decay. Our experimental value is about 40 ns, which agrees well with a previous experiment implying that the lifetime of the 1P state is governed by some unknown non-radiative process. Our experiment also suggests that the lifetime does not depend strongly on the surrounding temperature, implying that the normal fluid fraction does not play a major role in the non-radiative processes governing the bubble decay. Following this, we present a design of an experiment to probe the quantum structure of the SEB spectroscopically, extending the previous spectroscopic measurements of the 1P state by exciting the 1P bubble. Using experimentally and theoretically known properties of the SEB, we built a model of the energy transitions and simulated an experiment to optically probe the SEB for various experimental parameters, and estimated quantities that can be experimentally measured. The expected absorption signals were calculated to be very small ( 10ð€€€7) making the experiment extremely challenging to perform. Through our analysis we show that it is not possible to perform using our current experimental setup but this experiment can potentially resolve many questions regarding the 1P state for which contradictory studies exist.