Electrons are weakly attracted to liquid helium due to the small but finite polarizability of helium atoms. However, they cannot enter the liquid unless their energy is more than 1 eV, due to the Pauli exclusion principle. As a result, electrons are bound perpendicular to the surface but are free to move parallel to the surface i.e., they form a two-dimensional electron system (2DES). If the electron density of the 2DES is increased above a critical value ( 1013 per m2) the surface becomes un-stable leading to the formation of charged bubbles known as multielectron bubbles (MEBs). In MEBs the electrons are confined to the inner bubble surface and hence we have a 2DES on a curved surface. The critical density of electrons on the bulk surface is too low to study the quantum dominated phases of the 2DES. In contrast, due to the enormous surface defects and impurities, the electronic density of 2DES in semiconductors cannot be lowered below 1015 per m2, which is high enough such that the 2DES is always in a quantum liquid phase. Alternatively, the possibility of varying the electron density over a wide range and the effects of curvature implies that MEBs can be used to probe new phases of 2DES like Wigner crystallization with strong electron-ripplon coupling, quantum melting, superconductivity etc. In this thesis the experiments done on MEBs in liquid helium are described. In the initial experiments we generated MEBs which were observed to shrink in size. We saw a difference in their collapse behaviour: MEBs in super fluid helium though initially bigger in size collapse much faster than MEBs generated in normal fluid. The vapour present in the MEBs cannot condense fast in normal fluid due to the lower thermal conductivity. In subsequent experiments, we could trap these MEBs, generated in normal fluid and stabilised by their vapour content, in a linear Paul trap. We measured the charge and radius of these trapped MEBs by analysing their dynamics. Interestingly, the stably trapped MEBs were found not to lose charge as they shrink and disappear in hundreds of milliseconds, implying that the charge density inside increases at least two orders of magnitude from the initial value. MEBs so trapped can be used to study the properties of 2DES in the high electron density limit where the quantum confinement energy dominates. Later, we measured the charge of the MEB with respect to time when it was held on a solid substrate. We propose a charge loss mechanism as the tunneling of electrons across a thin lm of helium formed between the MEB and the substrate. We estimated the density of electrons on this thin lm by using a numerical model. We found that the maximum electron density (about a few 1015 per m2) which could be held on a thin lm is limited by tunneling. Moreover, the substrate surface roughness did not affect the charge loss due to the microscopic contact of MEBs with the substrate, resolving the complications in charge loss observed in previous experiments on macroscopic thin films on metallic substrates. Finally, we describe the experiments and the results on the stability of MEBs generated in super fluid helium. Highly charged MEBs (with more than 104 electrons which have an equilibrium radius that is easily visible) are found to be unstable against fission into smaller bubble showing a type of electro-hydrodynamic instability. However, the stability of bubbles with radius less than our detection limit ( 1 m) is still an open question.

Multielectron bubbles (MEBs) are micron sized cavities in liquid helium that contain electrons confined within a nanometer thick layer on the inner surface of a bubble. These objects present a rich platform to study the behavior of a two dimensional electron gas (2DES) on a curved surface. Most crucially, the surface electron densities in MEBs can vary over a wide range, making it a suitable candidate for studying classical Wigner crystallization and quantum melting in a single system. So far, there has been only limited experimental study of MEBs, with most of the previous investigation transient in nature. As we discuss in our presentation, we have built a cryogenic system for performing transport and optical measurements of MEBs down to 1.3 K. We have developed a new technique of generating MEBs, and trapping them using two different methods. In the first method, we trapped MEBs using a Paul trap for more than hundreds of milliseconds. This allows the MEBs to be further manipulated with buoyant and electric forces, such as to obtain reliable measurements of their physical properties. As we observe experimentally, the surface charge density of a single MEB can vary by orders of magnitude during the course of one measurement, thereby covering a previously unexplored section of the 2DES phase diagram. In the second method, we trapped MEBs using a dielectric coated metal electrode over many seconds. This also allowed the properties of MEBs to be measured in a non-destructive manner. Since MEBs are charged bubbles, their motion can be controlled by electric fields, which allowed us to measure the drag of MEBs as a function of Reynolds number by analysing the trajectories. Due to the low viscosity and surface tension of helium compared to other liquids, these measurements could be performed at Morton Numbers that have never been explored. We also show that how the shape of a single MEB evolves from spherical to ellipsoidal as their speeds vary. During the course of experiments, we observed number of interesting phenomena, such as coalescence of similarly charged bubbles, as well as their splitting into secondary bubbles at high speeds. Most interestingly, we have imaged their dynamics in the presence of static, as well as oscillating electric fields, which may provide insight into the phase of the electronic system present inside the bubbles.