Silvera Group

Harvard University Department of Physics

Multi-Electron Bubbles

Background. Electrons above the flat surface of bulk liquid helium feel an attractive force from their image charges towards the surface, but are prevented from penetrating into the bulk helium by a 1 eV energy barrier. The electrons are bound to the surface in hydrogenic states and form a charged film, a two-dimensional electron gas (2deg) at the helium surface; high densities are achieved by placing a grid with a positive potential or attractive electric field below the flat helium surface. There exists a critical density of electrons or electric field above which the charged surface becomes unstable, and electrons are subsumed into the bulk helium by formation of a multi-electron bubble (MEB). These bubbles are typically tens of nanometers to a several hundred microns in radius, and contain from a few to more than 108 electrons. The forces acting are Coulomb repulsion for which the energy is lowered if the electrons are distributed far from each other, opening a bubble, and surface tension for which the energy is lowered as the radius is reduced. The result is a stable spherical MEB when these forces balance each other with the electrons forming a 2deg on the inner spherical surface of the bubble with a width ~10 nm.

MEBs have a plethora of exciting properties including Wigner localization, quantum melting, a new form of localization called the ripple-polaron lattice, an unusual type of superconductivity as the single particle states are angular momentum states with discrete energy levels rather than a continuum of momentum states, sonoluminescence, quantum hall effect, etc.[1].

The diameter of an MEB scales as N2/3 where N is the electron number. The MEBs so formed have lifetimes of a several milliseconds as they move to the potential grid where they are annihilated. In experiments by Volodin et al. [2] and by Albrecht and Leiderer [3], multielectron bubbles were photographed during their short lifetimes. The short lifetime has frustrated experimental study of the properties of MEBs
It is believed that spherical bubbles with less than ~100 electrons are unstable to fissioning to single-electron bubbles. On the other hand there are speculations that large bubbles can break up into two smaller bubbles.

The current program is aimed at stabilizing these balls of electrons in a long-lived state and studying their properties. In our first experimental design electrons are created above liquid helium in a dome shaped cylindrical cell (fig. 1). The helium liquid level is raised and the electrons are corralled in by the helium surface and find themselves trapped at the top of the dome in the minimum energy state, an MEB. Although MEBs were observed in this cell they did not localize in the dome and after ~1s they moved out of the field of view. We now understand this. Our calculations show that the He film between the MEB and dome surface thins to about 5 Angstroms. MEBs attracted by their image charge tunnel into the surface and the bubble discharges. If the surface is a dielectric, it charges up and repels the bubbles.


We have developed a new approach. A tungsten filament can be powered to glow at T>1000 K, while the helium is at 1.5 K, shown in Fig. 2. The filament is insulated by a vapor sheath, filled with helium vapor and electrons due to thermionic emission. MEBs could be extracted from tethered vapor sheaths below the lambda point with large electric fields, up to 15 KV/cm. The released MEBs are very turbulent, undergoing large oscillations. They shed electrons and disappear.


Theory predicts that MEBs will be stable under negative pressures.  We have built a cell that could be filled with superfluid helium and expanded to create a negative pressure.  Recently we observed the creation of stable MEBs rising in the helium.  The next step is to capture MEBs with an electromagnetic trap to study their properties.


[1]       J. Tempere, I. F. Silvera, and J. T. Devreese, "Multielectron bubbles in helium as a paradigm for studying electrons on surfaces with curvature," Surface Science Reports, vol. 62, pp. 159-217, 2007.

[2] A. P. Volodin, M. S. Khaikin, and V. S. Edel'man, "Multielectron bubbles in helium," JETP Lett., vol. 26, pp. 543, 1977.

[3] U. Albrecht and P. Leiderer, "Multielectron Bubbles in Liquid Helium," Europhys. Lett., vol. 3, pp. 705-710, 1987.

[4] M. M. Salomaa and G. A. Williams, " Structure and Stability of Multielectron Bubbles in Liquid Helium," Phys. Rev. Lett., vol. 47, pp. 1730-1733, 1981.

[5] J. Tempere, I. F. Silvera, and J. T. Devreese, "The effect of pressure on statics, dynamics, and stability of multielectron bubbles," Phys. Rev. Lett., vol. 87, pp. 275301-277304, 2001.

[6] J. Tempere, I. F. Silvera, and J. DeVreese, " Fission of multi-electron bubbles in liquid helium." Phys. Rev. B, vol. 67, pp. 35402-35410, 2002

Led by Prof. Isaac F. Silvera, The Silvera Group is part of the Department of Physics at Harvard University. Some notable historic discoveries at high pressure include the discovery of megabar pressure phases in solid hydrogen and its isotopes, the metalization of xenon at megabar pressures, the metallization of hydrogen iodide, and highest pressures for NMR in a diamond anvil cell. In the study of low temperature quantum fluids, the stabilization and confinement of the first magnetic gas, spin-polarized hydrogen, started the experimental search for Bose-Einstein condensation. Current research focuses on the metallization of solid hydrogen and the stabilization of multi-electron bubbles in superfluid helium.