Multi-Electron Bubbles

Electrons above the flat surface of liquid helium feel an attractive force (from image charges) towards the surface, but are prevented from penetrating the helium surface by a 1 eV energy barrier. The electrons form a charged film at the helium surface; high densities are achieved by placing grid with a positive potential below the flat helium surface. There exists a critical density of electrons above which the charged surface becomes unstable, and electrons are subsumed into the bulk helium by formation of a multielectron bubble (MEB). These bubbles are typically tens of nanometers to a few 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 far from each other 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 2 dimensional gas on the inner spherical surface of the bubble.

                The diameter of an MEB scales as N^2/3 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] the multielectron bubbles were photographed  during their short lifetimes. The short lifetime has frustrated experimental study of the properties of MEBs

It is believed that 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. movie of fission

              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. The helium liquid level is raised; 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 movie of tethered sheath. The filament is insulated by a vapor sheath, filled with helium vapor and electrons due to thermionic emission. This sheath is tightly tethered to the filament and bubbles do not break loose, unless above the helium lambda point (normal fluid) movie of multiple bubble generation; however, in this case torrents of bubbles are formed, many without electrons. The solution was to extract single MEBs from tethered vapor sheaths below the lambda point with large electric fields, up to 15 KV/cm. This has been filmed using high-speed photography movie of MEB generation. A cell is under development to capture these rising MEBs in an electromagnetic trap.

Bubbles are highly compressible and a modest pressure of under 1 bar can lead to an enormous compression. The two dimensional gas on the surface can have a transition to a solid Wigner lattice This triangular lattice does not fit on a spherical surface so the ground state will have defects built into it. Very high surface densities should be achievable in bubbles so that not only Wigner solidification can be seen, but also quantum melting at high density.

A sperical bubble can have distortions of the helium surface and such excitations are called movie of sperical ripplons. The eigenmodes are spherical harmonics Y_Lm  and are characterized by their quantum numbers L, m.   The frequency of ripplon modes can be zero to multi-megaherz [5].  Electrons in the spherical shell have quantum states also characterized by L, m.  The electron energies are discrete and each level has a degeneracy 2L+1.  The fermi energy in a modest sized bubble can be quite high, tens of Kelvin, so it is not difficult to form a fermi degerate gas.

Due to the electron-ripplon interaction and the discrete energy levels, we expect an unusual form of superconductivity with Tc oscillating as the electron number changes. We plan to study the statics, dynamics, stability against fission, and tunneling of electrons. Low temperature techniques and various forms of spectroscopy will be used to study collective (plasmons) and single-particle excitations and states.

[1]        M. W. Cole, "Electronic surface states of liquid helium," Rev. Mod. Phys., vol. 46, pp. 451-463, 1974.

[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