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
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.  and by Albrecht and
Leiderer  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
eigenmodes are spherical harmonics
and are characterized by their quantum numbers
L, m. The frequency of ripplon
modes can be zero to multi-megaherz
. 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
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.
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