Brown University

Experimental Low Temperature Physics

Studies of Electron Bubbles and Quantized Vortices

Home

last update on

April 7, 2011

In our research we are trying to understand what happens when an electron is placed into liquid helium. Although this is, in principle, a very simple system (helium has essentially no chemical properties) , there are many interesting effects that are not understood.

 

An electron injected into liquid helium forces open a cavity of radius approximately 19 Å in the liquid, referred to as an “electron bubble”. The size of the bubble is determined by a balance between the zero-point energy of the electron, the surface energy of the cavity, and the work done in forming the cavity against the applied pressure. The total energy of the bubble is given by the expression

where R is the radius of the bubble, m is the mass of the electron, is the surface tension of the liquid, and P is the pressure. If no pressure is applied, the bubble has its minimum energy when Å.

 

Electrons can be introduced into the liquid from a sharp tip or by means of a radioactive source. In previous work we have developed a powerful new technique for the study of electron bubbles. When a negative pressure is applied to an electron bubble, the bubble grows, and at a critical pressure the bubble becomes mechanically unstable and explodes. This explosion occurs at a negative pressure P_c that has a considerably smaller magnitude than the pressure required to cause nucleation of a bubble in the absence of an electron, i.e., the pressure P_hom-nucl required for homogeneous nucleation. Negative pressures can be produced using an ultrasonic technique. A hemispherical transducer is used to generate sound of frequency typically in the range between 100 kHz and a few MHz. When the sound pulse passes through the acoustic focus, a large amplitude pressure oscillation is produced. If the pressure becomes sufficiently negative during this oscillation, a bubble can nucleate. To detect this bubble, light from a He-Ne laser is passed through the focus, and the light scattered by the bubble is detected by a photomultiplier. In the simplest form of the experiment, the directly measured quantity is the voltage that has to be applied to the transducer in order for a bubble to  appear. The pressure swing at the acoustic focus can be estimated from the voltage applied to the transducer. The accuracy of this estimate of the pressure varies according to the particular experiment that is being performed.

EXPERIMENT TO EXPLODE ELECTRON BUBBLES USING A SOUND WAVE

 

The electron bubbles have the unique property that the size and shape of the bubble changes by a large amount according to the quantum state of the electron. At each point on the bubble surface there is a balance between the outward pressure exerted by the electron , the inward force due to the surface tension of the bubble wall, and the force due to the applied pressure in the liquid. If the electron is in the ground 1S state, the bubble will be spherical since has the same value everywhere on the surface. For the P states, however, vanishes in the equatorial plane and so is zero around the waist of the bubble. This results in a shape similar to a peanut (see figure). So far no method has been devised to measure directly the shape of electron bubbles. However, a test of the theory is provided by a measurement of the pressure at which a bubble explodes. For an  electron in the ground state, one can calculate that the bubble should explode at a pressure of -1.9 bars, and we have confirmed this experimentally. For the 1P state, the explosion pressure is calculated to be -1.63 bars. We have used light of wavelength 11 μm from a CO₂ laser to excite electrons from the 1S to the 1P state and have measured the pressure required to cause the 1P bubbles to explode. The results are in good agreement with theory. In a separate experiment, we were able to measure the lifetime of the 1P state. This was found to be 50 ns, about three orders less than the calculated radiative decay time. This indicates that the decay is dominated by some form of non-radiative process in which the electron is able to transfer energy directly to the helium atoms at the bubble surface.

PHOTOGRAPH OF AN ELECTRON BUBBLE THAT HAS EXPLODED

 

As part of this study we have performed several calculations and experiments. Theoretical work includes detailed calculations of the shape of the absorption line for the 1S®1P and optical transitions, calculation of the cross section for the optical transition from the 1S to the 1D and 2D states, calculation of the change in shape that occurs when a bubble is moving at high velocity through the liquid, and calculation of the equilibrium shape of bubbles containing electrons in the 2S and 3S states, and how these shapes vary with pressure. Experimental work includes the discovery of a new type of electron bubble that appears to be larger than the normal electron bubble and which is detected at low temperatures and appears to be associated in some way with the presence of quantized vortices in the liquid, study of the nucleation of bubbles produced by electrons injected into the liquid by Penning ionization, studies of the escape of electron bubbles from vortices when the electron is excited optically.

 

SHAPES OF ELECTRON BUBBLES WHEN THE ELECTRON IS IN DIFFERENT QUANTUM STATES

As a further development of this work, we have constructed an apparatus which  can be used to make movies showing the motion of individual electrons in liquid helium. This requires the use of a planar (non-focusing) ultrasonic transducer to send an essentially planar sound pulse through a large volume (several cm³) of liquid and explode every electron within this volume. The helium is illuminated with light from a flash lamp that is synchronized to the sound pulses. Sample movies and some individual frames from the movies can be seen on this web site.

IMAGE OF AN ELECTRON SLIDING DOWN A QUANTIZED VORTEX LINE

As part of our efforts to improve the apparatus used for making movies of an electron, we looked for more efficient materials to use for sound generation. We collaborated with H.C. Materials Corporation who provided us with several samples of a new material, lead magnesium niobate-lead titanate (PMN-xPT), for testing. We measured the piezo-electric coefficient of this material at low temperature, and found the coupling to be larger than in any other material.

      

Recently we have also performed very detailed studies of the stability of bubbles containing a large number of electrons (MEB’s). These objects are interesting because one can show that when the applied pressure is zero a small distortion of the bubble with symmetry leads to no change in energy to second order. Thus, to determine whether MEB’s are stable it is necessary to consider how the energy changes for large shape changes, and whether the bubble shape can change in a continuous way from an initially spherical shape to lead to breakup into two smaller bubbles. The calculation is complicated because at each stage it is necessary to use a finite element method to find the way in which the electrons are distributed on the inside of the bubble surface.