Experiments with single electrons in liquid helium

We have developed an apparatus which can be used to make movies showing the motion of individual electrons in liquid helium. A sound wave is used to explode an electron bubble for a fraction of a microsecond and to make it grow to have a radius of around 10 microns. While the bubble has this large size it is illuminated with a flash lamp and its position recorded. We report on a number of interesting phenomena that have been observed in these experiments. Some electrons that first appear near the surface of the transducer are likely to be produced as a result of cosmic rays passing through the liquid in the experimental cell. We discuss the details of this process. In several previous experiments in our lab, the cavitation in liquid helium that results from nucleation at an electron bubble has been studied [1, 2, 3]. The energy of an electron bubble of radius R in helium is given by the approximate expression E = ~2 8meR + 4πRσ + 4π 3 RP, (1) where the three terms represent the zero-point energy of the electron confined in a spherical cavity, the surface energy, and the work done against the applied pressure P . σ is the surface tension and me is the mass of the electron. The equilibrium radius of the bubble is obtained by minimizing the total energy E. At zero pressure the equilibrium radius is about 19 Å [1]. For negative pressures, the radius increases and at a critical pressure Pc, the bubble becomes unstable against isotropic radial expansion and “explodes”. Pc has the value −1.9 bars in the low temperature limit and has a smaller magnitude at higher temperatures due to the temperature dependence of σ. Previously we reported [4] that by using a planar ultrasonic transducer, a transient negative pressure pulse was produced to pass across a large volume (∼1 cm3) of liquid helium. All electron bubbles within the volume were exploded. The bubble oscillates with the sound field and can reach a size of about 10 μm in radius. While the bubble has this large size it is illuminated with a flash lamp and its position recorded. Through the application of a series of sound pulses, we can then take images along the track of individual electrons. In the first experiments even though there was no electron source in the cell, tracks of electron bubbles were observed in the liquid helium. Some of the tracks were suspected to be related to bubbles being trapped on quantized vortices and sliding down the vortices [4]. In the present paper, we discuss the results obtained in our recent experiments with a tungsten electrode immersed in the liquid helium cell. A schematic diagram of the experimental setup is shown in Fig. 1. A tungsten electrode was placed in a cylindrical cell with inner diameter of 5 cm and height of nearly 15 cm. A planar lithium niobate transducer disc with radius of 1 cm was used to generate sound pulses. The transducer was mounted inside the helium cell at a height just below the bottom edge of the viewing window. The top surface of the transducer was grounded. When a negative voltage was applied to the tungsten electrode, the electric field between the electrode and the top surface of the transducer forced electrons away from the electrode. Pulsed oscillating voltage with duration of 30 μs was applied to the bottom surface of the transducer at a repetition rate of 32 Hz. The oscillation frequency of the voltage was chosen to be 1.31 MHz in order to drive the transducer in resonance. The generated sound pulses propagated upward in the cell. A flash lamp [5] with pulse duration of about 50 μs was placed at a distance of 20 cm from the center of the cell and was triggered at the end of the sound pulse. The light was directed horizontally into the cell through a homemade light guide installed in the cryostat. The electron bubbles in the viewing region were exploded by the sound pulse and illuminated with light from the flash lamp. Light that was scattered by the exploded bubble passed through the viewing window at 90◦. A camcorder running at 4 frames per second was placed in front of the viewing window to collect the scattered light from the exploded bubble and record its image.