Second Sound in Superfluid Helium

Superfluids “Superfluid” describes a phase of matter. In this phase, a liquid has no viscosity and may exhibit several “unusual” effects. Liquid Helium-4 transitions into a superfluid state at temperatures below 2.17 K, and is a good subject because of its weak intermolecular forces.

“Strange” Superfluid Effects The primary effect in which we are interested is “second sound.” This is a phenomenon in which heat travels as a compressional wave (as sound does), rather than through diffusion. The heat wave can reach speeds of ~20 m/s!* *Lane, C.T., Fairbank, H.A., and Fairbank, W.M. Second Sound in Liquid Helium II (1947) Phys. Rev. 71,

The Fountain Effect A fine filter that only superfluid can permeate covers the bottom of a chamber with a heater (resistor). The heated superfluid transitions to normal liquid, maintaining a gradient that drives superfluid into the chamber. The normal liquid builds up and can’t escape through the bottom filter, so it “fountains” out the top of the chamber. anaveral/2216/liquid_helium.html

Experimental Design To observe second sound, we started with a thin stainless steel tube, and wired a resistor into the bottom of the tube. This resistor will serve as the heater. We then installed two Cernox thermistors 7 cm and 14 cm along the tube from the heater. Their resistance increases as temperature decreases, so temperature changes can be measured by running a constant current and noting the change in voltage.

The Cernox Detector: Handle with Care!

Getting Everything Cold Our Dewar has four chambers: The outer chamber is a vacuum. The next chamber holds liquid nitrogen. The third chamber also is evacuated. In the inner chamber, there is liquid Helium! To change the normal liquid Helium into superfluid, we pumped on it to lower the vapor pressure above the Helium, effectively cooling it to temperatures as low as 1.5 K.

Evacuated Barriers Nitrogen Air Protective Barrier Helium

Dewar in Action!!

Pressure in Second Vacuum Chamber

Transferring Helium into Glass Dewar

It Worked! Temperature, in Kelvin 

Obtaining Measurements We used a voltage source to drive the resistor at a variable frequency, and used an oscilloscope to find the time lag between the responses of the two detectors. We read out the voltage of the two temperature sensors and used a signal analyzer to take the Fourier transform of their voltages to see if the superfluid’s temperature was varying at the same frequency as the voltage source.

Top Thermistor Middle Thermistor Heater

Top Thermistor Middle Thermistor Heater

Results What’s going on here? –We see a much stronger response once the temperature drops below the λ point (2.17 K) –This is expected, as superfluid helium conducts heat much more quickly. (Waves vs diffusion) Temperature (K)Frequency (Hz)Response Amplitude (mV/√Hz)

Signal Analyzer: FFT of Response at 70 Hz

Results What’s going on here? –Maybe the tube is interfering with the propagation of the heat wave at longer wavelengths –Maybe for the higher frequencies, the time delay is greater than the period of the driving frequency; perhaps we are measuring the delay between a given pulse and the arrival of an earlier pulse, instead of the arrival of the given pulse. Frequency (Hz)Time Delay at 1.54K for Sine Wave Driving Voltage (ms) Heater  Thermistor 1Heater  Thermistor

The Fountain Effect Set-up This experiment was done by a former class. We were able to use their set-up. Helium Chamber Vacuum Chamber Where you should look Nitrogen Chamber Fountain Chamber

Conclusions Heat travels faster in superfluid, which agrees with the theory of second sound. We were not able to experimentally measure the exact speed of second sound. The fountain effect was observed.