The experiments are performed on a dilution refrigerator built here at Wesleyan.  The running refrigerator system, contained in a 30 L superinsulated dewar with a 4 inch diameter neck, uses just under five liters per day of helium.  The mechanically pumped still limits the base temperature to 55 mK, cold enough for the present work.

Useful notes and inormation about the cryostat.

Third Sound Resonator

 The third sound is detected as resonances in a flat, circular cavity formed in the gap (typically 10 mm) between two glass plates.  The perimeter of the cavity is defined by glue wicked in the gap beyond a fixed radius, typically between 5 and 10 mm.  A hole through the plates allows the film to coat the inner surfaces of the cavity.

The resonance modes are Bessel functions with node lines through the hole and zero radial derivatives at the outer perimeter where the top and bottom surfaces are joined.  For a small enough hole, the radiation leaving the resonator is negligible compared to the inherent dissipation in the film.  The resonant frequencies are related to the third sound speed by the wave numbers kmn = xmn / a where a is the radius and xmn are the zeros of the derivative of Jm(x).  The dissipation is measured by quality factor of the resonances.  Both CW and free decay resonance techniques are routine.


Our resonators use capacitive transducers - much less heat is involved and the calibration is purely an exercise in electrostatics.  There are two drive plates in adjacent quadrants of the circle that can be driven up to about 30 V peak.  The film responds to the square of the electric field, so that there is a frequency doubling in the drive force.  The two drives allow for coupling to left and right polarized rotational modes.

The pickup capacitor is smaller - about 1/8 of the drive area - and located to maximize overlap with the wave antinodes.  The capacitance modulations are converted into frequency modulations by incorporating the capacitor into the tank circuit of a low temperature tunnel diode oscillator.  This oscillator is actually a current controlled oscillator, due to a weak dependence of the frequency on the supply current, and is used in place of the VCO in a direct conversion phase locked loop (PLL).  When locked to a fixed reference synthesizer, the error signal is proportional to the original thickness changes.  The complete PLL and room temperature recording electronics can be calibrated by introducing known modulations into the synthesizer.

Notes with details of the detection electronics chain.

Everything is run by IEEE-488 communication between the instruments and QuickBasic programs.

Stimuleted Condensation Apparatus Progress...

Summer 2004

As a result of a nasty leak that only opens up below 10 K, terrible things have had to be done to the dilution fridge unit.  The leak was between the fridge plumbing and the vacuum can.  It wouldn't open up until LHe temperatures, and would close back up upon warming to 77 K.  Many attempts were made to fix potential trouble spots with no luck.

After literally years of avoiding the inevitable by trying various fixes, the lower half of the dilution refrigerator was cut off.  Here's the 1 K pot and still with what's left of the support rods.   Here's the cell and the disconnected fridge parts consisting of the mixing chamber, a pair of step exchangers, and the counterflow exchanger.

Spring 2005

Fridge finally together and working with no leaks! We have also finished the development of a new design to hold the sapphire disk. The base post now has a small chuck opened by an 0-80 expander screw. This chuck clamps around a small sapphire puck glued to the center of the sapphire disk. This eliminates cracking problems with the sapphire/copper differential thermal expansion.

Fall 2005

Evaporatior Overhaul.

Summer 2006

Continued difficulty with low resonator Q. We suspect gap contact due to dust particles.

Summer 2007

We have developed a proceedure to unambiguously determine the presence of a bridge across the gap. We now know that there are dirt issues.

Summer 2008

The clean room area has been completely overhauled and dust collecion rates in and out of the clean area have been measured to be within specs. We have also improved the flatness of the electrode plate grinding process, and the overall assembly proceedure, as documented below.

Fall 2009

After several more attempts, we successfully assembled a reonator that passed the "gap-not-bridged tast, but only after swiping the gap with a small sheet kapton film -- a mechanical cleaning after the fact. Both the LN2 and LHe gap-fill test confirmed the absence of a bridge. This resonator had the highest third sound Q yet achieved (Q~17000) which would have been high enough to look for the stimulated condensation effect, but we have discovered two further problems: (1) there is an anomolously low critical velocity, and (2) the resonator sensitivity seems to be ~5x smaller than theoretical. This combination results in a small signal to noise ratio that prohibits our test of the gain effect.

Summer 2010

We continue to study the sensitivity discrepancy and possible causes of the low critical velocity

Notes on the Stimulated Condensation Resonator Construction

Useful Relationships and Documents

These topics refer to Mathcad worksheets, which you may download and open with Mathcad or PDF printouts.

Circular Third Sound Modes Mathcad or PDF

Transducer Coupling Mathcad or PDF

Tunnel Diode - PLL Detection Mathcad or PDF

Inductance-Capacitance chart GIF

CW Scans and Free Decays Mathcad or PDF

Complete Mode Calculator for cavity cell resonator Mathcad

Mode Calculator modified for the stimulated condensation resonator (Mathcad 13 worksheet) or PDF

Mechanical mode Mathcad worksheet:Mathcad 14 worksheet) or PDF)

Disk-Post-Plane Mode Table

Derivation of viscous loss in an oscillating gas-filled gap PDF

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