Superfluid helium is an absolutely remarkable state of matter: a neutral, quantum condensate which is easily prepared in liter quantities, demonstrates quantum coherence over macroscopic distances (~1m), and routable in circuits with simple tubes. It has been long understood that devices based on this material should be capable of ultra-sensitive matter-wave interferometry, specifically useful for ultra-sensitive gyroscopes.
A key element in a superfluid quantum circuit is a Josephson junction (JJ). The utility of this junction is that the non-linear transport properties, as a result of the AC and DC Josephson effect, reveal the quantum phase difference which has developed across the junction (such as the phase difference due to rotation.) For a single junction system, the shift in frequency of a resonance is used to monitor the quantum phase; for a double junction system, the modulation of a critical current is used to reveal the quantum phase difference.
The challenge for realizing a JJ for He-4 is due to a few factors. The quantum tunneling rate even through an atomically thin barrier (such as with graphene) is far too small due to the relatively large mass of a helium atom (compared to an electron) and the finite diameter of the helium atom (compared to the unmeasurable size of the electron). This leads to a very large energy barrier for the helium atom to tunnel through, ~20eV for a helium atom in the honeycomb of graphene, as opposed to ~1eV for an electron tunneling into an insulator, and as a result, a thin tunnel barrier geometry is not possible. This leads one to consider a narrow constriction as a junction, using geometry to pinch off the condensate wavefunction and produce a weak link. However, the very small zero-temperature coherence length for He-4, 0.3nm, becomes the challenge: how to fabricate an array of nearly atomic size apertures?
Recently, chemist such as Prof. Ben King (Univ. Nevada, Reno) have been able to fabricate new materials which near atomic size apertures. This material is an analogue of graphene, one molecule thick, with 1nm pores spaced ever few nanometers. The material has been suspended over 20 micron TEM grids, and gas effusion experiments have shown that the pores are open and of the expected size and density.
The experiments we are pursuing in the laboratory is to measure the transport properties of superfluid He-4 through this novel material. We will characterize the critical current and the current phase relationship. With these measurements, we can design an optimized circuit and our expectation is that we will make advances to the measurement of the quantum phase difference with sensitivity of 100-1000 times what has previously been accomplished. We are expecting to produce a rotation sensor with sensitivity beyond what has been accomplished with helium 3 or 4, cold atoms, and laser interferometers.
Why He-4 and not He-3?
The zero temperature coherence length of superfluid He-3 is 65 nm which is easily within the range standard microfabrication of aperture. However, the transition temperature of He-3 is 1mK, 1000 times lower than He-4, which adds very substantial cryogenic overhead (dilution refrigerator plus an additional stage of cooling to achieve temperatures below 1mK.) The He-4 device we are pursuing should be able to be operated at ~1K with a standard cryo-cooler, which can allow for operation on submarines or space craft. A device based on He-3 does have the advantage of a lower thermal noise limit and may be useful for ground-based sensing of the Earth's rotation.
Hasn't the Josephson effect in helium 4 been observed?
It has: the first observation of this effect in He-4 was at JPL in 2001 by Kalyani Sukhatme, Yury Mukharsky, Talso Chui, and David Pearson (Nature 2001). They used an array of ~100nm diameter apertures in a thin silicon nitride membrane as the junction structure. However, at temperatures far below the superfluid transition temperature, these apertures are much larger than the coherence length for He-4. In order to realize a weak link, they stabilized the temperature 1-100 micro-K from the transition temperature (2.172K), and utilized the fact that the coherence length diverges as one approaches the transition temperature from below. After this original success, Packard and Sato used this technique to further explore the Josephson effect in He-4. Although this technique is very useful for demonstrating the physics of the Josephson effect in He-4, it has major disadvantages for realizing ultra-sensitive matter-wave interferometers. Most importantly, both the superfluid fraction and the critical mass current tend to zero as the transition temperature is approached. This dramatically and negatively impacts the signal to noise which can be achieved when detecting quantum phase shifts. The junction structures we are exploring here, avoid this difficulty since they are expected to work as a weak link far below the transition temperature, in the same way that a Josephson junction used for superconducting devices works far below Tc.
What are the advantages/disadvantages comparing superfluid to cold atom interferometers?