Researchers at UC Berkeley, the Austrian Academy of Sciences, and Caltech proposed a quantum sensor to measure how Earth drags spacetime. The team uses superfluid helium inside a gyrometer to detect this tiny effect. "Keith knew Birgitta from his Ph.D. work at Berkeley," said Kai-Isaak Ellers, describing the project's origins.
Einstein's theory of general relativity describes gravity as the bending of spacetime, a mathematical model that combines three-dimensional space and time into a single, four-dimensional continuum. The theory also predicts that a rotating object, such as Earth, slightly drags the surrounding spacetime as it rotates, a phenomenon known as frame-dragging.
Researchers at the University of California, Berkeley (UC Berkeley), the Austrian Academy of Sciences and the California Institute of Technology (Caltech) recently introduced the idea of a quantum sensor that could measure this tiny effect in a laboratory setting. Their proposed experiment, described in a paper published in Physical Review Letters, would use helium cooled until it enters a special phase known as the superfluid state inside a gyrometer, an instrument that measures rotation.
"The inspiration for this project came when Birgitta Whaley and I were visiting Markus Aspelmeyer at the Institute for Quantum Optics and Quantum Information (IQOQI) in Vienna, Austria, during a sabbatical of Birgitta," Kai-Isaak Ellers, first author of the paper, told Phys.org.
"We were introduced to Marios Christodoulou, who was interested in new ideas for applications of superfluid helium in precision gravity experiments. Since Birgitta has a lot of background working on superfluidity in helium droplets and nanoaperture arrays and since I was working with Birgitta on ideas for tabletop gravity tests, it was a natural connection."
When discussing the possibility of using superfluid helium for precision gravity experiments, the researchers realized that it could potentially be used to collect frame-dragging measurements. As Ellers, Whaley and Christodoulou are theorists, they contacted an experimental physicist who leads a lab at Caltech to explore their idea further.
"We reached out to Keith Schwab, who builds superfluid devices," said Ellers. "Keith knew Birgitta from his Ph.D. work at Berkeley in Richard Packard's group and was enthusiastic to work with us to make sure our proposal would be grounded in reality."
Using superfluid helium to sense rotation
The gravitational frame-dragging effect predicted by Einstein's general theory of relativity is backed by real-world observations. For instance, Earth's rotation drags the surrounding spacetime, contributing to a slow change in the direction of nearby gyroscopes' spin axes relative to distant stars, a motion called precession.
"Essentially, the Earth drags local gyroscopes along with it very slightly as it spins," explained Ellers. "One can detect this tiny frame-dragging effect in several ways. In our paper, we propose a rotation sensor, or gyrometer, based on superfluid helium."
When it is cooled below 2.17 Kelvin, about −271°C (−456°F), helium-4 (the most common form of helium) becomes a superfluid. This is essentially a liquid that can flow without friction.
The researchers propose creating a rotation sensor by filling a doughnut-shaped tube with superfluid helium-4, then detecting changes in its flow via a specially designed barrier with tiny holes or nanopores (i.e., a Josephson junction).
"The experimental signature is a quantum mechanical phase difference that appears across the Josephson junction when the device is rotating," said Ellers. "This phase difference is measured by tracking the motion of a mechanical diaphragm connected to the loop of superfluid."
Notably, similar sensors have already been demonstrated by a research team at UC Berkeley led by professor Packard and used to measure the Earth's rotation. However, the small rotational signatures associated with the Earth's frame-dragging effect have so far proved very difficult to measure with these sensors.
"The additional phase deriving from the Earth's frame-dragging effect is extremely small and its contribution can be overwhelmed by random phases due to thermal noise," explained Ellers.
"Therefore, to assess the feasibility and potential sensitivity of this experiment, we performed a novel analysis of the thermal noise properties of the proposed device. This was guided by Keith's long experience working with superfluids and what is known about their noise properties over a range of temperatures."
Toward the sensor's experimental realization and testing
This study suggests that cooling superfluid rotation sensors far below the temperature at which helium becomes a superfluid could greatly reduce disturbances caused by heat. This could ultimately allow them to precisely detect extremely small rotations, including those linked with the Earth's frame-dragging effect.
"Our results show that, based on our current best understanding of thermal noise processes in superfluid helium at temperatures well below the superfluid transition (2.17 K), a superfluid gyrometer operating at, for example, 10 mK, has the potential to match or even exceed the sensitivity of the best frame-dragging measurements to date, with significantly less measurement time," said Ellers.
"In contrast to previous measurements, our proposal also has the advantage that it could be performed in a laboratory here on Earth, rather than in space."
The researchers also calculated that changes in the helium could reveal extraordinarily tiny differences in how much time passes along different paths around the sensor's loop. This could offer another way to study how gravity affects time and test Einstein's general theory of relativity.
"For instance, one could imagine probing physical processes occurring on time scales only a few orders of magnitude larger than the Planck time, which is thought to be an important time scale in quantum gravity," said Ellers.
"Finally, another interesting feature of our proposal is that it presents an opportunity to observe a truly general relativistic effect in a macroscopic quantum system, since frame-dragging is not predicted by Newtonian gravity."
Ellers and his colleagues are now planning new studies aimed at testing their proposed sensor. To realize their sensor experimentally, they will first need to develop Josephson junctions for superfluid helium-4 that can operate at millikelvin temperatures, just thousandths of a degree above absolute zero, rather than close to the superfluid transition temperature (as was required in previous related experiments).
"Work in that direction is underway in Keith's lab at Caltech," added Ellers. "On the theoretical side, we are starting to think about what kind of new physics we could have access to if we could probe time scales as short as a few orders of magnitude above the Planck time.
"We are especially curious about whether there could be some effects deriving from quantum gravity or other beyond-Einsteinian gravitational interactions that would leave signatures in a superfluid gyrometer experiment, like the one we have proposed."