When individuals jump into a lake and hold their head under water, everything will sound different to them. Besides the varied physiological response of a person’s ears in water and air, this derives from the varied sound propagation in the water when compared to air.
On a comfortable summer day of 25 °C, sound travels faster in water, checking in at 1493 m/second. Other liquids tend to have their own sound velocity, for example, alcohol with 1144 m/second, and helium, if one goes to a freezing –269 °C for its liquefied state, with 180 m/second.
These liquids are known as classical liquids, which are examples for one of the main states of matter. However, something dramatic occurs when helium is cooled down to a few degrees more—it becomes a quantum liquid. Such a macroscopic display of quantum mechanics is termed as a superfluid—a liquid flowing without friction.
So what would individuals hear if they happen to make the unfortunate decision to stick their head into this liquid? Unexpectedly, they will hear the same kind of sound twice.
Apart from the usual sound of a liquid, there is a second sound phenomenon that derives from this liquid’s quantum nature. While individuals immersed in superfluid helium, if someone says something to them, they would first hear it as sound and then get another chance to listen when it arrives as a second sound, despite being powerfully muted. The second sound for superfluid helium is relatively a bit slower when compared to the first sound, with 25 m/second versus 250 m/second, between 1 and 2 K.
While the traditional concept of second sound has been effective in the case of superfluid helium, the increased Bose-Einstein condensates of ultracold atoms have presented a new set of challenges.
A research team headed by Ludwig Mathey from the University of Hamburg has proposed a novel theory that has the ability to capture the second sound in these kinds of quantum liquids. The study has been recently reported in Physical Review A.
For superfluid helium, second sound is slower than first sound, but we were amazed to find that this is not necessarily true, that the second pulse can be faster.
Vijay Singh, Study Co-Author and Research Scientist, University of Hamburg
A latest theoretical approach was needed to capture this. As they say, modern problems require modern solutions.
“We generalized the Feynman path integral to expand the theory of superfluids,” stated lead author of the study Ilias Seifie, describing the conceptual advance. The path integral—excellently conceived by Richard Feynman—formulates quantum mechanics as a sum over trajectories, but such trajectories themselves are classical.
We modified what these trajectories look like. In our path integral they contain information about quantum fluctuations.
Ilias Seifie, Study Lead Author and PhD Student, University of Hamburg
Consider a pool noodle stretching from A to B as a poor man’s visualization of a trajectory that enters this Feynman path integral. The noodle’s cross-section is more or less spherical with a steady diameter along its length.
However, the shape of the cross-section can differ in the new path integral—it can take elliptical shapes, similar to squeezing the pool noodle together. Appropriately, these quantum mechanical states are dubbed as squeezed states by physicists.
“This approach is widely applicable”, explained Ludwig Mathey, “it can be applied to any method that is based on path integrals.”
Undeniably, a number of phenomena at the interface of classical physics and quantum physics can be believed to be better interpreted with this method. With this latest framework, one can perhaps gain some more insight from nature.