Exploding water

You probably already heard about superheated water. If you slowly heat up a cup of distilled water above 100ºC, the water will remain liquid. But as soon  you insert a spoon or some salt, the contents of the cup can suddenly vaporise in a very dangerous explosion.  This don't-try -at-home experiment can be seen on many videos on-line  [1] and spectacularizes  a well-known process which takes place through first order phase transitions. Water-vapour is the most common example of a first order phase transition and superheated water is nothing else than a metastable state. The energy cost to build up the bubble, given by surface tension,  prevents the system from reaching the stable vapour state that anyone would expect for water above 100ºC. Impurities in tap water or surface defects in the container usually  do not allow to reach this precarious equilibrium and explosions are prevented.

A more schematic way to see the physics behind the process is to think about an asymmetric two well energy potential. If we are able to prepare the state in the highest of the two minima, nothing prevents a classical energy fluctuation  above the barrier or a quantum tunnelling across it, allowing the system to reach the real lowest energy state. For a single particle living  in such an imposed energy potential, physics provides an exact solution of the event probability [2].

Real and false vacuum

Modern physics, however, finds a more intriguing situation with the same peculiarity. Our understanding of microcosm is based on quantum field theory where symmetry breaking and phase transitions are ubiquitous and at the heart of the Standard Model of particles. The  double-well energy is in this case not an imposed quantity from outside, but the energy itself of a macroscopic object (the field). And the crossing the barrier is not a single particle passage from one  point to another, but the full reconfiguring of the macroscopic state to another one with other properties.  In this framework, the metastable minimum is called "false vacuum", while the absolute ground state is referred to as "real vacuum". The decay from the false to the real vacuum state takes place with the appearance of a resonant bubble, similar to superheated water. Resonant bubbles stochastically form when the energy gain of the core is compensated by the energy cost of the surface tension, which in this case is related to the kinetic energy of the field. Connections to the Big Bang have been speculated and many open questions still remain, both about what concerns the mathematical tools to calculate the bubble appearance probability [3] and on the stability of our universe [4].

Now in the lab

The 50-year-long quest to understand false vacuum decay did not find an experimental platform to test the acquired knowledge. The energy or length scales were always too large for real life experiments. In the last 20 years, ultracold atoms have become the most powerful tool to emulate a large variety of quantum processes with unprecedented tunability of the experimental parameters in a defect-free environment. In particular, our group recently showed that coherently-coupled mixtures of hyperfine state of sodium atoms possess the ferromagnetic properties necessary to emulate a symmetry breaking like the one considered in false vacuum decay models [5].

Thanks to an accurate preparation of the initial state and a large control on vacuum energies and barrier height, we observe the appearance of bubbles in the atomic system  [6]. They manifest themselves as macroscopic region of the cloud where the atomic spin suddenly changes sign. The birth of resonant bubble is then followed by an increasing size of the bubble toward the lowest energy configuration; see second panel in Fig.1. By observing the occurrence of the bubble, we characterised the stochastic nature of the process and the appearance rate against parameters variations, as visible in Fig.2. The experimental results nicely match with numerical simulations based on the non-linear Gross-Pitaevskii equation.

The presence in our working group of experts in field theory and cosmology allows us to find excellent agreement between the experimental results and  the instanton solution, the most successful theory of false vacuum decay and the lines in Fig2. are fit to experimental and simulation data. 

Outlooks

These results pave the way for a new way to experimentally test the idea of false vacuum with unprecedented control on tuning parameters. Additionally, the theory of instanton applied to atomic systems is still not fully developed and requires new tools and extensions to fully grasp the physics of bubbles in superfluids.  We still do not know if our universe is in the false or true vacuum state, but now we have a new powerful gadget to try to understand it.

The work is an extended collaboration between the University of Trento, the Institute of Quantum Optics of the Italian National Research Council (CNR-INO), the Trento Institute for Fundamental Physics of INFN (TIFPA) and the University of Newcastle.

References

[1] https://www.youtube.com/watch?v=LpDs7Xm1uLo

[2] H. A. Kramer, Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7(4), 284-304 (1940)

[3]  S. R. Coleman, The Fate of the False Vacuum. 1. Semi- classical Theory, Phys. Rev. D 15, 2929 (1977)

[4] https://www.youtube.com/watch?v=ijFm6DxNVyI

[5] R. Cominotti et al, Ferromagnetism in an Extended Coherently Coupled Atomic Superfluid, Phys. Rev. X 13, 021037 (2023)

[6] A. Zenesini et al, False vacuum decay via bubble formation in ferromagnetic superfluids Nature Physics (2023)