We have succeeded in experimental simulations of several theoretically predicted properties of the quantum vacuum using the topological superfluid 3He. These are:
(i) Evidence of the existence of time crystals and quasi-crystals. A time crystal, as suggested by the Nobel Prize winner Frank Wilczek, is a structure that repeats not in space, such as normal crystals, but in time. The quantum vacuum also may form the time crystal structure, now realised in superfluid 3He. In particular, the quasi-crystals were demonstrated for the first time ever in the TOPVAC project. In future, it may even be possible to look at time itself, including the possibility of constructing the boundary between time going forward and back, as theory suggests. We also expect the investigation of the Landau-Zener effect the two-level time-crystal system.
(ii) Experimental observation of spontaneous formation of the non-topological soliton (NTS); the so-called "bulk matter" predicted by the quantum field theory. The TOPVAC results represent the first-ever observation of NTS in condensed matter. NTS are predicted to exist in forms of stars, quasars, the dark matter and nuclear matter. We propose NTS as the candidate of dark matter in cosmology, while suggesting another possible origin for dark matter: the oscillating decay of the vacuum energy. We are planning to study also this decay experimentally in superfluid 3He. Currently, there are no observations of NTS in cosmology.
(iii) Experimental observation of magnon Bose-condensation in the polar phase of 3He; that is the lowest accessible quantum state realised for the first time in a recently observed superfluid phase of helium. The TOPVAC results pave the way to the studies of nontrivial quantum vacua, that can only be realised in the polar phase. By improving the current measurement accuracy we expect to demonstrate the transformation from the metric that we live in (the Minkowski metric) to the metric of space (the Euclidean metric), where the time and space behave the same. This will allow us to study the Euclidean vacuum by using the superfluid 3He as a model system.
(iv) Experimental observation of half-quantum vortices in 3He -- the analogs of the Alice strings in cosmology, and subsequent observation of the analog of cosmic domain walls bounded by these strings. The TOPVAC results demonstrate the two ways to enter the mirror world; around the half-quantum vortex (safe/continuous route) and across the cosmic singularity of the domain wall (dangerous route). This gives new perspective to our understanding on the early evolution of the Universe through spacetime transitions.
(v) Experimental observation of the destruction of the long-range orientational order in specific type of superfluids by weak randomness produced by a nanostructured material. This is probably the most important experimental result in the physics of the disordered quantum vacuum. Another new result is the experimental observation of the extension of the Anderson theorem related to disorder in same type of superfluids, that is work in progress. We also expect the observation of different topological states in the disordered vacuum.
(vi) Prediction of new types of gravitational anomaly in topological materials, that builds on the description of the elasticity theory of crystals. Discovery of thermal gravitational anomaly in topological superfluids, which its the extension of the anomaly earlier suggested by Nieh and Yan for the relativistic quantum field theory and quantum gravity.
The ultimate target of TOPVAC is to construct a model of quantum vacuum, which is sufficient for satisfactory solution of the cosmological constant, hierarchy and Higgs field problems.
