Superfluid two-component ultracold quantum gases are becoming a cornerstone in the field of quantum mechanics due to the richness that arises in these systems with respect to the single-component case (different kind of couplings, new phases in the phase diagram, etc...). In this talk I will give an overview of the projects that are currently being carried out regarding two-component superfluids, paying an special attention to the Trento and Florence teams, both from the theoretical and the experimental side.

In the first part of my talk, I will focus on two-component quantum droplets, which appear as a new phase of the phase diagram arising from the compensation between a collapsing mean-field energy and the repulsive quantum fluctuations that balance the former force. This kind of droplets were recently experimentally produced [1,2] and in a recent article [3], the experimental study of the collisions between two quantum droplets came out to be a reality. These objects allowed us to study a transition from a regime in which the droplets behave as compressible, to a regime in which they effectively behave as incompressible classical droplets.

In the last part, I will discuss the stability of domain walls, which are topological excitations in coherently-coupled two-component condensates characterized by a localized gradient of the relative phase in a region of the order of a length scale that is directly associated to the coherent coupling [4]. These objects, although plausibly observed [5], have not been experimentally identified at the moment, and, their decay, is still under debate. I will discuss which is the decay mechanism of domain walls by using the Bogoliubov theory, and compare the predictions given by this theory with the solutions of real-time dynamical simulations.

[1] C. R. Cabrera, L. Tanzi, J, Sanz, B, Naylor, P. Thomas, P. Cheiney and L. Tarruell, Science, 359, 301 (2018).
[2] G. Semeghini, G. Ferioli, L. Masi, C. Mazzinghi, L. Wolswijk, F. Minardi, M. Modugno, G. Modugno, M. Inguscio and M. Fattori, Phys. Rev. Lett., 120, 235301 (2018).
[3] G. Ferioli, G. Semeghini, L. Masi, G. Giusti, G. Modugno, M. Inguscio, A. Gallemí, A. Recati and M. Fattori, Phys. Rev. Lett., 122, 090401 (2019).
[4] D. T. Son and M. A. Stephanov, Phys. Rev. A, 65, 063621 (2002).
[5] S. Kang, S. W. Seo, H. Takeuchi and Y. -I. Shin, Phys. Rev. Lett., 122, 095301 (2019).