The pinning quantum phase transition can be observed in both weakly interacting quantum many-body systems described by a 1D Bose-Hubbard model and strongly interacting 1D systems modelled by Luttinger liquid theory. In both these cases an ultra-cold quantum gas can be driven to Mott-insulating state by imposing an infinitesimal small external lattice potential 
Recently an analogue to this transition was found for a Tonks-Girardeau gas that is immersed in a Bose-Einstein condensate, which corresponds to a situation of self-pinning state without imposing any external lattice potential .
Based on these studies, I present our work on this phase transition by studying a mixture two non-identical Luttinger liquids, whose physical properties can be adjusted from being weakly to strongly correlated. In addition the system allows one to tune the interaction between the components, which therefore gives access to the full phase diagram of the two-component gas. While we are particularly interested in the behaviour of the phase transition as a function of correlations, I will also point out the implications for these systems to act as phonon-carrying matter wave lattices.
 E. Haller, R. Hart, M. J. Mark, J. G. Danzl, L. Reichsöllner, M. Gustavsson, M. Dalmonte, G. Pupillo, and H.-C. Nägerl, Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons, Nature (London) 466, 597 (2010)
 T. Keller, T. Fogarty and T. Busch, Self-Pinning Transition of a Tonks-Girardeau Gas in a Bose-Einstein Condensate, Phys. Rev. Lett., 128, 053401 (2022)
|Presenter name||Serhan Seyyare Aksu|
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