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How disorder can localize fermions and bosons in interaction?


How disorder can localize fermions and bosons in interaction?

In the beginning of the years 2000, the possibility of trapping cold atoms in optical lattices has created a strong bound between the field of cold-atoms and condensed matter physics.
These experiments provide a different and new perspective on old condensed matter problems such as the localization of an electronic gas in a disordered potential. The extraordinary ability to control a large number of experimental parameters allows to explore some theoretical concepts and models which are not perfectly realized in solids but also to envision new physical situations which were inconceivable before. For instance, the dimensionality of the system can be tuned by changing the configuration of the lasers. In the theory group of the LPS, and in collaboration with G. Zaránd from the university of Budapest, François Crépin and Pascal Simon have revisited the fundamental issue of the localization of a matter wave in a one dimensional disordered potential in the context of ultra-cold atoms systems [1].

 

Anderson localization is a quantum phenomenon originating from destructive interferences of waves with themselves. Especially strong in one dimension, localization effects can be suppressed when particles interact. One then faces a many-body problem and the question of quantum statistics – whether particles are fermions or bosons – becomes crucial. A mixture of interacting particles with different statistics was therefore an intriguing situation, and these scientists came across a very rich phase diagram.

 

 

Indeed, disorder tries to localize each component of the gas separately while inter-species interactions tend to favour the global superfluidity of the system. In the case of a realistic mixture of rubidium 87 and potassium 40, three phases emerge: a fully superfluid phase in the regime of strong inter-species interactions, an intermediate phase where the fermionic component is localized while bosons remain superfluid and finally a phase where both species are localized. The latter is of particular interest since, despite localization, interactions remain important. The calculation of dynamic quantities such as the structure factor clearly exhibits the coupled character of the fully localized phase.

 

[1] F. Crépin, G. Zaránd, P. Simon, Phys. Rev. Lett. 105, 115301 (2010)