MADANI Farid : Étude expérimentale des systèmes quantiques désordonnés en présence d’interactions avec un condensat de Bose-Einstein

Résumé de thèse :

Phase transitions are prevalent throughout physics, spanning thermal phenomena like water boiling to magnetic transitions in solids. Quantum phase transitions, particularly intriguing, occur at temperatures near absolute zero and are driven by quantum fluctuations rather than thermal ones. The strength of the fluctuations is very sensitive to dimensionality, which determines the existence and nature of phase transitions. For many systems there exists a certain upper critical dimension (UCD) above which mean-field theories accurately describe the properties of the phase transitions (e.g. the values of the critical exponents). Previously observed experimentally in 3D, the Anderson metal-insulator transition [1] is an example of quantum phase transition for which the UCD has been controversial. While its UCD has been predicted to be equal to four by the so-called self-consistent theory, numerical simulations indicate that this is not the case, at least up to dimension six – hinting the possibility that the UCD be in fact infinite.

In this work, using an Ultracold atom quantum simulator to engineer synthetic dimensions, we experimentally observe and study the Anderson transition in four dimensions. Our system is an atomic kicked rotor [2] of dilute potassium atoms, submitted to a quasi-periodically modulated pulsed laser standing wave used to engineer both synthetic dimensions and disorder [3]. Varying the experimental parameters, we are able to observe the Anderson localization-delocalization phase transition in dimension four. We precisely locate the critical point using a model-independent analysis based only on the existence of a scale-invariant behavior at criticality. We then characterize the universal dynamics in the vicinity of the phase transition, and measure the values of the critical exponents, proving the non-mean-field character of the Anderson transition in 4D. The measured exponents are shown to be in agreement with Wegner’s scaling law in dimension four. This work marks the first observation and characterization of the Anderson transition in four dimensions.

References:

[1] F.Evers and A.D.Mirlin, “Anderson transitions”, Rev.Mod.Phys.80, 1355-1417 (2008),

[2] F.L.Moore, J.C.Robinson, C.F.Bharucha, B.Sundaram, and M.G.Raizen, Phys.Rev.Lett.75, 4598 (1995),

[3] G.Casati et al, Phys. Rev. Lett. 62, 345 (1989).

Doctorant : MADANI Farid

Directeur de thèse : CHICIREANU Radu, SZRIFTGISER Pascal