Generalized kicked-rotor Anderson quantum phase transitions experiment with a potassium Bose-Einstein condensate – K-BEC

The aim of this project is the experimental study of metal/insulator phase transitions of Anderson type. For this purpose, we use a paradigmatic system of classical and quantum chaos: The kicked rotor (KR), obtained by submitting an atom to periodic kicks of a far detuned laser standing wave. Classically, this chaotic system is fully diffusive. The corresponding quantum dynamic leads to the suppression of the classical diffusive dynamics and to an exponentially localized wave function in momentum representation. This phenomenon is known as dynamical localization. In a similar manner, for a one dimensional system, Anderson localization manifests itself by an exponentially localized wave function in configuration space. This comparison is not reduced to a mere qualitative analogy. A major feature of dynamical localization is that it is mathematically equivalent to Anderson localization. Chaos then plays the role of the disorder. Furthermore, by adding incommensurable frequencies in the KR excitation sequence, one formally increases the system dimensionality, and the equivalence with a spatial disordered system of the same dimensionality still holds. In the framework of our Lille (PhLAM) / LKB (Paris) collaboration we have reported the first experimental observation of a 3D Anderson transition with non-interacting matter waves in 2008, and the first measurement of its critical exponent. This experiment is performed with the cesium atom, which is quite difficult to condensate. This project proposes a thoroughly new and much more flexible experimental device based on a potassium Bose-Einstein condensate. The purpose is in a first time the study of Anderson metal/insulator phase transitions in dimension higher than 3, i.e. 4, and possibly 5. An experimental measurement of the critical exponents at such high dimensionality would indeed give unique information to be compared with mean-field theory predictions. Furthermore, this would constitute the first-ever experimental observation of a quantum transition for dimensionality >3. A key advantage of potassium is its broad and easily accessible Feshbach resonance that allows a fine tuning of atom-atom interactions. We then propose to observe the behavior of the metal/insulator transition in momentum space while simultaneously tuning the atom-atom interaction in the configuration space. Finally, the KR flexibility makes it possible to explore other symmetry classes than that of the Anderson (orthogonal) class, as well as other quantum phases, either metallic or insulating. For example, in the so-called symplectic symmetry class, a metal-insulator transition is expected in dimension as low as 2.

All these new experiments require a technological breakthrough. The key point is to obtain a ten-fold increase of the maximum number of kicks, that can be reached without significant decoherence processes. The potassium condensate will open doors for new physics, and extend the accessible parameter range far beyond what is now possible.