Ultra-cold atomic gases by themselves and in combination with disorder are a highly active and innovative field of research. Since the first experimental realization of Bose-Einstein condensation in 1995, ultra-cold quantum gases have become a powerful tool to study condensed matter, quantum optics, and quantum information problems. Disordered systems have traditionally been extremely difficult to study, but recent advances of ultra-cold experiments have brought about new tools and approaches to tackle these problems as well. In particular, ultra-cold quantum gases can be subject to controlled spatially disordered potentials. Most notably, this has allowed for the seminal observation of Anderson Localization in 2008. Such breakthroughs illustrate the powerful control of quantum systems experimentally that is achievable today. Nonetheless, the physics of disordered systems is still a field with many open problems and challenges.

This thesis reports on the applicability and robustness of a new phenomenon called disorder-induced order. In essence, it is the process by which certain systems order when a specific type of controlled disorder is applied. The systems we consider present, in the absence of disorder, a continuous symmetry, e.g. a rotational U(1) symmetry as in the ferromagnetic XY model. If we apply a homogenous magnetic field along a given direction of the XY plane, all spins will align (roughly) in this direction. If we replace this homogenous field by a spatially randomly oscillating field in the same direction at low temperature, the system tends to avoid this external field and orders in a direction orthogonal to the field, inside the XY plane. Interestingly, the effect turns out to be robust enough to occur with regularly oscillating fields (i.e. staggered fields, sinusoidally oscillating fields), pseudo-random fields experimentally realizable by a superposition of optical lattices, and random fields as created by speckle plates. However, we stress that these disordered fields must not be distributed according to the symmetry of the continuous symmetry of the system but restricted to a subspace: e.g. in the case of the XY model, the spins can orient in any direction of the XY plane -- and, if the disordered field is also oriented with random angles, the system will not magnetize at all. The effect only occurs if the disorder is always along a given direction with random orientation (and possibly real-valued amplitude).

We study several configurations of disorder-induced order numerically and analytically, and present possible experimental realizations. In particular, we consider
- the classical XY system as an illustration of the basic intuition of the effect,
- a system of two Raman-coupled Bose-Einstein condensates, where disorder allows to control the relative phase of the two condensates,
- superfluid BCS pairs in presence of a diatomic reservoir, where disorder fixes the complex phase of the pairing function, and
- the quantum XY spin chain, where disorder leads to spontaneous magnetization in the direction orthogonal to the disordered field.

Other systems in which we expect disorder-induced order to occur, but not discussed in this thesis, are spinor condensates and possibly systems using synthetic gauge fields. At the time of writing, there are reports of randomness-induced XY ordering in a graphene quantum Hall ferromagnet as well as disorder-induced ordering of superfluid 3HE-A in aerogel.


Monday, December 13, 11:00. ICFO Auditorium

Thesis Advisor: Prof. Maciej Lewenstein
Thesis Co-Advisor: Dr. Fernando Cucchietti