Spin polarized fermions in a box – SPIFBOX

Ultracold atoms have emerged as unique tools to study strongly correlated quantum systems. 50 years ago, an intriguing prediction was made by Fulde, Ferrell, Larkin and Ovchinnikov (FFLO) for a superconductor in a magnetic field with imbalanced electron spin populations. They predicted the existence of a superfluid phase where the order parameter is inhomogeneous and oscillates spatially across the sample. In SPIFBOX, we aim at producing and studying this FFLO phase using spin-imbalanced Fermi gases in a box-shaped potential where the density of atoms is uniform.

The experimental part of the project will be realized at ENS with two experimental setups using lithium isotopes. The first one is already operational and the flat bottom potential is realized in 3 dimensions by the repulsive mean field of a Bose-Einstein condensate of lithium 7 mixed with the spin-imbalanced Fermi superfluid in an harmonic trap. The second setup is a new generation experiment with much greater flexibility where the flat bottom potential is realized optically using a digital micro-mirror device (DMD). This new machine will enable us to search for the FFLO phase in reduced dimensions for which theoretical predictions and numerical simulations predict a much wider domain of stability for the FFLO state in the phase diagram. The construction of this setup has already started and the SPIFBOX funding will be used to bring it to completion.


The theoretical part of the project will be conducted by Giuliano Orso from Paris Diderot University, a specialist of spin imbalanced Fermi systems, and one post-doc that we wish to recruit with SPIFBOX funding. The theory team will determine the optimal conditions for producing the FFLO phase. In particular, exact solutions exist when the fermions live in one dimension for which the existence of the FFLO phase is clearly established. They will also construct the phase diagram when the Fermi gas is mixed with a Bose gas and they will explore the possible stabilization of the FFLO phase in two and three dimensions by controlling the Fermi-Bose interaction strength. Numerical simulations using DMRG and Monte-Carlo methods will be compared to the ENS experimental observations.

With the powerful tools of atomic physics, in SPIFBOX we gather together the best experimental conditions for the observation of the FFLO state: no orbital coupling, no disorder, low dimensional samples, and, most importantly, direct spin-resolved imaging of the associated spatial modulation of the atomic cloud. We hope that by solving one of the most outstanding quantum many-body problems, the outcome of SPIFBOX will stimulate new theoretical and experimental concepts at the interface with condensed matter systems. Ultimately this advanced understanding of quantum matter will help to design new materials with unprecedented properties.