Ultra-cold alkaline-earth atoms in one dimension

V. Bois

Fermionic ultra-cold alkaline-earth atomic gases have recently acquired a great interest both 
experimental and theoretical . Recent experiences have shown that at very low energy, interactions 
between such atoms hardly depend, except via the fermionic statistic, on their nuclear spin. This 
so particular structure provides very high degrees of symetries to these systems, in particular the 
realisation of a degenerate fermionic gas with an extended SU(N) symmetry, N being the number of 
nuclear-spin states. In this work, we study, by low-energy approach and by numerical methods, the 
nature of Mott-insulating phases of these ultra-cold atoms trapped on unidimensional-optical 
lattices.