We present an introduction to the field of ultracold gases where many-body quantum physics can be studied with unprecedented accuracy and controllability of the system parameters. One fascinating possibility is to distort the symmetry of the two spins in the usual BCS-type superconductivity scenario. We present experimental advances on this topic as well as several examples of our related work.
One such example is the the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state where spin-density imbalance and superconductivity can coexist due to spatial oscillations of the superconduting order parameter. We consider ultracold Fermi gases with two pseudospin components and present three different topics where the ability to control and manipulate the pseudospins separately plays a key role. 1) We show that the FFLO state is stabilized in lattice geometries [1] and present a full finite-temperature phase diagram for the one-dimensional (1D) to three-dimensional (3D) crossover of the FFLO state in an attractive Hubbard model of 3D-coupled chains in a harmonic trap, calculated with dynamical mean field theory [2]. 2) We show that imposing different potentials (voltages) for the spins reveals an inherent single particle interference effect in Josephson oscillations [3]. 3) We propose a novel way of distorting the two spin species that are forming Cooper pairs: namely, a mixed-geometry system of fermionic species selectively confined in lattices of different geometry [4]. A rich phase diagram of interband pairing with gapped and gapless excitations is found at zero temperature. We also show that the Fermi surface topology further divides the gapless phase into subclasses between which the system undergoes density-driven Lifshitz transitions.
[1] T.K. Koponen, T. Paananen, J.-P. Martikainen, and P. Törmä, Phys. Rev. Lett. 99, 120403 (2007).
[2] M.O.J. Heikkinen, D-H. Kim, and P. Törmä, Phys. Rev. B 87, 224513 (2013).
[3] M.O.J. Heikkinen, F. Massel, J. Kajala, M.J. Leskinen, G.S. Paraoanu, and P. Törmä, Phys. Rev. Lett. 105, 225301 (2010).
[4] D-H. Kim, J.S.J. Lehikoinen, and P. Törmä, Phys. Rev. Lett. 110, 055301 (2013).