Resonante Superfluidität und Dynamik ultrakalter Fermionen in optischen Gittern
Final Report Abstract
We have investigated degenerate mixtures of ultracold fermions (such as 40 K) in two hyperfine states close to a Feshbach resonance in optical lattices, giving rise to the BEC-BCS crossover. While most studies so far have focused on single-channel models with attractive interaction only, here we fully take into account the bosonic molecular (Feshbach) channel. Two complementary, nonperturbative approaches are applied for a fully quantitative description: in higher spatial dimensions we have developed and applied a generalized Dynamical Mean-Field Theory, while in one dimension the Density Matrix Renormalization Group is employed. Within our DMFT analysis, we have first investigated a simplified single-band Bose-Fermi Hamiltonian at commensurate filling, where supersolid and alternating Mott-insulating phases have been found. We have subsequently developed a realistic model for the resonant superfluid that fully includes effects of higher bands, which is crucial close to the Feshbach resonance. Remarkably, we find that the critical temperature of the fermionic superfluid is minimal at resonance, in sharp contrast to the free case without lattice. For commensurate filling we found that the crossover is intercepted by a first-order Mott transition. In one dimension, we have analyzed the phase diagram of an imbalanced mixture of two species of fermions, both in the absence and presence of a gap, including the possibility of bosonic molecule formation (Bose-Fermi resonance model) in order to study the BCS-BEC crossover. The method used was the density-matrix renormalization group (DMRG). Our main focus was on the existence and stability of the 1D Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which so far had been studied mostly in the absence of the possibility of molecule formation. Most notably, we found that FFLO correlations are suppressed in the crossover region due to the presence of the diatomic molecules. In particular, the 1D FFLO phase gives room for a regime of molecules, quasi-condensed at zero momentum. The latter is first immersed into partially polarized fermions, which is then replaced by a Bose-Fermi mixture with spinless fermions below saturation. Thus, the system undergoes two phase transitions in the crossover region at critical polarizations (degrees of species imbalance) as the polarization increases. We also discussed the question how the FFLO state can be detected in an experiment. Several proposals have been put forward; regarding the spin correlations, one expects a peak at nonzero momentum in the presence of FFLO order. As we showed here, this behavior is also realized in the FFLO phase of the Bose-Fermiresonance model.
Publications
-
Phys. Rev. Lett. 100, 100401 (2008)
I. Titvinidze, M. Snoek and W. Hofstetter
-
Phys. Rev. B 79, 144506 (2009)
I. Titvinidze, M. Snoek and W. Hofstetter
-
New J. Phys. 12 (2010) 065030
I. Titvinidze, M. Snoek and W. Hofstetter
-
Phys. Rev. A 81, 023629 (2010)
F. Heidrich-Meisner, A. E. Feiguin, U. Schollwöck and W. Zwerger
