Collapse in Boson–Fermion Mixtures of Cold Atoms Trapped in One-Dimensional Space

Fermi gases in one dimension: From Bethe ansatz to experiments

“…In light of the experimental realizations of Fermi-Bose mixtures, various theoretical methods have been used to study phases of superfluids and Mott insulators, instabilities of collapse and demixing and quantum correlations of the 1D Fermi-Bose mixtures, such as the mean-field approach (Das, 2003), TLL theory (Cazalilla and Ho, 2003;Lewenstein et al, 2004;Mathey et al, 2004;Mathey, 2007;Orignac et al, 2010;Rizzi and Imambekov, 2008) and numerical methods (Pollet et al, 2008;Takeuchi and Mori, 2007;Varney et al, 2008;Zujev et al, 2008). The TLL field theory (Cazalilla and Ho, 2003;Mathey et al, 2004; predicts that the binary mixtures of bosons and spin-polarized fermions with population imbalance present competing ordering -i) strong attraction between the two species leads to collapse; ii) a strong repulsion leads to demixing; iii) subtle tuning of the intra-and inter-particle scattering leads to pairing and two-component TLLs.…”

Competition of superfluidity and density waves in one-dimensional Bose-Fermi mixtures

“…[29][30][31][32][33], in which a two-component Tomonaga-Luttinger liquid was found. The mixture has also been investigated in numerical calculations [34][35][36][37][38][39][40]. More recent experimental work has considered mixtures of fermionic atoms.…”

Response functions in multicomponent Luttinger liquids

“…In parallel, techniques for trapping atoms in one dimension have been developed [34][35][36][37][38][39][40][41] . In Bose-Fermi mixtures trapped in one dimension, a multicomponent LL behavior is expected [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] . Similarly, multicomponent systems with repulsive interactions are also expected to exhibit in one dimension a multicomponent LL behavior 57,58 The real space correlation function of the multicomponent Luttinger liquid can be readily obtained 8,50,59 .…”