Temperature crossover between a coherent and an incoherent Luttinger liquid

Fermions confined to one-dimension (1D) belong to the Tomonaga-Luttinger liquid (TLL) universality class, in which low-energy collective excitations decouple into charge- and spin-modes that are bosonic in nature and propagate with different velocities. Several regimes, however, extend beyond the spin-charge separation paradigm and into new classes of unconventional Luttinger liquids. Given a sufficiently high temperature, for instance, thermal fluctuations disrupt the coherence in the spin sector, and the system enters the spin-incoherent (SI) Luttinger liquid regime. Although the SI regime has been investigated theoretically [1], experimental studies remain scarce. Here, we report on the characterization of the temperature crossover between a coherent and an incoherent Luttinger liquid. We realize a pseudospin-1/2 system with the lowest- and third-to-lowest hyperfine sublevels of ⁶Li. The sample is loaded into a 2D optical lattice, thus creating an array of quasi-1D waveguides. Using Bragg spectroscopy we measure an exponential decay of correlations as the system transitions into the SI regime, as well as a full suppression of spin-charge separation— one of the most representative features of the TLL theory. Our results clearly demonstrate the signatures of a disrupted Luttinger liquid and expand our understanding of the mixing between charge and spin degrees of freedom that occurs in spin-incoherent 1D systems.

[1] Fiete, G. A. Colloquium: The spin-incoherent Luttinger liquid. Rev. Mod. Phys. 79, 801 (2007).