Coherent backscattering in the Fock space of Bose- and Fermi-Hubbard systems

Coherent backscattering generally refers to a significant and robust enhancement of the average backscattering probability of a wave within a disordered medium, which from a semiclassical point of view arises due to the constructive interference between backscattered trajectories and their time-reversed counterparts. We recently investigated the manifestation of this wave interference phenomenon in the Fock space of a disordered Bose-Hubbard system of finite extent [1], which can potentially be realized using ultracold bosonic atoms within optical lattices. Preparing the atoms in a well-defined Fock state of the lattice and letting the system evolve for a finite time will, for suitable parameters of the system and upon some disorder average over random on-site energies of the lattice, generally give rise to an equidistribution of the occupation probability within the energy shell of the Fock space that corresponds to the initial energy of the system, in accordance with the quantum microcanonical ensemble. We find, however, that the initial state is twice as often encountered as other Fock states with comparable total energy, which is a consequence of coherent backscattering [1]. Most recently, we showed that this phenomenon also arises in spin 1/2 Fermi-Hubbard rings that involve Rashba hopping terms (which combine inter-site hoppings with spin flips and arise from spin-orbit coupling), for which a newly developed semiclassical theory [2] correctly predicts a coherent enhancement of the occupation probabilities of the initial state and its spin-flipped counterpart. Moreover, performing a global spin flip within this Fermi-Hubbard system will give rise to significant spin echo peaks on those two Fock states, which is again a consequence of quantum many-body interference [3]. The semiclassical predictions of these enhancements and peaks are found to be in very good agreement with numerical findings obtained from the exact quantum time evolution within this Fermi-Hubbard system. [1] T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, and J. D. Urbina, Phys. Rev. Lett. 112, 140403 (2014). [2] T. Engl, P. Plößl, J. D. Urbina, and K. Richter, Theoretical Chemistry Accounts 133, 1563 (2014). [3] T. Engl, J. D. Urbina, and K. Richter, arXiv:1409.5684.