Theory of coherent transport by an ultra-cold atomic Fermi gas through linear arrays of potential wells

There has been a growing interest in transport of ultra-cold atomic gases through optical lattices generated by the interference of laser beams. In this connection we evaluate the phase-coherent transport of a spin-polarized gas of fermionic atoms along linear structures made from potential wells set in four alternative types of sequence. These are periodic chains of either identical wells or pairs of different wells, and chains of pairs of wells arranged in either a Fibonacci quasi-periodic sequence or a random sequence. The transmission coefficient of fermionic matter is evaluated in a T-matrix scattering approach by describing each array through a tight-binding Hamiltonian and by reducing it to an effective dimer by means of a decimation/renormalization method. The results are discussed in comparison with those pertaining to transport by Fermi-surface electrons coupled to an outgoing lead and by an atomic Bose–Einstein condensate. Main attention is given to: (i) Bloch oscillations and their mapping into alternating-current flow through a Josephson junction; (ii) interference patterns that arise on period doubling and their analogy with beam splitting in optical interferometry; (iii) localization by quasi-periodic disorder inside a Fibonacci-ordered structure of double wells; and (iv) Anderson localization in a random structure of double wells.