A Haldane conjecture is revealed for spin-singlet charge modes in
2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of a low-energy approach and density matrix renormalization group calculations, we show the emergence of gapless and gapped phases depending on the parity of
N for attractive interactions at half-filling. The analog of the Haldane phase of the spin-1 Heisenberg chain is stabilized for
N=2 with nonlocal string charge correlation and pseudo-spin-1/2 edge states. At the heart of this even-odd behavior is the existence of a spin-singlet pseudo-spin-
N/2 operator which governs the low-energy properties of the model for attractive interactions and gives rise to the Haldane physics.
We propose a method to create a nontrivial Haldane phase in an atomic two-component Fermi gas loaded on a one-dimensional optical lattice with trap potential. The Haldane phase is naturally formed on a p-band Mott core in a wide range of the strong on-site repulsive interaction. The present proposal is composed of two steps, one of which is theoretical derivation of an effective 1D S=1 interacting-chain model from the original tight-binding Hamiltonian handling the two p orbitals, and the other of which is a numerical demonstration employing the density-matrix renormalization group for the formation of the Haldane phase on a p-band Mott core and its associated features in the original tight-binding model with the harmonic trap potential.
In this paper, we consider the transmission characteristics of an optical cavity loaded with ultra cold atoms in a one dimensional optical lattice at absolute zero temperature. In particular, we consider the situation when the many body quantum state of the ultra cold atoms is an insulating state with fixed number of atoms at each site, which can be either density wave (DW) or Mott insulator (MI) phase, each showing different type of discrete lattice translational symmetry. We provide a general framework of understanding the transmission spectrum from a single and two cavities/modes loaded with such insulating phases. Further, we also discuss how such a transmission spectrum changes when these insulating phases make a cross over to the superfluid (SF) phase with the changing depth of the optical lattice potential.