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Bulletin of the American Physical Society

Incommensurate superfluidity of bosons in the optical lattice of double-well potentials

Vladimir M. Stojanović, Congjun Wu, W. Vincent Liu, S. Das Sarma

Published Mar 12, 2008• 0 citations
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We study bosons in the first excited Bloch band of a double-well optical lattice, recently realized at NIST. By calculating the relevant parameters from a realistic nonseparable lattice potential, we find that in the most favorable cases, the boson lifetime in the first excited band can be several orders of magnitude longer than the typical nearest-neighbor tunneling time scales, in contrast with that of a simple single-well lattice. In addition, for sufficiently small lattice depths, the excited band has minima at nonzero momenta incommensurate with the lattice period, which opens a possibility to realize an exotic superfluid state that spontaneously breaks the time-reversal, rotational, and translational symmetries. We discuss possible experimental signatures of this novel state.
We analyze the ground-state properties of three-body constrained bosons in a one-dimensional optical lattice with staggered hoppings analogous to the double-well optical lattice. By considering attractive and repulsive on-site interactions between the bosons, we obtain the phase diagram which exhibits various quantum phases. Due to the double-well geometry and three-body constraint, several gapped phases such as the Mott insulators and dimer--bond-order phases emerge at commensurate densities in the repulsive interaction regime. Attractive interaction leads to the pair formation which leads to the pair--bond-order phase at unit filling, which resembles the valence-bond solid phase of composite bosonic pairs. At incommensurate densities, we see the signatures of the gapless pair superfluid phase.
The superfluid-to-Anderson-insulator transition of a strongly repulsive Bose gas is studied in a one-dimensional incommensurate optical lattice. In the hard-core limit, the Bose-Fermi mapping allows us to deal with the system using the exact numerical method. Based on the Aubry-Andr\'e model, we exploit the phase transition of the hard-core boson system from the superfluid phase with all single-particle states extended to the Bose-glass phase with all the single-particle states being Anderson localized as the strength of the incommensurate potential increases relative to the hopping amplitude. We evaluate the superfluid fraction, one-particle density matrices, momentum distributions, the natural orbitals, and their occupations. All of these quantities show that there exists a superfluid-to-insulator phase transition in the system.