January 2016: A consortium between the CNRS and LENS groups and well as the ICFO group report the first quantitative determination of the superfluid to Mott insulator transition for strongly-interacting one-dimensional bosons in arbitrary weak periodic potentials. Theoretical calculations and direct experimental measurements are in excellent agreement and show a significant shift of the transition compared to previous calculations. It raises new challenges to field-theoretic calculations.
The superfluid to Mott insulator transition is one of the most emblematic examples of a quantum phase transition. It appears in periodic potentials at integer particle fillings. One dimensional geometry is special for strong correlations allow for the Mott transition to appear in arbitrary weak periodic potentials. This transition had previously been observed experimentally in the Innsbruck group. The new quantum Monte Carlo simulations and ultracold-atom experiments with interaction strength controlled by a Feshbach resonance reported here provide values for these critical parameters with unprecedented accuracy. They unambiguously show for the first time that the periodic potential, even arbitrary weak, induces unexpectedly strong renormalization of the effective Luttinger parameter. Calculating this effect is a new challenge to field-theoretic calculations. The excellent agreement between exact numerics and experiments also validates the latter as an efficient quantum simulator.
G. Boéris, L. Gori, M.D. Hoogerland, A. Kumar, E. Lucioni, L. Tanzi, M. Inguscio, T. Giamarchi, C. D’Errico, G. Carleo, G. Modugno, and L. Sanchez-Palencia, Mott transition for strongly-interacting one-dimensional bosons in a shallow periodic potential, Phys. Rev. A 93, 011601(R) (2016).
G. E. Astrakharchik, K. V. Krutitsky, M. Lewenstein, and F. Mazzanti, One-dimensional Bose gas in optical lattices of arbitrary strength, Phys. Rev. A 93, 021605(R) (2016)