Matter wave spectroscopy of the many-body physics in optical lattices
Final Report Abstract
The aim of this project has been to assess the suitability of matter-wave scattering as a probing mechanism of strongly correlated phases in quantum systems. This is a fundamental question for the development of non-destructive monitoring techniques for ultracold atom systems. In particular, we intended to investigate, using a combination of analytical and numerical tools, the superfluid to Mott insulator phase transition in interacting bosonic trapped gases, and to identify the fingerprint, if any, on the scattering signal. On the first part of the project, we considered the case of weakly interacting bosonic targets, modelled by a one-dimensional Bose-Hubbard hamiltonian. With the help of Bogoliubov theory, we constructed an analytical expression for the inelastic cross section and developed a deep understanding between the decay of the inelastic scattering with the interaction strength and the behaviour of the condensate depletion at zero temperature. We found a ’universal’ emergence of the linear decay of the inelastic scattering, independent of the number of particles and the system size, which is a consequence of the quadratic dependence of the condensate depletion on the interaction. On a second part, we focused on strongly interacting targets. A strong-coupling expansion, where the bosonic hopping is treated as a perturbation, revealed itself as a valuable tool to understand the numerical observations. In this regime, we built an analytical description of the phase transition (phase diagram) and the scattering cross section. Interaction-induced Mott localization manifests itself in the quadratic decay of the inelastic scattering signal with the interaction strength. We also proved analytically that, at least in one-dimensional systems, the inelastic scattering does not vanish inside the Mott lobe in the thermodynamic limit. The results of both parts provided a remarkable analytical description of the decay of the inelastic cross section in almost the entire range of interaction strength. Nevertheless, it remains to be clarified if in 1-D the phase transition induces a non-analyticity in the scattering signal. A complementary mean-field approach failed to describe the numerical results, and predicted a vanishing of the inelastic signal at the transition point. This latter behaviour could perhaps occur in higher dimensions.
Publications
- Matter-wave scattering from interacting bosons in an optical lattice, Phys. Rev. A 90, 023629 (2014)
K. Mayer, A. Rodriguez, A. Buchleitner
(See online at https://doi.org/10.1103/PhysRevA.90.023629) - Stringent and Efficient Assessment of Boson-Sampling Devices, Phys. Rev. Lett. 113, 020502 (2014)
M. C. Tichy, K. Mayer, A. Buchleitner, K. Mølmer
(See online at https://doi.org/10.1103/PhysRevLett.113.020502) - Matter-wave scattering from strongly interacting bosons in an optical lattice, Phys. Rev. A 91, 053633 (2015)
K. Mayer, A. Rodriguez, A. Buchleitner
(See online at https://doi.org/10.1103/PhysRevA.91.053633)
