Dynamic response of 1D bosons in a trap

Abstract

We calculate the dynamic structure factor S(q,omega) of a one-dimensional (1D) interacting Bose gas confined in a harmonic trap. The effective interaction depends on the strength of the confinement enforcing the 1D motion of atoms; interaction may be further enhanced by superimposing an optical lattice on the trap potential. In the compressible state, we find that the smooth variation of the gas density around the trap center leads to softening of the singular behavior of S(q,omega) at Lieb-1 mode compared to the behavior predicted for homogeneous 1D systems. Nevertheless, the density-averaged response remains a non-analytic function of q and omega at Lieb-1 mode in the limit of weak trap confinement. The exponent of the power-law non-analyticity is modified due to the inhomogeneity in a universal way, and thus, bears unambiguously the information about the (homogeneous) Lieb-Liniger model. A strong optical lattice causes formation of Mott phases. Deep in the Mott regime, we predict a semi-circular peak in S(q,ω) centered at the on-site repulsion energy, omega=U. Similar peaks of smaller amplitudes exist at multiples of U as well. We explain the suppression of the dynamic response with entering into the Mott regime, observed recently by D. Clement et al., Phys. Rev. Lett. v. 102, p. 155301 (2009), based on an f-sum rule for the Bose-Hubbard model.

24 pages, 11 figures

References in corpus (7)

• Universal theory of nonlinear Luttinger liquids
• Bragg spectroscopy of a strongly interacting 85Rb Bose-Einstein condensate
• Dynamical density-density correlations in the one-dimensional Bose gas
• Exploring correlated 1D Bose gases from the superfluid to the Mott-insulator state by inelastic light scattering
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas

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• Finite temperature correlations in the Lieb-Liniger 1D Bose gas
• Momentum-resolved study of an array of 1D strongly phase-fluctuating Bose gases
• Theory of superfluidity and drag force in the one-dimensional Bose gas
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Dynamic structure factor and drag force in a one-dimensional strongly-interacting Bose gas at finite temperature
• Localization-Delocalization Transition in the Random Dimer Model
• Order-by-disorder and quantum Coulomb phase in quantum square ice
• A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas
• Probing non-thermal density fluctuations in the one-dimensional Bose gas
• Bragg spectroscopy of clean and disordered lattice bosons in one dimension: a spectral fingerprint of the Bose glass
• Pseudoparticle approach to 1D integrable quantum models
• Dimensional crossover in a Fermi gas from one to effective six dimensions and a cross-dimensional Tomonaga-Luttinger model
• Mesoscopic density grains in the 1d interacting Bose gas from the exact Yang-Yang solution
• Nature of Lieb's "hole" excitations and two-phonon states of a Bose gas
• Light scattering in inhomogeneous Tomonaga-Luttinger liquids