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Journal of Physics Conference Series

Inelastic light scattering to probe strongly correlated bosons in optical lattices

C. Fort, Nicole Fabbri, L. Fallani, David Clément, M. Inguscio

Published Jan 10, 2011• 3 citations
Publisher

Abstract

We have used inelastic light scattering to study correlated phases of an array of one-dimensional interacting Bose gases. In the linear response regime, the observed spectra are proportional to the dynamic structure factor. In particular we have investigated the superfluid to Mott insulator crossover loading the one-dimensional gases in an optical lattice and monitoring the appearance of an energy gap due to finite particle-hole excitation energy. We attribute the low frequency side of the spectra to the presence of some superfluid and normal phase fraction between the Mott insulator regions with different fillings produced in the inhomogeneous systems. In the Mott phase we also investigated excitations to higher excited bands of the optical lattice, the spectra obtained in this case being connected to the single particle spectral function. In one-dimensional systems the effect of thermal fluctuations and interactions is enhanced by the reduced dimensionality showing up in the dynamic structure factor. We measured the dynamic structure factor of an array of one-dimensional bosonic gases pointing out the effect of temperature-induced phase fluctuations in reducing the coherence length of the system.

DOI
10.1088/1742-6596/264/1/012018

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We have used inelastic light scattering to study correlated phases of an array of one-dimensional interacting Bose gases. In the linear response regime, the observed spectra are proportional to the dynamic structure factor. In particular we have investigated the superfluid to Mott insulator crossover loading the one-dimensional gases in an optical lattice and monitoring the appearance of an energy gap due to finite particle-hole excitation energy. We attribute the low frequency side of the spectra to the presence of some superfluid and normal phase fraction between the Mott insulator regions with different fillings produced in the inhomogeneous systems. In the Mott phase we also investigated excitations to higher excited bands of the optical lattice, the spectra obtained in this case being connected to the single particle spectral function. In one-dimensional systems the effect of thermal fluctuations and interactions is enhanced by the reduced dimensionality showing up in the dynamic structure factor. We measured the dynamic structure factor of an array of one-dimensional bosonic gases pointing out the effect of temperature-induced phase fluctuations in reducing the coherence length of the system.
We report the Bragg spectroscopy of interacting one-dimensional Bose gases loaded in an optical lattice across the superfluid to the Mott-insulator phase transition. Elementary excitations are created with a nonzero momentum and the response of the correlated 1D gases is in the linear regime. The complexity of the strongly correlated quantum phases is directly displayed in the spectra which exhibit novel features. This work paves the way for a precise characterization of the state of correlated gases in optical lattices.
We study Bragg spectroscopy of ultracold atoms in one-dimensional optical lattices as a method for probing the excitation spectrum in the Mott-insulator phase, in particular the one-particle-hole excitation band. Within the framework of perturbation theory we obtain an analytical expression for the dynamic structure factor and use it to calculate the imparted energy which was shown to be a relevant observable in recent experiments. We test the accuracy of our approximations by comparing them with numerically exact solutions of the Bose-Hubbard model in restricted cases and establish the limits of validity of our linear-response analysis. Finally we show that when the system is deep in the Mott-insulator regime, its response to the Bragg perturbation is temperature dependent. We suggest that this dependence might be used as a tool to probe temperatures of order of the Mott gap.
Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate-like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly-interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a 87^{87}87Rb condensate in a 2D lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at T>0T > 0T>0. Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.
We study Bragg spectroscopy of strongly interacting one-dimensional bosons loaded in an optical lattice plus an additional parabolic potential. We calculate the dynamic structure factor by using Monte Carlo simulations for the Bose-Hubbard Hamiltonian, exact diagonalizations and the results of a recently introduced extended fermionization model. We find that, due to the system's inhomogeneity, the excitation spectrum exhibits a multibranched structure, whose origin is related to the presence of superfluid regions with different densities in the atomic distribution. We thus suggest that Bragg spectroscopy in the linear regime can be used as an experimental tool to unveil the shell structure of alternating Mott insulator and superfluid phases characteristic of trapped bosons.
In condensed-matter physics, inelastic light-scattering provides a powerful method to investigate the system under study. It allows accessing the correlation functions which could identify dierent many-body states. We will report on the investigation of ultracold atoms in optical potentials, which have proved to be an excellent way of realizing simplied models of condensed-matter physics theory in experimental practice. In particular, we studied the modication of the response of an array of one-dimensional samples of 87Rb in a periodic potential across the superfluid to Mott-insulator transition, extracting information about both the dynamical spectral function and the one-particle spectral function.
We investigate the dynamic structure factor of atomic Bose and Fermi gases in one-dimensional optical lattices at zero temperature. The focus is on the generic behaviour of S ( k , ω) as a function of filling and interaction strength with the aim of identifying possible experimental signatures for the different quantum phase transitions. We employ the Hubbard or Bose–Hubbard model and solve the eigenvalue problem of the Hamiltonian exactly for moderate lattice sizes. This allows us to determine the dynamic structure factor and other observables directly in the phase transition regime, where approximation schemes are generally not applicable. We discuss the characteristic signatures of the various quantum phases appearing in the dynamic structure factor and illustrate that the centroid of the strength distribution can be used to estimate the relevant excitation gaps. Employing sum rules, these quantities can be evaluated using ground-state expectation values only. Important differences between bosonic and fermionic systems are observed, e.g., regarding the origin of the excitation gap in the Mott-insulator phase.