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arXiv:cond-mat/0508054 · Physical Review A

Energy absorption of a Bose gas in a periodically modulated optical lattice

Anı́bal Iucci, Miguel A. Cazalilla, A. F. Ho, Thierry Giamarchi

Published Apr 26, 2006• 55 citations
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Abstract

We compute the energy absorbed by a one-dimensional system of cold bosonic atoms in an optical lattice subjected to lattice amplitude modulation periodic with time. We perform the calculation for the superfluid and the Mott insulator created by a weak lattice, and the Mott insulator in a strong lattice potential. For the latter case we show results for three-dimensional systems as well. Our calculations, based on bosonization techniques and strong-coupling methods, go beyond standard Bogoliubov theory. We show that the energy absorption rate exhibits distinctive features of low-dimensional systems and Luttinger liquid physics. We compare our results with experiments and find good agreement.

DOI
10.1103/physreva.73.041608

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We compute the energy absorbed by a one-dimensional system of cold bosonic atoms in an optical lattice subjected to lattice amplitude modulation periodic with time. We perform the calculation for the superfluid and the Mott insulator created by a weak lattice, and the Mott insulator in a strong lattice potential. For the latter case we show results for three-dimensional systems as well. Our calculations, based on bosonization techniques and strong-coupling methods, go beyond standard Bogoliubov theory. We show that the energy absorption rate exhibits distinctive features of low-dimensional systems and Luttinger liquid physics. We compare our results with experiments and find good agreement.
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We discuss a technique to probe the properties of an interacting cold atomic gas that can be viewed as a dynamical compressibility measurement. We apply this technique to the study of the superfluid-to-Mott-insulator quantum phase transition in one and three dimensions for a bosonic gas trapped in an optical lattice. Excitations of the system are detected by time-of-flight measurements. The experimental data for the one-dimensional case are in good agreement with the results of a time-dependent density-matrix-renormalization-group calculation.
We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasiperiodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the noncommensurate case, mapping the problem to the Anderson model allows us to study the Bose-glass phase. Surprisingly, we find that a perturbative treatment in both cases, weak and strong disorders, gives a good description at all frequencies. In particular, we find that the infrared-absorption rate in the thermodynamic limit is quadratic in frequency. This result is unexpected since for other quantities, like the conductivity in one-dimensional systems, perturbation theory is only applicable at high frequencies. We discuss applications to recent experiments on optical lattice systems and, in particular, the effect of the harmonic trap.
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Motivated by the recent rapid development of the field of quantum gases in optical lattices, we present a comprehensive study of the spectrum of ultracold atoms in a one-dimensional optical lattice subjected to a periodic lattice modulation. Using the time-dependent density matrix renormalization group method, we study the dynamical response due to lattice modulations in different quantum phases of the system with varying density. For the Mott-insulating state, we identify several excitation processes, which provide important information about the density profile of the gases. For the superfluid, the dynamical response can be well described in a local density approximation. This simplification can be valuable in understanding the strong-correlated superfluid in a slow-varying harmonic potential. All these spectroscopic features of an inhomogeneous system can be used as a test for the validity of the Bose-Hubbard model in a parabolic trapping potential.
Lattice modulation spectroscopy is a powerful tool for probing low-energy excitations of interacting many-body systems. By means of bosonization we analyze the absorbed power in a one-dimensional interacting quantum gas of bosons or fermions, subjected to a periodic drive of the optical lattice. For these Tomonaga-Luttinger liquids we find a universal ω3 scaling of the absorbed power, which at very low-frequency turns into an ω2 scaling when scattering processes at the boundary of the system are taken into account. We confirm this behavior numerically by simulations based on time-dependent matrix product states. Furthermore, in the presence of impurities, the theory predicts an ω2 bulk scaling. While typical response functions of Tomonaga-Luttinger liquids are characterized by exponents that depend on the interaction strength, modulation spectroscopy of cold atoms leads to a universal power-law exponent of the absorbed power. Our findings can be readily demonstrated in ultracold atoms in optical lattices with current experimental technology.