Abstract
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 $\omega^3$ scaling of the absorbed power, that at very low-frequency turns into an $\omega^2$ 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 $\omega^2$ 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.
Highlights
Cold atomic systems offer an unprecedented level of control of the properties of interacting quantum systems [1,2] and allow for the realization of a plethora of novel phases and phenomena that were previously inaccessible in other experiments
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
We have analyzed in the linear response the power absorbed by one-dimensional fermions and bosons in the Tomonaga-Luttinger liquid [25] or Luther-Emery liquid [51] phase, for the amplitude modulation of an optical lattice
Summary
Cold atomic systems offer an unprecedented level of control of the properties of interacting quantum systems [1,2] and allow for the realization of a plethora of novel phases and phenomena that were previously inaccessible in other experiments. Only quasi-long-range order can exist as characterized by a power-law decay of certain correlation functions This result is part of the more general properties of TomonagaLuttinger liquids (TLLs) that are expected to describe most of the interacting one-dimensional (1D) quantum problems [17,18]. Given the absence of true long-range superfluid order, one may wonder whether the response to shaking in a onedimensional bosonic system would show traces of a Higgs mode as in higher dimensions [4] This prompts an analysis of the response to shaking of a one-dimensional TLL.
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