# Accessing finite momentum excitations of the one-dimensional Bose-Hubbard model using superlattice modulation spectroscopy

## TL;DR

This paper explores how superlattice modulation spectroscopy can probe finite momentum excitations in the one-dimensional Bose-Hubbard model, providing insights into the system's excitation spectrum and interaction strength measurement.

## Contribution

It introduces a spectroscopic method to access finite momentum excitations in the 1D Bose-Hubbard model using superlattice modulation, supported by numerical and analytical analysis.

## Key findings

- Response reveals a narrow peak at the onsite interaction in the Mott-insulator phase.
- The technique enables accurate measurement of the effective interaction strength.
- Response behavior varies with lattice filling in the superfluid phase.

## Abstract

We investigate the response to superlattice modulation of a bosonic quantum gas confined to arrays of tubes emulating the one-dimensional Bose-Hubbard model. We demonstrate, using both time-dependent density matrix renormalization group and linear response theory, that such a superlattice modulation gives access to the excitation spectrum of the Bose-Hubbard model at finite momenta. Deep in the Mott-insulator, the response is characterized by a narrow energy absorption peak at a frequency approximately corresponding to the onsite interaction strength between bosons. This spectroscopic technique thus allows for an accurate measurement of the effective value of the interaction strength. On the superfluid side, we show that the response depends on the lattice filling. The system can either respond at infinitely small values of the modulation frequency or only above a frequency threshold. We discuss our numerical findings in light of analytical results obtained for the Lieb-Liniger model. In particular, for this continuum model, bosonization predicts power-law onsets for both responses.