We study the dynamic response of bosons in a one-dimensional optical lattice and obtain the dynamic structure factor $S(k,\omega)$ for perturbations in the linear regime, as well as the non-linear response to strong density perturbations . In our work, we use a continuous description of the system. Based on the time-dependent variational Monte Carlo method (tVMC) , we simulate the time propagation of a parametrized many-body wavefunction responding to an external probe pulse. A Jastrow-Feenberg ansatz with single particle and pair correlation functions is used as the model wavefunction.
For deep optical lattices we can compare $S(k,\omega)$ to exact diagonalization results obtained on a lattice in the Bose-Hubbard limit. When considering shallow optical lattices, the influence of higher Bloch bands is observed, indicating that the treatment in continuous space is appropriate for simulating the dynamics of the system. The non-linear response to strong pulses, with amplitudes equal to the optical lattice depth and a fixed wave number, is also investigated. From the power spectrum of the density fluctuations we can again infer the full excitation spectrum, albeit broadened, due to higher harmonic generation. In addition, we use different pulse strengths to investigate the transition from linear to non-linear response. A remarkable feature of tVMC is that the full excitation spectrum can also be retrieved from the power spectrum of the density fluctuations due to the stochastic noise inherent in any Monte Carlo method, without applying an actual perturbation.
 M. Gartner, F. Mazzanti and R.E. Zillich, Time-dependent variational Monte Carlo study of the dynamic structure factor for bosons in an optical lattice, arXiv preprint arXiv:2202.07535 (2022).
 G. Carleo, F. Becca, M. Schiró and M. Fabrizio, Localization and Glassy Dynamics Of ManyBody Quantum Systems, Scientific Reports 2(1), 243 (2012)
|Presenter name||Mathias Gartner|
|How will you attend ICAP-27?||I am planning on in-person attendance|