Excitation spectra of strongly correlated ultra-cold dipolar gases from first-principle thermodynamic simulations

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Ultracold gases with large dipole moments, such as chromium, erbium, dysprosium and polar molecules are a subject of growing interest, being an example of strongly nonideal Bose systems. Their accurate description has to go beyond the mean-field treatment calling for a microscopic theory. In the current project we develop a numerical approach - a combination of path integral Monte Carlo simulations with a stochastic optimization method. This approach allows for a first-principle reconstruction of the collective excitation spectrum (spectral density) from the imaginary-time correlation functions. We concentrate on a detailed study of the combined effects of temperature, density, damping and quasi-particle decay processes on the collective modes for both, homogeneous and trapped dipolar Bose gases. The approach is then generalized to describe the spectrum of rotating Bose condensates and Bose gases with vortex states. The analysis will be complemented by a comparison with the predictions based on the Bogoliubov, Bogoliubov-de-Gennes and Thomas-Fermi approximations, as well as the sum rule approach involving the frequency-weighted moments. To check our predictions for a set of experimental parameters (including finite temperature), a close collaboration with the experimental group of Prof. S.Ospelkaus (Institute of Quantum Optics, Universität Hannover) is planned.