Synthetic quantum systems, such as those based on bosonic and fermionic trapped quantum gases, offer an excellent opportunity to study the complexities of quantum many-body physics. Recently, a set of efficient tools called “Hamiltonian learning (HL)” has been developed to uncover the underlying microscopic interactions in these systems from experiment and verify the performance of engineered quantum devices used for quantum simulation. While HL is well developed for discrete lattice-based many-body systems, its application to continuous quantum systems faces a challenge due to the absence of a lattice scale. However, by utilizing the spatial scale introduced by measurement resolution, effective field theories can emerge as suitable descriptions. In this talk, I will present a protocol that capitalizes on the locality of effective field theories to extract their Hamiltonians from experimental data. Our approach involves constraining the Hamiltonian through relationships among correlation functions, which we derive from a field theory ansatz. The effectiveness of our method is demonstrated in theoretical studies of both classical and (free) quantum fields. Furthermore, I showcase its application in a ultracold quantum gas experiment in the classical-statistical regime. The present work paves the way for quantitatively certifying emergent field theories in quantum simulators.
Presenter: Robert Ott