Dr. Lucas Hackl

Dr. Lucas Hackl

MPHQ Postdoc

Main Focus

Since August 2018 Dr. Lucas Hackl is working as MPHQ fellow in the group of Prof. Ignacio Cirac. His Co-PI in Harvard is Prof. Eugene Demler.

Research goal

In order to study complex quantum systems, one needs to overcome the exponentially large or even infinite dimensionality of the state manifold. The goal of my research is to find suitable classes of states that can capture relevant physical properties but have a sufficiently small dimension to make computations and even some analytical studies feasible. In particular, we are interested in generalizing and extending existing methods for Gaussian states to new classes of non-Gaussian states.

Possible applications

The applications of such generalized Gaussian states range from fundamental theory (in particular, quantum fields) to condensed matter physics and the study of cold atoms in quantum optics. An efficiently parametrized new class of states can lead to novel analytical results about concrete physical systems whose ground or eigenstates can be approximated, but also to develop numerical tools exploiting these methods to compute physical quantities.

Collaboration with Harvard

Apart from the development of new variational classes of states, we are collaborating with researchers at Harvard to develop systematic methods for the study of ground states, low lying excitations and linear response of many body quantum systems. A recent application includes the paradigmatic Bose-Hubbard model, for which we extended the well-known Bogoliubov theory to a tangent plane approximation capturing both one- and two-particle excitations to compute spectra and quasi particle decay.

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