At the beginning of the 20th century, several breakthroughs in physics lead to the birth of quantum mechanics and, subsequently, to an improved description of a wide range of phenomena and to many new discoveries.

Today we benefit in our daily lives from the great technological progress that followed. Despite these dramatic technological advances, it is humbling to note that very few problems can be solved exactly when it comes to the quantum world. For the most part, well defined approximations are used to properly characterize the systems of interest.

For some problems however, it is well understood that previously used classes of approximations are inappropriate.

Strongly Correlated systems

                          systems away from equilibrium

This encompasses the family of strongly correlated systems. Here, the Coulomb interaction is of the same order of magnitude as the kinetic energy or even higher sometimes. While the wide array of energy scales at play in these materials gives them many technologically promising properties such as high temperature superconductivity, colossal magnetoresistance, heavy fermions, ..., it is also the reason  why their  microscopic description has been  rather elusive  despite  decades of efforts.

With the advent of petascale computing, Computational methods coupled with analytical approaches have become  valuable tools in the study of these systems. One important aspect of Computational Science is that the tools are constrained by the scaling of the available algorithms. The interesting phenomena are seldom accessible through brute force approaches. Better algorithms are needed.

Quantum Simulators and Quantum Information Processing

                                                            Spin qubit communicating via E&M field

On the other hand, great progress has been achieved in our ability to trap and control ultracold atoms in optical lattices allowing the experimental realization of various physical models.  These experiments are either intrinsically out of equilibrium or useful in modeling nonequilibrium dynamics. To analyze the results, theoretical predictions are needed and this is another instance in which advances in computer technology provide a useful tool.

Furthermore, the exponential growth of the computer infrastructure (Moore's law) that we have become accustomed to is now flirting with physical limits. This means that a new paradigm will be required to further advance our computing abilities. Indeed, along with the aforementioned quantum simulators, Quantum Computing and Quantum Information Processing have seen great strides over the recent years. This is a new computing paradigm that is being built from the fundamental principles of quantum mechanics and the interaction of many-spin (qubits) systems.

My work is focused on using a combination of analytical and computational tools to study strongly correlated quantum systems in and out of equilibrium at the intersection of Condensed Matter Physics and ultracold  atomic gases. I am also interested in the dynamics of quantum systems that are relevant for QIP. In particular, I study processes that can allow optimal protection of key properties of qubits from their fluctuating environment.