Research

In my office at MPQ, 2016

My research is at the interface between theoretical quantum mechanics and modern technological applications, in a field that has come to be known as Quantum Optics, and nowadays comprises any system that can be understood through quantum electrodynamics at low energies.

I am particularly interested in open and critical quantum optical systems in the many-body regime. By open I mean systems that exchange energy and information with its surrounding environment (e.g., through dissipation). By critical, I refer to systems that undergo some kind of phase transition or sudden change of behavior as their parameters are changed.

My main contributions to this broad discipline can be divided in three groups:

Mathematical techniques. Critical systems are very difficult to analyze because the temporal and/or spatial scales of the problem grow wild when working around phase transitions (divergence of spatiotemporal correlations). On the other hand, open systems are hard to study because one necessarily needs to deal with mixed states and evolution equations for operators, rather than for vectors in the Hilbert space. I develop or apply mathematical techniques that are capable of dealing with these problems efficiently either in a numerical or an analytical approximate way.

Implementations. The last decades have seen the birth of a plethora of new experimental platforms that work in the quantum coherent regime. Apart from their potential to shape the future of technology through quantum computation, simulation, metrology, and communication, all these technologies have allowed us to reach physical scenarios that were nothing but a dream (or a “gedanken” experiment) for the founding fathers of quantum mechanics. A huge part of my work is devoted to proposals for the implementation of interesting critical and open mathematical models in several platforms: nonlinear optics, superconducting circuits, mechanical devices, trapped atoms, and exciton polaritons.

Applications. Apart from posing very fundamental and challenging problems that make us learn new things about quantum mechanics, open and critical systems have great potential for many applications. In my case, I use them for the robust preparation of nontrivial quantum states such as squeezed, entangled, nonclassical, or localized. This type of states are of great practical relevance for modern quantum technologies. In addition, systems undergoing phase transitions can get very sensitive to external stimuli, and have therefore great potential for high-precision metrology. This is a venue I'm also interested in.

Apart from this main line of research on open and critical quantum systems, I also work on and off on other topics. These include quantum information with continuous variables, quantum simulators, and quantum walks.