In our group we study many-body quantum systems out-of-equilibrium. In particular, we focus on gases of ultracold atoms (Bose-Einstein condensate, optical lattices); quantum optics (optical amplifiers, resonators, lasers), andcondensed matter (high-temperature superconductors, Josephson junctions). The technical details of these systems are very different. For example, their temperature varies from room temperature (~300K) to below one-millionth of a degree above the absolute zero (<1uK). The number of atoms involved goes from a few hundreds, to ten-to-the-twenty. However, the theoretical questions that we ask follow a common thread.

  1. Thermalization. When a system is not perturbed by any external force, we can always assume it to be found at thermal equilibrium and to be described by a Boltzmann distribution. What happens when a system is driven by a time-dependent force? How is Boltzmann (classical) statistics recovered in a system obeying quantum mechanics? In some cases, if the system is observed for long enough time, it is still possible to define an effective Boltzmann distribution or better, a “low-frequency effective temperature” (LET) (See for example hereor here). When does this concept apply and when does it not?
  2. Universality. At equilibrium, the concept of universality is intimately related to the integration over “imaginary time”. Can we achieve a similar degree of universality by integrating over “real-time”? By considering small perturbations around a quantum critical point, it is possible to show that, in non-equilibrium systems, the time coordinate follows the same scaling laws as the other dimensions. (See here and here). How do time and space coordinates differ?
  3. Minimal model. Sometimes, complicate phenomena such as “exceptional points” (see here) and “non-equilibrium quantum phase transitions” (see here) can be understood by mapping them to a harmonic oscillator. Similarly, competing orders in cuprates, can be explained by considering the effects of a single impurity inside a superconductor (see here). What are the limitations of this minimalistic approach?  When do we need more complicate models?