Laboratoire de Physique Théorique
Toulouse - UMR 5152

In the nineties and early two thousands it was proposed by several authors that instead of using feedback control, non classical states could be prepared by tweaking the interaction between a quantum system and its environment. This technique is called reservoir engineering. Recent experiments have implemented the idea.

In this talk I will present an ongoing work in collaboration with B. Cloez, C. Pellegrini and F. Ticozzi where we extend the convergence results of reservoir engineering by taking into account a continuous measurement of the environment. The system state evolution is then described by a specific non linear Markov stochastic process called a quantum trajectory.

We show that the almost sure convergence of the quantum trajectory is equivalent to the convergence without measurement on the environment. The trajectory converges almost surely exponentially fast with a rate at least equivalent to the convergence rate without measurement.

Moreover, based on some simulations, we find that the stochastic evolution of the system state can be drastically different from the average one. This peculiar behavior appear when an asymptotic convergence rate is greater for the trajectory than for the evolution without measurement.

This result hints at the importance of the type of continuous measurement performed. It could be useful for future experiments of reservoir engineering.