The sixth lesson looked at the evolution of superpositions of position states of a material particle or coherent states of a field mode, the famous Schrödinger's cat problem. We began by recalling a few notions about decoherence in the case of Brownian motion, and showed the similarity between the pilot equation of Brownian motion and that of a field in quantum optics. We described the decoherence of superpositions of field states by different types of trajectories with complementary physical interpretations: photon number parity jumps, localization and quantum phase scattering.
We completed the lecture by linking it to the lectures planned for next year. In the 2003-2004 lecture, continuous observation of a single quantum system coupled to an environment was described as a thought experiment to determine the stochastic trajectories of the system. These are generally useful intermediates for calculating the density operator, which contains all the information we can have about the system. There are, however, experiments in which these trajectories can actually be observed, by continuous explicit measurement performed on a single quantum system. The system then remains described by a wave function. Its coherence can be preserved, but with a quantum phase that varies randomly from one realization of the measurement to another. In the course of next year's lecture, we'll be describing some of these experiments, already carried out or planned.
We will also seek to answer an essential question: can decoherence be controlled in practice, or even effectively combated, in order to maintain an open system in a coherent superposition for a very long or even indefinite time? This question is important for improving the precision of spectroscopic or metrological measurements, or for enabling complex quantum information logic operations. Several strategies have been proposed to control or limit decoherence. Two types of method are particularly important:
- The implementation of error-correcting codes, which consist in measuring a symptom of decoherence on the system, then acting accordingly to correct the effect of decoherence and restore the system's previous state. These methods systematically exploit the properties of multi-particle entanglement. Some are directly inspired by the corrective codes of conventional computers (redundant coding of information). Others are more akin to conventional feedback methods.
- The development of methods for preparing and controlling the environment (environment engineering), which consist in fabricating artificial reservoirs admitting as pointing states the states we are seeking to preserve from decoherence. We have briefly introduced these methods and announced that we will be giving examples of them next year, while attempting to analyze their limitations.
