Observing the environment : quantum eraser and servo control

The second lesson, covering the second and third chapters, began by presenting a simple classification of the different types of decoherence and the means of correcting or controlling them. First, we described "classical" decoherence, produced by deterministic noise acting on the system. In principle, this type of decoherence is perfectly correctable, by measuring the noise and then compensating for its effects. In some cases, deterministic noise can be eliminated by simply reversing the direction of time, inducing the system to undo the evolution that led to the loss of coherence. This is a generalization of the spin echo method, widely used in nuclear magnetic resonance. We have recalled the principle of this method and given a simple physical interpretation. The second type of decoherence involves the entanglement of the system under study with its environment. It cannot then be described as classical noise, and its description requires the full formalism of quantum physics. Correcting the effects of this quantum decoherence is far more delicate than that of classical noise. We have simply enumerated the various possible avenues, which are described by the titles of chapters 3 to 9 of the lecture. We concluded the second lesson with a discussion of two decoherence control methods based on direct observation of the system's environment (Chapter 3). The first is the "quantum eraser": the aim is to re-establish, by means of a "read-out" measurement, the quantum coherences between states of the system A that have been erased by coupling with the environment E. We measure an observable on E that gives no information on the "path" followed by A, and we correlate the measurements on A and E. We can then re-establish coherences that have disappeared on the unconditional measurements of A alone. The problem of this type of experiment (correlated quantum measurements on two intricate systems) is that of the EPR problem, studied in detail in the 2001-2002 lecture. The second method corresponds to what is known as "quantum feed-back": we continuously observe the quantum jumps of the system as it dampens itself by emitting quanta into the environment. Although irreversible in the Hilbert space_HA of A, each jump can be locally inverted in a subspace of_HA by a unitary transformation. We then restore coherence restricted to the_HA subspace, by unitary operations conditional on the results of measurements carried out on the environment.