Arecchi's research starts with the onset of the laser age (early sixties). Rather than looking for new materials and excitation techniques (spectroscopy) or new cavity configurations (optical engineering) Arecchi focuses on the coherence aspects, measured in terms of photon statistics (research lines #1 and #2). Thus the coherent interaction of matter (atoms, molecules) and electromagnetic radiations which is the basis of the laser action does not need a description in terms of each microscopic component, but it can be epitomized in terms of a small number of collective variables.|
This leads to the discovery that the laser threshold is like the critical point of a thermodynamic phase transition, marking the onset of a new type of order; however, the laser threshold occurs far from thermal equilibrium. Furthermore, the laser threshold is just the first of many possible bifurcation phenomena to qualitatively new states.
Two concepts play a crucial role in these phenomena. The first is nonlinear dynamics, which gives rise to different bifurcations as a control parameter is changed; the second one is that of open system, which means that the dynamics is non conservative and influenced by the environment.
As said, dynamics of the single mode laser is epitomized by a very small number of degrees of freedom. If this small number is equal to, or larger than, three, then deterministic chaos arises as shown in the research line # 3.
The standard use of laser systems in the research laboratory and in applications is based on single, or a few, mode operation plus some modulation or feedback, amounting to a small number of coupled variables sufficient to induce chaos. For this reason chaos has been a crucial topics of laser research since 1982.
Increasing the number of modes or introducing a delayed feedback brings a large number of degrees of freedom, thus giving rise to problems of pattern formation and competition, already explored in other areas of physics, as fluid dynamics or chemical reactions. Doing it in optics implies a careful control of the operating conditions, thus it has put in evidence fundamental phenomena such as the role of symmetries and the competition between the bulk dynamics and the driving due to the boundary effects (research line #4).
Whatever has been explored in laser and nonlinear optics has a counterpart in any physical system which is driven away from thermal equilibrium through input/output channels; this includes not only meteorology, geophysics and oceanography, but also living systems and social phenomena.
The same formation of scientific theories is affected by the discovery that most phenomena are complex, thus any description is never complete. This means that in general different competing models are available for the same phenomenon. In such cases, the choice of the best strategy is the result of a “trial and error” search, which is common to all cognitive tasks. Hence, exploring complex phenomena and developing adaptive recognition strategies provides an insight into the language operations. The inverse Bayes inference yields novel algorithms, beyond the single algorithm approach of standard perceptual processes.