In the last century, Quantum Mechanics has been a story of unabashed success, reshaping our understanding of physical reality not only at the smallest length scales of elementary particles, but providing us with an exquisite control over many phenomena which are crucial for the technology development of our species. Examples span from transistor and light-emitting diodes, through lasers and superconductors, up to the disruptive potential of quantum information science. Many concepts once thought to be definitely settled have been uprooted over the decades, and rotations are no exceptions.
Now, interest in rotational dynamics dates back to ancient astronomy and its mathematical description proved highly non-trivial even in the classical world of our macroscopic experience, whether we look at kids’ tops or at gyroscopes and other engine components. Quantum mechanically, it was clear that a certain divide emerged over the last decades. On one hand, the mathematical formulation of quantized angular momentum (i.e. the “propensity” of a body to rotate) was quite quickly implemented in the Fifties by towering figures like E. Wigner and G. Racah; they clearly had in mind how, for instance, reactivity of molecules depends on their relative orientation, a crucial issue for chemistry. However, coupling different angular momenta can quickly escalate to an intractable problem, hindering our understanding about quantum rotations happening in quantum liquids (Helium, cold atoms, even light in properly engineered cavities).
Here, we aim exactly to untangle this dynamics, by making use of a versatile set of theoretical tools, easily expendable in different context, such as molecules in liquid Helium or ultracold atomic vapours, nanoparticles trapped by electromagnetic radiation or electronic devices whose conduction properties are modified by the presence of molecular potential. The perspective is often the one of “impurity problem”, originally employed for electrons moving in positively charged ionic crystals (the so-called “polaron problem”). If there is no internal structure, and the impurity is point-like, the particle experiences friction, i.e. a linear slowing-down force. On the other hand, we show how objects able to perform rotations in real space can exchange angular momentum with their environment; the features of this exchange dynamics can help us parse different behaviour, depending on how the system is prepared initially, or on how strongly it is coupled with its environment. In parallel, it is crucial to keep in mind the rotational dynamics being affected by the surrounding environment is only half of the story, and the medium can itself be modified by the presence of the impurity. A clear example is provided by chiral molecules (i.e. structures not superimposable with their mirror image, like our hands or DNA helices).
