Embracing gauge-freedom in ultrastrong-coupling quantum electrodynamics

The underlying descriptions of nearly all quantum systems, from the atomic-scale upwards, are provided by quantum electrodynamics (QED). The increasingly strong light-matter interactions encountered in molecular and solid-state cavity and circuit QED systems offer an important platform for probing fundamental quantum phenomena resulting in new discoveries and new insight into the foundations of physics. For example, although the term "photon" (meaning a light particle) is commonly used, the true nature of photons remains elusive to the extent that entire conferences are dedicated to trying to establish "what is a photon"? Strong light-matter interactions open up a wealth of new questions concerning the fundamental nature of light and matter, because in this regime the boundary between them becomes blurred.

Our understanding of contemporary physics is predicated on the assumption that larger (composite) systems can be divided into constituent parts known as subsystems. For example, an atom and its environment are both subsystems of the atom-environment whole. QED describes such systems at the quantum scale, but it can be expressed in many different forms (known as gauge freedom). Each form (i.e. gauge choice) provides a different theoretical division of the overall system into constituent light and matter subsystems. Moreover, the theory does not itself favour the use of any one subsystem division over any other. While QED is an exceptionally well-established theory within the conventional weak-coupling regime of atomic light-matter physics, distinct subsystem divisions corresponding to distinct forms of QED become increasingly different as the interactions within the system increase in strength. For example, the available definitions of a "photon" can vary significantly in the strong-coupling regime. Therefore, to accurately predict the number of clicks registered by a photo-detector in an experiment involving strong light-matter interactions, we must determine which of the infinite possible definitions of photon actually corresponds to what is registered by the detector.

The objective of this proposal is to provide new fundamental understanding of light, matter and their interaction in the strong-coupling regime. To this end an original and more powerful formulation of QED will be developed, which unlocks its full generality by allowing the boundaries drawn between subsystems to vary. This will be achieved by leaving the choice of gauge open, rather than fixing it from the outset. The proposal has significant potential to produce transformative results of importance for fundamental physical understanding.