Fifty years of Jaynes–Cummings physics

Abstract

This special issue commemorates the 50th anniversary of the seminal paper published by E T Jaynes and F W Cummings [1], the fundamental model which they introduced and now carries their names, and celebrates the remarkable host of exciting research on Jaynes–Cummings physics throughout the last five decades.The Jaynes–Cummings model has been taking the prominent stance as the ‘hydrogen atom of quantum optics’ [2]. Generally speaking, it provides a fundamental quantum description of the simplest form of coherent radiation–matter interaction. The Jaynes–Cummings model describes the interaction between a single electromagnetic mode confined to a cavity, and a two-level atom. Energy is exchanged between the field and the atom, which leads directly to coherent population oscillations (Rabi oscillations) and superposition states (dressed states). Being exactly solvable, the Jaynes–Cummings model serves as a most useful toy model, and as such it is a textbook example of the physicists’ popular strategy of simplifying a complex problem to its most elementary constituents.Thanks to the simplicity of the Jaynes–Cummings model, this caricature of coherent light–matter interactions has never lost its appeal. The Jaynes–Cummings model is essential when discussing experiments in quantum electrodynamics (indeed the experimental motivation of the Jaynes–Cummings model was evident already in the original paper, dealing as it does with the development of the maser), and it has formed the starting point for much fruitful research ranging from ultra-cold atoms to cavity quantum electrodynamics. In fact, Jaynes–Cummings physics is at the very heart of the beautiful experiments by S Haroche and D Wineland, which recently earned them the 2012 Nobel Prize in physics. Indeed, as with most significant models in physics, the model is invoked in settings that go far beyond its initial framework. For example, recent investigations involving multi-level atoms, multiple atoms [3, 4], multiple electromagnetic modes, arrays of coupled cavities [5–7], and optomechanical systems [8] have further enriched the physics of the Jaynes–Cummings model. From the early interests in masers and the consistent quantum description of radiation and atom–photon interaction, the Jaynes–Cummings model has evolved into a cornerstone of quantum state engineering [9].The authors of this editorial had not been born when Jaynes and Cummings wrote their remarkable paper. It is, therefore, a special honour for us to be able to draw the reader’s attention to the accompanying reminiscence contributed by Frederick Cummings where he gives us a glimpse of the early history of the Jaynes–Cummings model from his perspective [11]. By now, the original 1963 paper by Jaynes and Cummings has gathered numerous citations and, at the time of writing, the number of articles involving Jaynes–Cummings physics is approaching 15 000.1This special issue does not attempt to review this impressive wealth of research. The interested reader, however, is urged to consult the definitive article by Shore and Knight [10] for a comprehensive review of the first 30 years of Jaynes–Cummings physics. The collection of 26 papers presented in this issue, showcases a snapshot of some of the most recent and continuing research devoted to Jaynes–Cummings physics.We begin our special issue with Professor Cumming’s recollections [11]. We then have six papers on quantum information aspects of the Jaynes–Cummings model [12–17]. The next topic includes seven papers on the Dicke and generalized Jaynes–Cummings models [18–24], followed by six papers on circuit QED, which is one of the most important experimental frameworks for Jaynes–Cummings systems [25–30]. Finally, we have six papers on the extension to many cavities, the Jaynes–Cummings–Hubbard model [31–36].The snapshot of research captured in this special issue illustrates the unifying language provided by the Jaynes–Cummings model, tying together research in a number of subfields in physics. Jaynes–Cummings physics started with the diagonalization of a 2 × 2 matrix, as Frederick Cummings points out. There is no doubt that this elegance of simplicity will continue to guide exciting new research in the decades to come.