Abstract
Experiments with ions in traps on the one hand, and with Rydberg atoms in cavities on the other were recognized by the 2012 Nobel Prize in Physics. They have illustrated from two different angles the same physics, that of the coupling of two-level atoms - denoted spin-1/2 particles or qubits, depending on the context - with a quantum harmonic oscillator. In the first case, the ions’ internal states are the spins and one mode of vibration of harmonic motion in the trap is the oscillator, whose quanta are phonons. In the second case, the internal states of Rydberg atoms act as spins and the field in the cavity as the oscillator, quantized in terms of photons. This physics of spin-oscillator coupling is described by a very simple Hamiltonian, which was introduced to quantum optics by Jaynes and Cummings sixty years ago. This theoretical simplicity conceals a very rich physics involving the phenomena of state superpositions, quantum jumps, quantum interference, entanglement and decoherence. These phenomena were observed two or three decades ago in parallel experiments showing great similarities. They demonstrated the possibilities opened up by manipulating these systems for quantum information processing. Trapped ions and Rydberg atoms have lived up to their promise and continue to play an important role in quantum simulation experiments. After briefly recalling the history of this field of quantum optics, we'll describe some recent experiments and discuss the perspectives they open for future research.
