Climbing the Jaynes-Cummings ladder and observing its √n nonlinearity in a cavity QED system

The field of cavity quantum electrodynamics ( QED), traditionally studied in atomic systems(1-3), has gained new momentum by recent reports of quantum optical experiments with solid- state semiconducting(4-8) and superconducting(9-11) systems. In cavity QED, the observation of the vacuum Rabi mode splitting is used to investigate the nature of matter - light interaction at a quantum-mechanical level. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators(12). It has been suggested that an observation of the scaling of the resonant atom - photon coupling strength in the Jaynes - Cummings energy ladder(13) with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature(14). Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous spectroscopic evidence for the quantum nature of the resonant atom - field interaction in cavity QED. We explore atom - photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED set- up(15), in which very strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high- quality on- chip microwave cavity. Circuit QED systems also provide a natural quantum interface between flying qubits ( photons) and stationary qubits for applications in quantum information processing and communication(16).