Abstract

Superconducting qubits in on-chip microwave resonators allow for the exploration of novel quantum optics regimes enabled by their large and constant dipole coupling strength to individual photons [1]. Utilizing these properties we are able to directly prove field quantization in a strongly coupled matter-light system. We observe the square root of n nonlinearity of the Jaynes-Cummings energy ladder by measuring the vacuum Rabi spectrum in the presence of coherent [2] and thermal [3] photons n. More recently we have performed measurements with up to three qubits to study cavity mediated multi-qubit interactions. Tuning N qubits in resonance with the cavity field individually, we demonstrate the square root of N scaling of the collective dipole coupling strength as described by the Tavis-Cummings model [4]. To our knowledge this is the first observation of this nonlinearity in a system in which the atom number can be changed one by one in a discrete fashion. In addition, the energies of both bright and dark coupled multi-qubit/photon states are well explained by the Tavis-Cummings model over a wide range of detunings. Finally, we present single qubit time-resolved and spectroscopic vacuum Rabi measurements with thermal photon numbers varied by five orders of magnitude. We find good agreement with a master equation model over a large range of equivalent thermal field temperatures and observe the emergence of the classical limit of cavity QED as expected from the correspondence principle.

[1] A. Wallraff et al. Nature 431 (2004).

[2] J. M. Fink et al. Nature 454, 315 (2008).

[3] J. M. Fink et al. arXiv:0911.3797 (2009).

[4] J. M. Fink et al. Phys. Rev. Lett. 103 (2009).