Breakdown of gauge invariance in ultrastrong-coupling cavity QED

  1. Daniele De Bernardis,
  2. Philipp Pilar,
  3. Tuomas Jaako,
  4. Simone De Liberato,
  5. and Peter Rabl
We revisit the derivation of Rabi- and Dicke-type models, which are commonly used for the study of quantum light-matter interactions in cavity and circuit QED. We demonstrate that the
validity of the two-level approximation, which is an essential step in this derivation, depends explicitly on the choice of gauge once the system enters the ultrastrong coupling regime. In particular, while in the electric dipole gauge the two-level approximation can be performed as long as the Rabi frequency remains much smaller than the energies of all higher-lying levels, it can dramatically fail in the Coulomb gauge, even for systems with an extremely anharmonic spectrum. We extensively investigate this phenomenon both in the single-dipole (Rabi) and multi-dipole (Dicke) case, and considering the specific examples of dipoles confined by double-well and by square-well potentials, and of circuit QED systems with flux qubits coupled to an LC resonator.

Light-matter decoupling and A^2 term detection in superconducting circuits

  1. Juan José García-Ripoll,
  2. Borja Peropadre,
  3. and Simone De Liberato
We study the spontaneous emission of a qubit interacting with a one-dimensional waveguide through a realistic minimal-coupling interaction. We show that the diamagnetic term A2 leads
to an effective decoupling of a single qubit from the electromagnetic field. This effects is observable at any range of qubit-photon couplings. For this we study a setup consisting of a transmon that is suspended over a transmission line. We prove that the relative strength of the A2 term is controlled with the qubit-line separation and show that, as a consequence, the spontaneous emission rate of the suspended transmon onto the line can increase with such separation, instead of decreasing.