Many Body Physics with Coupled Transmission Line Resonators

  1. Martin Leib,
  2. and Michael J. Hartmann
We present the Josephson junction intersected superconducting transmission line resonator. In contrast to the Josephson parametric amplifier, Josephson bifurcation amplifier and Josephson
parametric converter we consider the regime of few microwave photons. We review the derivation of eigenmode frequencies and zero point fluctuations of the nonlinear transmission line resonator and the derivation of the eigenmode Kerr nonlinearities. Remarkably these nonlinearities can reach values comparable to Transmon qubits rendering the device ideal for accessing the strongly correlated regime. This is particularly interesting for investigation of quantum many-body dynamics of interacting particles under the influence of drive and dissipation. We provide current profiles for the device modes and investigate the coupling between resonators in a network of nonlinear transmission line resonators.

Photon Blockade in the Ultrastrong Coupling Regime

  1. Alessandro Ridolfo,
  2. Martin Leib,
  3. Salvatore Savasta,
  4. and Michael J. Hartmann
We explore photon coincidence counting statistics in the ultrastrong-coupling regime where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. In this
regime usual normal order correlation functions fail to describe the output photon statistics. By expressing the electric-field operator in the cavity-emitter dressed basis we are able to propose correlation functions that are valid for arbitrary degrees of light-matter interaction. Our results show that the standard photon blockade scenario is significantly modified for ultrastrong coupling. We observe parametric processes even for two-level emitters and temporal oscillations of intensity correlation functions at a frequency given by the ultrastrong photon emitter coupling. These effects can be traced back to the presence of two-photon cascade decays induced by counter-rotating interaction terms.

Bose-Hubbard dynamics of polaritons in a chain of circuit QED cavities

  1. Martin Leib,
  2. and Michael J. Hartmann
We investigate a chain of superconducting stripline resonators, each interacting with a transmon qubit, that are capacitively coupled in a row. We show that the dynamics of this system
can be described by a Bose-Hubbard Hamiltonian with attractive interactions for polaritons, superpositions of photons and qubit excitations. This setup we envisage constitutes one of the first platforms where all technological components that are needed to experimentally study chains of strongly interacting polaritons have already been realized. By driving the first stripline resonator with a microwave source and detecting the output field of the last stripline resonator one can spectroscopically probe properties of the system in the driven dissipative regime. We calculate the stationary polariton density and density-density correlations $g^{(2)}$ for the last cavity which can be measured via the output field. Our results display a transition from a coherent to a quantum field as the ratio of on site interactions to driving strength is increased.