Quantum electrodynamics in the ultrastrong coupling limit

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We aim to experimentally implement and explore (circuit) quantum electrodynamics (QED) in the so-called ultrastrong coupling regime. Ultra-strong QED is a situation where a single atom is coupled to a vacuum quantum field with an effective fine structure constant exceeding a unity. Obviously, such a situation cannot exist with real atoms and fields because the fine structure constant of the free space is too small (α ~ 1/137) and the atom-field interaction is fundamentally perturbative.

Our fresh approach to ultrastrong QED is to couple superconducting qubits, which take the role of "atoms", to microwaves in linear superconducting resonators, which take the role of "light". This architecture is often referred to as circuit QED. The following novelty is essential: we will make resonators with very high characteristic impedance Z, such that Z ~ RK = h/e2 = 26.5 kΩ, i.e. of the order of resistance quantum (or Klitzing resistance). This is in sharp contrast with conventional low-impedance microwave resonators in both 2D and 3D circuit QED geometries, where Z is governed by the scale of the vacuum impedance Zvac = (μ00)0.5 ~ 377 Ω. Recalling that α = Zvac/2RK, it becomes evident that in order to make α > 1, one needs to raise the impedance Z to all the way up to resistance quantum.

The nearly 3 orders of magnitude enhancement of impedance will be achieved by making resonators from high kinetic inductance superconductors – either a discrete array of Al/AlOx/Al Josephson tunnel junctions or a highly disordered superconducting film, such as TiN or NbN. The effective fine structure constant for microwave fields in such resonators becomes a material property, because the “magnetic” energy of the radio-frequency (RF) field is created predominantly due to the inertia of the moving Cooper pairs (hence the term kinetic inductance) rather than due to stressing the vacuum with a magnetic field.