Abstract
Photon-based strongly correlated lattice models like the Jaynes–Cummings and Rabi lattices differ from their more conventional relatives like the Bose–Hubbard model by the presence of an additional tunable parameter: the frequency detuning between the pseudo-spin degree of freedom and the harmonic mode frequency on each site. Whenever this detuning is large compared to relevant coupling strengths, the system is said to be in the dispersive regime. The physics of this regime is well-understood at the level of a single Jaynes–Cummings or Rabi site. Here, we extend the theoretical description of the dispersive regime to lattices with many sites, for both strong and ultra-strong coupling. We discuss the nature and spatial range of the resulting qubit–qubit and photon–photon coupling, demonstrate the emergence of photon-pairing and squeezing and illustrate our results by exact diagonalization of the Rabi dimer.
Highlights
Bosonic and fermionic lattice systems, realized experimentally with ultracold atoms or trapped ions, have long served as a paradigm for quantum simulators of strongly-correlated many-body systems [1, 2, 3]
In the Jaynes-Cummings and Rabi lattice, each lattice site consists of a photon mode interacting locally with a two-level system, and is described by the ordinary JaynesCummings [11] or Rabi model [12]
We show that the system reduces to an effective spin model with XY-type interaction for the Jaynes-Cummings lattice, and to a transverse Ising model for the Rabi lattice
Summary
Bosonic and fermionic lattice systems, realized experimentally with ultracold atoms or trapped ions, have long served as a paradigm for quantum simulators of strongly-correlated many-body systems [1, 2, 3]. In circuit QED lattices, photons can hop between transmission line resonators (which are coupled capacitively) and locally interact with a superconducting qubit. Its usual description is based on employing a perturbative SchriefferWolff transformation, which eliminates the Jaynes-Cummings or Rabi coupling by switching to an appropriate dressed-state basis. We extend this procedure to an entire lattice of sites and systematically discuss all contributions in second-order perturbation theory (section 2). Due to the ultrastrong coupling, approached in a recent experiment for a single site in circuit-QED architecture [18], the non-trivial nature of the ground state makes the Rabi lattice interesting.
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