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Bulletin of the American Physical Society

Experimental study of a 72-site Jaynes-Cummings lattice in the nonlinear dispersive regime

Mattias Fitzpatrick, Neereja Sundaresan, Andy C. Y. Li, Jens Koch, Andrew Houck

Published Mar 14, 2016• 0 citations
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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.
The Jaynes-Cummings quantum optics model allows us to understand the dialogue between light and matter at its most fundamental level, which is crucial for advancements in quantum science and technology. Several generalizations of the model have been proposed, emphasizing their dynamic behavior but paying less attention to their spectroscopy. Here we obtain analytical expressions of the time-dependent spectral response of a nonlinear Jaynes-Cummings model based on deformed field operators. We show that the long-time response of the resulting nonlinear cavity field resembles the one experimentally obtained in the strong-dispersive regime of circuit quantum electrodynamics. The spectrum is intrinsically asymmetric with the nonlinear coupling, a signature of the impossibility of getting resonant conditions for finite field excitations.