The Jaynes–Cummings–Hubbard (JCH) model is a many-body quantum system modeling the quantum phase transition of light. As the name suggests, the Jaynes–Cummings–Hubbard model is a variant on the Jaynes–Cummings model; a one-dimensional JCH model consists of a chain of N coupled single-mode cavities, each with a two-level atom. Unlike in the competing Bose–Hubbard model, Jaynes–Cummings–Hubbard dynamics depend on photonic and atomic degrees of freedom and hence require strong-coupling theory for treatment. One method for realizing an experimental model of the system uses circularly-linked superconducting qubits.
History The combination of Hubbard-type models with Jaynes-Cummings (atom-photon) interactions near the photon blockade regime originally appeared in three, roughly simultaneous papers in 2006. All three papers explored systems of interacting atom-cavity systems, and shared much of the essential underlying physics. Nevertheless, the term Jaynes–Cummings–Hubbard was not coined until 2008.
Properties Using mean-field theory to predict the phase diagram of the JCH model, the JCH model should exhibit Mott insulator and superfluid phases.
Hamiltonian The Hamiltonian of the JCH model is ( ℏ = 1 {\displaystyle \hbar =1} ):
H = ∑ n = 1 N ω c a n † a n + ∑ n = 1 N ω a σ n + σ n − + κ ∑ n = 1 N ( a n + 1 † a n + a n † a n + 1 ) + η ∑ n = 1 N ( a n σ n + + a n † σ n − ) {\displaystyle H=\sum _{n=1}^{N}\omega _{c}a_{n}^{\dagger }a_{n}+\sum _{n=1}^{N}\omega _{a}\sigma _{n}^{+}\sigma _{n}^{-}+\kappa \sum _{n=1}^{N}\left(a_{n+1}^{\dagger }a_{n}+a_{n}^{\dagger }a_{n+1}\right)+\eta \sum _{n=1}^{N}\left(a_{n}\sigma _{n}^{+}+a_{n}^{\dagger }\sigma _{n}^{-}\right)}
… excerpt ends here. Continue reading the full article.
