Jaynes–Cummings–Hubbard model

The Jaynes–Cummings–Hubbard (JCH) model is a many-body quantum system modeling the quantum phase transition of light.

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.

[1] One method for realizing an experimental model of the system uses circularly-linked superconducting qubits.

[2] The combination of Hubbard-type models with Jaynes-Cummings (atom-photon) interactions near the photon blockade [3][4]regime originally appeared in three, roughly simultaneous papers in 2006.

[5][6][7] All three papers explored systems of interacting atom-cavity systems, and shared much of the essential underlying physics.

[8] Using mean-field theory to predict the phase diagram of the JCH model, the JCH model should exhibit Mott insulator and superfluid phases.

are Pauli operators for the two-level atom at the n-th cavity.

is the tunneling rate between neighboring cavities, and

is the vacuum Rabi frequency which characterizes to the photon-atom interaction strength.

[5] Note that the model exhibits quantum tunneling; this process is similar to the Josephson effect.

[10][11] Defining the photonic and atomic excitation number operators as

, the total number of excitations is a conserved quantity, i.e.,

[citation needed] The JCH Hamiltonian supports two-polariton bound states when the photon-atom interaction is sufficiently strong.

In particular, the two polaritons associated with the bound states exhibit a strong correlation such that they stay close to each other in position space.

[12] This process is similar to the formation of a bound pair of repulsive bosonic atoms in an optical lattice.