Analytic approximations to the phase diagram of the Jaynes-Cummings-Hubbard model with application to ion chains

Abstract

We discuss analytic approximations to the ground state phase diagram of the homogeneous Jaynes-Cummings-Hubbard (JCH) Hamiltonian with general short-range hopping. The JCH model describes e.g. radial phonon excitations of a linear chain of ions coupled to an external laser field tuned to the red motional sideband with Coulomb mediated hopping or an array of high-$Q$ coupled cavities containing a two-level atom and photons. Specifically we consider the cases of a linear array of coupled cavities and a linear ion chain. We derive approximate analytic expressions for the boundaries between Mott-insulating and superfluid phases and give explicit expressions for the critical value of the hopping amplitude within the different approximation schemes. In the case of an array of cavities, which is represented by the standard JCH model we compare both approximations to numerical data from density-matrix renormalization group (DMRG) calculations.

9 pages, 5 figures, extended and corrected second version

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• Quantum phase transitions of light
• Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays
• Quantum Many-Body Phenomena in Coupled Cavity Arrays
• Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities
• Mixtures of Bosonic and Fermionic Atoms in Optical Lattices
• Superfluid-Mott Insulator Transition of Light in the Jaynes-Cummings Lattice
• Strong coupling theory for the Jaynes-Cummings-Hubbard model
• Quantum Fluctuations, Temperature and Detuning Effects in Solid-Light Systems
• Quantum phase transitions in photonic cavities with two-level systems
• Excitation spectra of strongly correlated lattice bosons and polaritons
• Quantum Phase Transitions of Light in the Dicke-Bose-Hubbard model

Cited by in corpus (21)

• Quantum simulations and many-body physics with light
• Simulation of a quantum phase transition of polaritons with trapped ions
• Non-equilibrium many-body effects in driven nonlinear resonator arrays
• Observation of Hopping and Blockade of Bosons in a Trapped Ion Spin Chain
• Repulsively induced photon super-bunching in driven resonator arrays
• Band Structure, Phase transitions and Semiconductor Analogs in One-Dimensional Solid Light Systems
• Polariton Mott insulator with trapped ions or circuit QED
• Exact $k$-body representation of the Jaynes-Cummings interaction in the dressed basis: Insight into many-body phenomena with light
• Supersolid and pair correlations of the extended Jaynes-Cummings-Hubbard model on triangular lattices
• Two-polariton bound states in the Jaynes-Cummings-Hubbard model
• Scattering and bound states of two polaritons in an array of coupled cavities
• Equilibrium and Disorder-induced behavior in Quantum Light-Matter Systems
• Worm quantum Monte-Carlo study of phase diagram of extended Jaynes-Cummings-Hubbard model
• The ergodic and non-ergodic phases in one dimensional clean Jaynes-Cummings-Hubbard system
• Fermionized photons in the ground state of one-dimensional coupled cavities
• Emergent photon pair propagation in circuit QED with superconducting processors
• Collective Modes in the Cooperative Jahn-Teller Model: Path Integral Approach
• A Parafermionic Generalization of the Jaynes Cummings Model
• Effective spin physics in two-dimensional cavity QED arrays
• Quantum simulation of superexchange magnetism in linear ion crystals
• Quantum phase transitions in the multiphoton Jaynes-Cummings-Hubbard model