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Register a new userDynamical critical exponent of the Jaynes-Cummings-Hubbard model
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An array of high-Q electromagnetic resonators coupled to qubits gives rise to the Jaynes-Cummings-Hubbard model describing a superfluid to Mott insulator transition of lattice polaritons. From mean-field and strong coupling expansions, the critical properties of the model are expected to be identical to the scalar Bose-Hubbard model. A recent Monte Carlo study of the superfluid density on the square lattice suggested that this does not hold for the fixed-density transition through the Mott lobe tip. Instead, mean-field behavior with a dynamical critical exponent z=2 was found. We perform large-scale quantum Monte Carlo simulations to investigate the critical behavior of the superfluid density and the compressibility. We find z=1 at the tip of the insulating lobe. Hence the transition falls in the 3D XY universality class, analogous to the Bose-Hubbard model.
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Jaynes-Cummings-Hubbard lattices provide unique properties for the study of correlated phases as they exhibit convenient state preparation and measurement, as well as in situ tuning of parameters. We show how to realize charge density and supersolid phases in Jaynes-Cummings-Hubbard lattices in the presence of long-range interactions. The long-range interactions are realized by the consideration of Rydberg states in coupled atom-cavity systems and the introduction of additional capacitive couplings in quantum-electrodynamics circuits. We demonstrate the emergence of supersolid and checkerboard solid phases, for calculations which take into account nearest neighbour couplings, through a mean-field decoupling.
We analyze the driven resonantly coupled Jaynes-Cummings model in terms of a quasienergy approach by switching to a frame rotating with the external modulation frequency and by using the dressed atom picture. A quasienergy surface in phase space emerges whose level spacing is governed by a rescaled effective Planck constant. Moreover, the well-known multiphoton transitions can be reinterpreted as resonant tunneling transitions from the local maximum of the quasienergy surface. Most importantly, the driving defines a quasienergy well which is nonperturbative in nature. The quantum mechanical quasienergy state localized at its bottom is squeezed. In the Purcell limited regime, the potential well is metastable and the effective local temperature close to its minimum is uniquely determined by the squeezing factor. The activation occurs in this case via dressed spin flip transitions rather than via quantum activation as in other driven nonlinear quantum systems such as the quantum Duffing oscillator. The local maximum is in general stable. However, in presence of resonant coherent or dissipative tunneling transitions the system can escape from it and a stationary state arises as a statistical mixture of quasienergy states being localized in the two basins of attraction. This gives rise to a resonant or an antiresonant nonlinear response of the cavity at multiphoton transitions. The model finds direct application in recent experiments with a driven superconducting circuit QED setup.
We study the ground state phase diagrams of two-photon Dicke, the one-dimensional Jaynes-Cummings-Hubbard (JCH), and Rabi-Hubbard (RH) models using mean field, perturbation, quantum Monte Carlo (QMC), and density matrix renormalization group (DMRG) methods. We first compare mean field predictions for the phase diagram of the Dicke model with exact QMC results and find excellent agreement. The phase diagram of the JCH model is then shown to exhibit a single Mott insulator lobe with two excitons per site, a superfluid (SF, superradiant) phase and a large region of instability where the Hamiltonian becomes unbounded. Unlike the one-photon model, there are no higher Mott lobes. Also unlike the one-photon case, the SF phases above and below the Mott are surprisingly different: Below the Mott, the SF is that of photon {it pairs} as opposed to above the Mott where it is SF of simple photons. The mean field phase diagram of the RH model predicts a transition from a normal to a superradiant phase but none is found with QMC.
We present a dynamical mean-field study of two-particle dynamical response functions in two-band Hubbard model across several phase transitions. We observe that the transition between theexcitonic condensate and spin-state ordered state is continuous with a narrow strip of supersolidphase separating the two. Approaching transition from the excitonic condensate is announced bysoftening of the excitonic mode at theMpoint of the Brillouin zone. Inside the spin-state orderedphase there is a magnetically ordered state with 2x2 periodicity, which has no precursor in thenormal phase.
We consider the Jaynes-Cummings model of a single quantum spin $s$ coupled to a harmonic oscillator in a parameter regime where the underlying classical dynamics exhibits an unstable equilibrium point. This state of the model is relevant to the physics of cold atom systems, in non-equilibrium situations obtained by fast sweeping through a Feshbach resonance. We show that in this integrable system with two degrees of freedom, for any initial condition close to the unstable point, the classical dynamics is controlled by a singularity of the focus-focus type. In particular, it displays the expected monodromy, which forbids the existence of global action-angle coordinates. Explicit calculations of the joint spectrum of conserved quantities reveal the monodromy at the quantum level, as a dislocation in the lattice of eigenvalues. We perform a detailed semi-classical analysis of the associated eigenstates. Whereas most of the levels are well described by the usual Bohr-Sommerfeld quantization rules, properly adapted to polar coordinates, we show how these rules are modified in the vicinity of the critical level. The spectral decomposition of the classically unstable state is computed, and is found to be dominated by the critical WKB states. This provides a useful tool to analyze the quantum dynamics starting from this particular state, which exhibits an aperiodic sequence of solitonic pulses with a rather well defined characteristic frequency.
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