We investigate the simulation of Jahn-Teller models with two nondegenerate vibrational modes using a circuit QED architecture. Typical Jahn-Teller systems are anisotropic and require at least a two-frequency description. The proposed simulator consists of two superconducting lumped-element resonators interacting with a common flux qubit in the ultrastrong coupling regime. We translate the circuit QED model of the system to a two-frequency Jahn-Teller Hamiltonian and calculate its energy eigenvalues and the emission spectrum of the cavities. It is shown that the system can be systematically tuned to an effective single-mode Hamiltonian from the two-mode model by varying the coupling strength between the resonators. The flexibility in manipulating the parameters of the circuit QED simulator permits the isolation of the effective single-frequency and pure two-frequency effects in the spectral response of Jahn-Teller systems.

We consider the nonlinear effects in Jahn-Teller system of two coupled resonators interacting simultaneously with flux qubit using Circuit QED. Two frequency description of Jahn Teller system that inherits the networked structure of both nonlinear Josephson Junctions and harmonic oscillators is employed to describe the synchronous structures in multifrequency scheme. Emergence of dominating mode is investigated to analyze frequency locking by eigenvalue spectrum. Rabi Supersplitting is tuned for coupled and uncoupled synchronous configurations in terms of frequency entrainment switched by coupling strength between resonators. Second order coherence functions are employed to investigate self-sustained oscillations in resonator mode and qubit dephasing. Snychronous structure between correlations of priviledged mode and qubit is obtained in localization-delocalization and photon blockade regime controlled by the population imbalance.

The boundary effects on the Bose-Einstein condensation with a nonvanishing chemical potential on an ultra-static space-time are studied. High temperature regime, which is the relevant regime for the relativistic gas, is studied through the heat kernel expansion for both Dirichlet and Neumann boundary conditions. The high temperature expansion in the presence of a chemical potential is generated via the Mellin transform method as applied to the harmonic sums representing the free energy and the depletion coefficient. The effects of boundary conditions on the relation between the depletion coefficient and the temperature are analyzed. Both charged and neutral bosons are considered.

We consider the single photon transistor in coupled cavity system of resonators interacting with multilevel superconducting artificial atom simultaneously. Effective single mode transformation is used for the diagonalization of the hamiltonian and impedance matching in terms of the normal modes. Storage and transmission of the incident field are described by the interactions between the cavities controlling the atomic transitions of lowest lying states. Rabi splitting of vacuum induced multiphoton transitions is considered in input/output relations by the quadrature operators in the absence of the input field. Second order coherence functions are employed to investigate the photon blockade and delocalization-localization transitions of cavity fields. Spontaneous virtual photon conversion into real photons is investigated in localized and oscillating regimes. Reflection and transmission of cavity output fields are investigated in the presence of the multilevel transitions. Accumulation and firing of the reflected and transmitted fields are used to investigate the synchronization of the bunching spike train of transmitted field and population imbalance of cavity fields. In the presence of single photon gate field, gain enhancement is explained for transmitted regime.

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We consider the Molecular Opto-mechanical systems in back-action amplification of single molecule Raman imaging. Surface Enhanced Raman Scattering (SERS) is mapped into the dissipative cavity optomechanics system of coupled resonators. We investigate the plasmon molecular vibration interactions in strong coupling regimes of cavity opto-mechanics in the presence of impurities. Eigenfunction spectrum is analyzed for the normal mode splitting of photonic and mechanical hybrid system. Back-action transduction of photons into mechanical modes is investigated by avoided crossing due to the nonlinear interactions and Casimir forces in the presence of virtual photons and radiation pressure. In Input-output coupled cavity scheme, both cavity and driving fields are analyzed for the absorption and dissipation of heat in weak and strong coupling regimes of the cascaded cavity setup. In terms of the second order coherence functions, thermodynamic work and heat engine is investigated via phonon lasing of mechanical mode in opto-mechanical implementation of Brownian motors by tuning the competing coupling strengths of impurities and nonlinearities.