Detecting Photon-Photon Interactions in a Superconducting Circuit

A local interaction between photons can be engineered by coupling a nonlinear system to a transmission line. The required high impedance transmission line can be conveniently formed from a chain of Josephson junctions. The nonlinearity is generated by side-coupling this chain to a Cooper pair box. We propose to probe the resulting photon-photon interactions via their effect on the current-voltage characteristic of a voltage-biased Josephson junction connected to the transmission line. Considering the Cooper pair box to be in the weakly anharmonic regime, we find that the dc current through the probe junction yields features around the voltages $2eV=n\hbar\omega_s$, where $\omega_s$ is the plasma frequency of the superconducting circuit. The features at $n\ge 2$ are a direct signature of the photon-photon interaction in the system.Comment: 10 pages, 7 figure

Spatial organization and evolutional period of the epidemic model using cellular automata

We investigate epidemic models with spatial structure based on the cellular automata method. The construction of the cellular automata is from the study by Weimar and Boon about the reaction-diffusion equations [Phys. Rev. E 49, 1749 (1994)]. Our results show that the spatial epidemic models exhibit the spontaneous formation of irregular spiral waves at large scales within the domain of chaos. Moreover, the irregular spiral waves grow stably. The system also shows a spatial period-2 structure at one dimension outside the domain of chaos. It is interesting that the spatial period-2 structure will break and transform into a spatial synchronous configuration in the domain of chaos. Our results confirm that populations embed and disperse more stably in space than they do in nonspatial counterparts.Comment: 6 papges,5 figures. published in Physics Review

Electron Removal Self Energy and its application to Ca2CuO2Cl2

We propose using the self energy defined for the electron removal Green's function. Starting from the electron removal Green's function, we obtained expressions for the removal self energy Sigma^ER (k,omega) that are applicable for non-quasiparticle photoemission spectral functions from a single band system. Our method does not assume momentum independence and produces the self energy in the full k-omega space. The method is applied to the angle resolved photoemission from Ca_2CuO_2Cl_2 and the result is found to be compatible with the self energy value from the peak width of sharp features. The self energy is found to be only weakly k-dependent. In addition, the Im Sigma shows a maximum at around 1 eV where the high energy kink is located.Comment: 5 pages, 3 figure

Primary thermometry triad at 6 mK in mesoscopic circuits

Quantum physics emerge and develop as temperature is reduced. Although mesoscopic electrical circuits constitute an outstanding platform to explore quantum behavior, the challenge in cooling the electrons impedes their potential. The strong coupling of such micrometer-scale devices with the measurement lines, combined with the weak coupling to the substrate, makes them extremely difficult to thermalize below 10 mK and imposes in-situ thermometers. Here we demonstrate electronic quantum transport at 6 mK in micrometer-scale mesoscopic circuits. The thermometry methods are established by the comparison of three in-situ primary thermometers, each involving a different underlying physics. The employed combination of quantum shot noise, quantum back-action of a resistive circuit and conductance oscillations of a single-electron transistor covers a remarkably broad spectrum of mesoscopic phenomena. The experiment, performed in vacuum using a standard cryogen-free dilution refrigerator, paves the way toward the sub-millikelvin range with additional thermalization and refrigeration techniques.Comment: Article and Supplementar

Sharp interface limits of phase-field models

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the ``sharp interface limit'' from phase field models which have interfaces that are diffuse on a length scale $\xi$. In particular,phase-field equations are mapped onto sharp interface equations in the limits $\xi \kappa \ll 1$ and $\xi v/D \ll 1$, where $\kappa$ and $v$ are respectively the interface curvature and velocity and $D$ is the diffusion constant in the bulk. The calculations provide one general set of sharp interface equations that incorporate the Gibbs-Thomson condition, the Allen-Cahn equation and the Kardar-Parisi-Zhang equation.Comment: 17 pages, 9 figure

Monte Carlo Simulation Calculation of Critical Coupling Constant for Continuum \phi^4_2

We perform a Monte Carlo simulation calculation of the critical coupling constant for the continuum {\lambda \over 4} \phi^4_2 theory. The critical coupling constant we obtain is [{\lambda \over \mu^2}]_crit=10.24(3).Comment: 11 pages, 4 figures, LaTe

Quadrupole collective modes in trapped finite-temperature Bose-Einstein condensates

Finite temperature simulations are used to study quadrupole excitations of a trapped Bose-Einstein condensate. We focus specifically on the m=0 mode, where a long-standing theoretical problem has been to account for an anomalous variation of the mode frequency with temperature. We explain this behavior in terms of the excitation of two separate modes, corresponding to coupled motion of the condensate and thermal cloud. The relative amplitudes of the modes depends sensitively on the temperature and on the frequency of the harmonic drive used to excite them. Good agreement with experiment is found for appropriate drive frequencies.Comment: 4 pages, 3 figure

Spatial soliton robustness against spatially anisotropic phase perturbations

We demonstrate experimentally that spatial solitons in AlGaAs waveguides are resilient against spatially anisotropic perturbations in their phase caused by introducing a wedge in the soliton propagation path. In agreement with numerical simulations, the solitons maintained their initial beam shape and width, independent of the fraction of the soliton beam intercepted by the wedge