Many Body Physics with Coupled Transmission Line Resonators

We present the Josephson junction intersected superconducting transmission line resonator. In contrast to the Josephson parametric amplifier, Josephson bifurcation amplifier and Josephson parametric converter we consider the regime of few microwave photons. We review the derivation of eigenmode frequencies and zero point fluctuations of the nonlinear transmission line resonator and the derivation of the eigenmode Kerr nonlinearities. Remarkably these nonlinearities can reach values comparable to Transmon qubits rendering the device ideal for accessing the strongly correlated regime. This is particularly interesting for investigation of quantum many-body dynamics of interacting particles under the influence of drive and dissipation. We provide current profiles for the device modes and investigate the coupling between resonators in a network of nonlinear transmission line resonators.Comment: submitted to the proceedings of the CEWQO 2012 conferenc

Synchronized Switching in a Josephson Junction Crystal

We consider a superconducting coplanar waveguide resonator where the central conductor is interrupted by a series of uniformly spaced Josephson junctions. The device forms an extended medium that is optically nonlinear on the single photon level with normal modes that inherit the full nonlinearity of the junctions but are nonetheless accessible via the resonator ports. For specific plasma frequencies of the junctions a set of normal modes clusters in a narrow band and eventually become entirely degenerate. Upon increasing the intensity of a red detuned drive on these modes, we observe a sharp and synchronized switching from low occupation quantum states to high occupation classical fields, accompanied by a pronounced jump from low to high output intensity.Comment: 13 pages, 5 figure

A "Single-Photon" Transistor in Circuit Quantum Electrodynamics

We introduce a circuit quantum electrodynamical setup for a "single-photon" transistor. In our approach photons propagate in two open transmission lines that are coupled via two interacting transmon qubits. The interaction is such that no photons are exchanged between the two transmission lines but a single photon in one line can completely block respectively enable the propagation of photons in the other line. High on-off ratios can be achieved for feasible experimental parameters. Our approach is inherently scalable as all photon pulses can have the same pulse shape and carrier frequency such that output signals of one transistor can be input signals for a consecutive transistor.Comment: Analysis of pure dephasing, time delays between pulses and gain added. Word "quantum" dropped from title, to appear in Phys. Rev. Let

Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities

We study the properties of an array of QED-cavities coupled by nonlinear elements in the presence of photon leakage and driven by a coherent source. The main effect of the nonlinear couplings is to provide an effective cross-Kerr interaction between nearest-neighbor cavities. Additionally, correlated photon hopping between neighboring cavities arises. We provide a detailed mean-field analysis of the steady-state phase diagram as a function of the system parameters, the leakage, and the external driving, and show the emergence of a number of different quantum phases. A photon crystal associated to a spatial modulation of the photon blockade appears. The steady state can also display oscillating behavior and bistability. In some regions the crystalline ordering may coexist with the oscillating behavior. Furthermore we study the effect of short-range quantum fluctuations by employing a cluster mean-field analysis. Focusing on the corrections to the photon crystal boundaries, we show that, apart for some quantitative differences, the cluster mean field supports the findings of the simple single-site analysis. In the last part of the paper we concentrate on the possibility to build up the class of arrays introduced here, by means of superconducting circuits of existing technology. We consider a realistic choice of the parameters for this specific implementation and discuss some properties of the steady-state phase diagram.Comment: 11 pages, 12 figure

Photon solid phases in driven arrays of nonlinearly coupled cavities

We introduce and study the properties of an array of QED cavities coupled by nonlinear elements, in the presence of photon leakage and driven by a coherent source. The nonlinear couplings lead to photon hopping and to nearest-neighbor Kerr terms. By tuning the system parameters, the steady state of the array can exhibit a photon crystal associated with a periodic modulation of the photon blockade. In some cases, the crystalline ordering may coexist with phase synchronization. The class of cavity arrays we consider can be built with superconducting circuits of existing technology.Comment: 8 pages, 8 figures. Published versio

An infant mouse model of brain damage in pneumococcal meningitis

Bacterial meningitis due to Streptococcus pneumoniae is associated with an significant mortality rate and persisting neurologic sequelae including sensory-motor deficits, seizures, and impairments of learning and memory. The histomorphological correlate of these sequelae is a pattern of brain damage characterized by necrotic tissue damage in the cerebral cortex and apoptosis of neurons in the hippocampal dentate gyrus. Different animal models of pneumococcal meningitis have been developed to study the pathogenesis of the disease. To date, the infant rat model is unique in mimicking both forms of brain damage documented in the human disease. In the present study, we established an infant mouse model of pneumococcal meningitis. Eleven-days-old C57BL/6 (n=299), CD1 (n=42) and BALB/c (n=14) mice were infected by intracisternal injection of live Streptococcus pneumoniae. Sixteen hours after infection, all mice developed meningitis as documented by positive bacterial cultures of the cerebrospinal fluid. Sixty percent of infected C57BL/6 mice survived more than 40h after infection (50% of CD1, 0% of BALB/c). Histological evaluations of brain sections revealed apoptosis in the dentate gyrus of the hippocampus in 27% of infected C57BL/6 and in 5% of infected CD1 mice. Apoptosis was confirmed by immunoassaying for active caspase-3 and by TUNEL staining. Other forms of brain damage were found exclusively in C57BL/6, i.e. caspase-3 independent (pyknotic) cell death in the dentate gyrus in 2% and cortical damage in 11% of infected mice. This model may prove useful for studies on the pathogenesis of brain injury in childhood bacterial meningiti