Eigenstates of a Small Josephson Junction Coupled to a Resonant Cavity

We carry out a quantum-mechanical analysis of a small Josephson junction coupled to a single-mode resonant cavity. We find that the eigenstates of the combined junction-cavity system are strongly entangled only when the gate voltage applied at one of the superconducting islands is tuned to certain special values. One such value corresponds to the resonant absorption of a single photon by Cooper pairs in the junction. Another special value corresponds to a {\em two-photon} absorption process. Near the single-photon resonant absorption, the system is accurately described by a simplified model in which only the lowest two levels of the Josephson junction are retained in the Hamiltonian matrix. We noticed that this approximation does not work very well as the number of photons in the resonator increases. Our system shows also the phenomenon of ``collapse and revival'' under suitable initial conditions, and our full numerical solution agrees with the two level approximation result.Comment: 7 pages, and 6 figures. To be published in Phys. Rev.

Letters of Comment

Letters from readers in The Mythic Circle #

Resonant-Cavity-Induced Phase Locking and Voltage Steps in a Josephson Array

We describe a simple dynamical model for an underdamped Josephson junction array coupled to a resonant cavity. From numerical solutions of the model in one dimension, we find that (i) current-voltage characteristics of the array have self-induced resonant steps (SIRS), (ii) at fixed disorder and coupling strength, the array locks into a coherent, periodic state above a critical number of active Josephson junctions, and (iii) when $N_a$ active junctions are synchronized on an SIRS, the energy emitted into the resonant cavity is quadratic with $N_a$. All three features are in agreement with a recent experiment [Barbara {\it et al}, Phys. Rev. Lett. {\bf 82}, 1963 (1999)]}.Comment: 4 pages, 3 eps figures included. Submitted to PRB Rapid Com

Gradient mapping of pattern ground characteristics from a photomosaic of the IBP tundra biome site near Barrow, Alaska

An air photographic mosaic covering an area of 44.5×10 5 m 2 was subdivided into 741 rectangular cells (60×100 m). Pattern frequency, center relief, shape, and wedge image clarity were tabulated using three states for each character on a nominal scale. These state variables were converted to an interval scale by the application of a spatial smoothing filter. The new values were subjected to a principal components analysis which indicated that a parsimonious classification of pattern spatial variation could be constructed by equally weighting the first three nominal variables (frequency, relief, shape). The maps derived from this scheme indicate the areas on the tundra surface where polygon evolution may be occurring at the present time.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43203/1/11004_2005_Article_BF02082889.pd

Benevolent characteristics promote cooperative behaviour among humans

Cooperation is fundamental to the evolution of human society. We regularly observe cooperative behaviour in everyday life and in controlled experiments with anonymous people, even though standard economic models predict that they should deviate from the collective interest and act so as to maximise their own individual payoff. However, there is typically heterogeneity across subjects: some may cooperate, while others may not. Since individual factors promoting cooperation could be used by institutions to indirectly prime cooperation, this heterogeneity raises the important question of who these cooperators are. We have conducted a series of experiments to study whether benevolence, defined as a unilateral act of paying a cost to increase the welfare of someone else beyond one's own, is related to cooperation in a subsequent one-shot anonymous Prisoner's dilemma. Contrary to the predictions of the widely used inequity aversion models, we find that benevolence does exist and a large majority of people behave this way. We also find benevolence to be correlated with cooperative behaviour. Finally, we show a causal link between benevolence and cooperation: priming people to think positively about benevolent behaviour makes them significantly more cooperative than priming them to think malevolently. Thus benevolent people exist and cooperate more

Dynamics of a Josephson Array in a Resonant Cavity

We derive dynamical equations for a Josephson array coupled to a resonant cavity by applying the Heisenberg equations of motion to a model Hamiltonian described by us earlier [Phys. Rev. B {\bf 63}, 144522 (2001); Phys. Rev. B {\bf 64}, 179902 (E)]. By means of a canonical transformation, we also show that, in the absence of an applied current and dissipation, our model reduces to one described by Shnirman {\it et al} [Phys. Rev. Lett. {\bf 79}, 2371 (1997)] for coupled qubits, and that it corresponds to a capacitive coupling between the array and the cavity mode. From extensive numerical solutions of the model in one dimension, we find that the array locks into a coherent, periodic state above a critical number of active junctions, that the current-voltage characteristics of the array have self-induced resonant steps (SIRS's), that when $N_a$ active junctions are synchronized on a SIRS, the energy emitted into the resonant cavity is quadratic in $N_a$, and that when a fixed number of junctions is biased on a SIRS, the energy is linear in the input power. All these results are in agreement with recent experiments. By choosing the initial conditions carefully, we can drive the array into any of a variety of different integer SIRS's. We tentatively identify terms in the equations of motion which give rise to both the SIRS's and the coherence threshold. We also find higher-order integer SIRS's and fractional SIRS's in some simulations. We conclude that a resonant cavity can produce threshold behavior and SIRS's even in a one-dimensional array with appropriate experimental parameters, and that the experimental data, including the coherent emission, can be understood from classical equations of motion.Comment: 15 pages, 10 eps figures, submitted to Phys. Rev.

Intraneural pseudocyst (so-called ganglion) in an unusual retroperitoneal periadnexal location?

A case of an unusual unilocular cystic lesion of diameter 7 cm located retroperitoneally in the pelvis in close connection to the right adnexa of a 61 year-old woman is presented. Macroscopically, the lesion had a smooth outer and inner surface and was filled with translucent fluid. Histological examination revealed a fibrous and hyalinized wall which lacked a specific lining. Numerous nerve bundles in the cyst wall constituted the most conspicuous element of its histology possibly with some contribution of perineurial and/or mesothelial components. The morphology and immunohistochemistry speak for an intraneural pseudocyst sometimes called intraneural ganglion cyst which is rare in this location