A Continuous Non-demolition Measurement of the Cs Clock Transition Pseudo-spin

We demonstrate a weak continuous measurement of the pseudo-spin associated with the clock transition in a sample of Cs atoms. Our scheme uses an optical probe tuned near the D1 transition to measure the sample birefringence, which depends on the z-component of the collective pseudospin. At certain probe frequencies the differential light shift of the clock states vanishes and the measurement is non-perturbing. In dense samples the measurement can be used to squeeze the collective clock pseudo-spin, and has potential to improve the performance of atomic clocks and interferometers.Comment: 4 pages, 4 figures, ReVTeX, modified text in response to referee's comment

Inequalities of wealth distribution in a conservative economy

We analyze a conservative market model for the competition among economic agents in a close society. A minimum dynamics ensures that the poorest agent has a chance to improve its economic welfare. After a transient, the system self-organizes into a critical state where the wealth distribution have a minimum threshold, with almost no agent below this poverty line, also, very few extremely rich agents are stable in time. Above the poverty line the distribution follows an exponential behavior. The local solution exhibits a low Gini index, while the mean field solution of the model generates a wealth distribution similar to welfare states like Sweden.Comment: 7 pages, 4 figures, submitted to Physica A, Proceedings of the VIII LAWNP, Salvador, Brazil, 200

Effect of disorder on the far-infrared conductivity and on the microwave conductivity of two-band superconductors

We consider the far-infrared and the microwave conductivities of a two-band superconductor with non-magnetic impurities. The strong coupling expressions for the frequency and temperature dependent conductivity of a two-band superconductor are developed assuming isotropic bands and interactions. Our numerical results obtained using realistic interaction parameters for MgB$_{2}$ are compared with experiments on this compound. We find that the available experimental results for the far-infrared conductivity of MgB$_{2}$ are consistent with multi-band superconductivity in the presence of a sufficiently strong interband impurity scattering. On the other hand, our numerical results for the microwave conductivity in the superconducting state indicate that the experimental results obtained on samples with the highest transition temperature $T_{c}$ are consistent with a low interband impurity scattering rate but depend sensitively on the ratio of the total scattering rates in the two bands. For the $\pi$-band scattering rate $\gamma_{\pi}$ not greater than the $\sigma$-band scattering rate $\gamma_{\sigma}$ there is a single, broad, low-temperature (at about 0.5$T_{c}$) coherence peak in the microwave conductivity. For $\gamma_{\pi}/\gamma_{\sigma}$=4--7 a high-temperature (at about 0.9$T_{c}$) coherence peak is dominant, but there is also a low-temperature peak/shoulder resulting from the contribution of the $\pi$-band carriers to the microwave conductivity. For $\gamma_{\pi}/\gamma_{\sigma}\gg$1 only the high-temperature coherence peak should be observable.Comment: 11 pages, 6 figure