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APPLIED PHYSICS LETTERS 92 212504 2008 A semiempirical model for two level system noise in superconducting microresonators Jiansong Gao 1 a Miguel Daal 2 John M Martinis 3 Anastasios Vayonakis 1 Jonas Zmuidzinas 1 Bernard Sadoulet 2 Benjamin A Mazin 4 Peter K Day 4 and Henry G Leduc4 1 Division of Physics Mathematics and Astronomy California Institute of Technology Pasadena California 91125 USA 2 Physics Department University of California at Berkeley Berkeley California 94720 USA 3 Department of Physics University of California Santa Barbara California 93106 USA 4 Jet Propulsion Laboratory California Institute of Technology Pasadena California 91109 USA Received 2 April 2008 accepted 9 May 2008 published online 29 May 2008 We present measurements of the low temperature excess frequency noise of four niobium superconducting coplanar waveguide microresonators with center strip widths sr ranging from 3 to 20 m For a fixed internal power we find that the frequency noise decreases rapidly with increasing center strip width scaling as 1 sr1 6 We show that this geometrical scaling is readily explained by a simple semiempirical model which assumes a surface distribution of independent two level system fluctuators These results allow the resonator geometry to be optimized for minimum noise 2008 American Institute of Physics DOI 10 1063 1 2937855 Thin film superconducting microresonators are of great interest for a number of applications see Refs 1 4 and references therein Excess frequency noise is universally observed in these resonators2 5 6 and is very likely caused by two level systems TLSs in dielectric materials 3 7 Indeed the TLS hypothesis is supported by the observed dependence of the noise on resonator internal power7 8 and temperature 3 In a recent paper4 paper A hereafter we presented measurements of the TLS induced low temperature frequency shifts of five niobium Tc 9 2 K coplanar waveguide CPW resonators with varying center strip widths sr From the observed

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