Ž . Materials Science and Engineering C 19 2002 333–337 www.elsevier.comrlocatermsec Similarities between single charge and Josephson effects and devices. A fast and sensitive radio frequency single electron transistor A. Aassime, K. Bladh, T. Claeson ) , P. Delsing, D. Gunnarsson Physics and Engineering Physics, Chalmers UniÕersity of Technology and Goteborg UniÕersity, S-41296 Gothenburg, Sweden ¨ Abstract Ž . There are several dualities between Josephson and single charge tunneling, being conjugate phenomena, where either the phase flux Ž . Ž . or the number charge states are well determined while the complementary entity number, phase is undetermined. A zero voltage, phase-dependent current flows in the Josephson junction up to a critical current value while no current flows in the Coulomb blockade region, up to a threshold voltage, in a single charge element having high resistance and small Josephson coupling. The dual of the Ž . Ž . extremely flux sensitive DC superconducting quantum interference device SQUID is the single charge transistor SET . It has an outstanding charge sensitivity but its high impedance severely limits its bandwidth. A superconducting radio frequency version, RF-SET, is related to the common RF-SQUID and its bandwidth is improved orders of magnitude compared to the usual SET. A charge sensitivity of the order of 3 =10 y6 er6Hz has been demonstrated. It can be used, e.g., as a read out of the charge of a quantum Aqu-bitB. The latter is, in this case, based upon the charge state of a small island, being a superposition of a charge or not a charge, which can be compared with a flux based qu-bit where currents go clock- or anti-clockwise in a SQUID loop. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Josephson tunneling; Coulomb blockade; Single electron transistor 1. Introduction Josephson and single charge tunneling are conjugate Ž phenomena occurring in strongly and weakly coupled low . and high resistance superconducting tunnel junctions. They lead to complementary effects and devices. The phase f Ž . Ž . flux, F or the number n charge, Q states are well determined in the two situations, respectively, while the Ž . complementary entity number, phase is undetermined. Ž As well as we write E xE p G hr2p for the uncertainties in position and momentum of a particle, we get E F E Q F hr2p for the uncertainties in phase and charge of a supercon- . ducting element. A phase-dependent current flows in the Josephson junction, at zero voltage, up to a critical current value, I s I sin f, while no current flows in the Coulomb c blockade region, up to a threshold voltage V , in the single th w x charge regime 1,2 . The single charge transistor, consist- ing of an island coupled to the environment via two high impedance tunnel junctions, is the dual of the extremely flux sensitive DC superconducting quantum interference Ž . device DC-SQUID . Charge can be coupled externally to the island via a gate and this charge controls the current ) Corresponding author. Tel.: q 46-31-7723304; fax: q 46-31-7723471. Ž . E-mail address: f4atc@fy.chalmers.se T. Claeson . through the series coupled junctions. The single-electron Ž . w x transistor SET 3,4 has a charge sensitivity that is not matched by any other device. However, its high impedance severely limits its bandwidth. Significant effort has been undertaken to increase the bandwidth by impedance trans- w x formation and subsequent cold stage amplification 5,6 . This work describes a novel mode of operation, called RF Ž . wx radio frequency -SET 7 , related to the dual RF-SQUID wx 8 based on low resistance Josephson junctions. Its band- width is improved by several orders of magnitude as compared to previous directly coupled devices. Its sensitiv- y6 wx ity has reached a value of about 6 = 10 er6Hz 9 , now being improved to about 3 = 10 y6 er6Hz. The RF-SET may be used in applications from very w x sensitive charge meters and current standards 10 , where electrons are counted one by one, to the read out of w x quantum bits, i.e. qubits, 11,12,13,14 . A qubit, or a Ž . w x Single Cooper pair Box SCB 15 is, in this case, based upon the charge state of a small island connected via a Josephson junction to a reservoir. It is possible to create a superposition of charge states involving a discrete number of excess Cooper pairs on the island. These charge qubits can be compared with recently suggested flux state-based w x qubits 14 where the flux in a SQUID loop is a superposi- tion of fluxes, which are due to currents going clock- or 0928-4931r02r$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. Ž . PII: S0928-4931 01 00412-X