948 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO. 2, JUNE 2003 Feasibility Studies of Ultra-Small Josephson Junctions for Qubits Alexander Ya. Tzalenchuk, Tobias Lindström, Serge A. Charlebois, Evgueni A. Stepantsov, Alexandre M. Zagoskin, Zdravko Ivanov, and Tord Claeson Abstract—Most proposed realizations of a high temperature su- perconductor (HTS) qubit (e.g., [1]) require the use of very small Josephson junctions. The properties of bicrystal junctions are es- pecially interesting since they make it possible to implement several types of flux qubits in a relatively simple way. We have developed a technique that allows us to produce high quality sub-micrometer junctions in a reproducible way using bicrystal technology. We have successfully fabricated and characterized a large number of YBCO junctions and SQUIDs with bridge width as small as 0.2 micrometer on 0 –3 ,0 –40 and 0 –45 bicrystal STO substrates. The properties of these junctions have been extensively exam- ined at temperatures down to 20 mK. The effects of external mag- netic fields on these structures have been investigated. Figures of merit for the proposed qubits were also extracted from these mea- surements. Index Terms—D-wave symmetry, high-temperature supercon- ductivity, Josephson effect, quantum computing, sub-micrometer grain boundary Josephson junctions. I. INTRODUCTION I T IS WELL known that bicrystal Josephson junctions fabri- cated on high-angle substrates exhibit a number of unusual features [2], [3]. The fact that most of these properties are di- rect consequences of the predominant d-wave symmetry of the superconducting wave-function is well established. Much progress in the field of quantum computing has been achieved over the past few years. A number of groups have suc- cessfully demonstrated that it is indeed possible to fabricate the basic building blocks of quantum computers, so-called qubits, using solid-state technology [4]–[6]. Most of these implemen- tations have used superconducting elements as an integral part of their design, yet all of these structures have been fabricated using conventional (i.e., low- ) superconductors. It has been suggested that junctions and SQUIDs fabricated in YBCO might have certain advantages over their conventional counterparts [7]. In phase-qubits, the d-wave symmetry can be Manuscript received August 6, 2002. The work is supported in parts by D-Wave Systems, Canada, and the Fonds québécois de la recherche sur la nature et les technologies, Canada. A. Ya. Tzalenchuk is with the National Physics Laboratory. (e-mail: alexander.tzalenchuk@npl.co.uk). E. A. Stepantsov is with the Institute of Crystallography, Russian Academy of Science, Moscow, Russia. T. Lindström, S. A. Charlebois, Z. Ivanov, and T. Claeson are with the Department of Microelectronics and Nanoscience, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden. (e-mail: f4azi@fy.chalmers.se) A. M. Zagoskin is with D-Wave Systems, Canada and the Physics and As- tronomy Department, University of British Columbia, Vancouver, Canada. Digital Object Identifier 10.1109/TASC.2003.814158 used to self-bias the qubit. There are a number of suggested qubit-implementations that uses high- superconductor (HTS) but so far none has been demonstrated experimentally. One of the greatest obstacles has been that the existing technologies for fabrication HTS nanostructures are very limited and the repro- ducibility is very poor. We have developed a technique that allows us to produce high quality sub-micrometer junctions in a reproducible way using bicrystal technology. Using this technology we have fabricated and characterized a large number of Josephson junctions and SQUIDs on 0 –30 ,0 –40 and a 0 –45 bicrystal substrates. The bridge width can be as small as 0.2 m. We have extracted figures of merit for the proposed qubits using our data. II. THEORETICAL BACKGROUND A. D-Wave Symmetry In the case of an order parameter with d-wave symmetry, the current-phase relation (CPR) of HTS Josephson junctions is not a simple sinusoidal function of the phase but rather the sum of many harmonics. A consequence of the d-wave symmetry is that in 0 –45 grain boundary Josephson junctions (GBJJ) the first harmonic of the CPR is suppressed by symmetry, tunneling from a lobe to a node of the order parameter being forbidden. The supercurrent is then only due to higher harmonics of the CPR, mainly the second. This simple picture is only valid in the clean ballistic limit. It can however be shown that the 1st harmonic will still be sup- pressed for a more realistic interface but with a strong temper- ature dependence [10], [12]. The 2nd harmonic will only dom- inate below some definite temperature . Any form of scat- tering will also tend to reestablish the domination of the 1st harmonic. The interplay between the 1st ( -periodic) and 2nd ( -periodic) harmonics of the CPR of 0 –45 GBJJ has unique effects that could prove to be very useful for qubit implementa- tion. B. Phase Qubits Utilizing the D-wave Symmetry There are two classes of superconducting qubits characterized by the ratio of the Josephson energy to the charging energy . The phase qubits are those for which sets the scale of operation . An important distinction between the concept described in this paper and phase-qubits based on conventional superconductivity is that in our case the double-well potential, with relevant Josephson energy scale 1051-8223/03$17.00 © 2003 IEEE Authorized licensed use limited to: Universite De Sherbrooke. Downloaded on September 29, 2009 at 11:36 from IEEE Xplore. Restrictions apply.