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IEEE Transactions on Applied Superconductivity

Superconducting Coulomb-Blockade electrometers with tunable Josephson coupling

A. Amar, D. Song, Christopher J. Lobb, F. C. Wellstood

Published Jun 1, 1997• 5 citations
Publisher

Abstract

We report measurements made on superconducting Al-AlO/sub x/-Al Coulomb-blockade electrometers with fixed gap /spl Delta/ and charging energy E/sub c/, but tunable Josephson coupling E/sub j/ via application of a magnetic field. This allows us to investigate the effects of changing the E/sub j//E/sub c/ ratio on the device characteristics. We compare the observed modulation with respect to magnetic field and gate voltage with the theoretical predictions in the supercurrent region.

DOI
10.1109/77.622162

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We report measurements made on superconducting Al-AlO/sub x/-Al Coulomb-blockade electrometers with fixed gap /spl Delta/ and charging energy E/sub c/, but tunable Josephson coupling E/sub j/ via application of a magnetic field. This allows us to investigate the effects of changing the E/sub j//E/sub c/ ratio on the device characteristics. We compare the observed modulation with respect to magnetic field and gate voltage with the theoretical predictions in the supercurrent region.
We have measured the current-voltage gate charge characteristics and noise in superconducting Coulomb-blockade electrometers from 50 mK to 1.05 K. The Al-AlO/sub x/-Al junctions in our devices have capacitances which range from 0.3 fF to 1 fF and tunneling resistances from 20 k/spl Omega/ to 200 k/spl Omega/. We find that our normal and superconducting electrometers have comparable charge noise but that the latter have much larger modulation which persists to significantly higher temperatures. The maximum operating temperature in the superconducting state is close to T/sub c/. This behavior Is consistent with a simple model and makes the superconducting electrometer preferable for many applications.>
We report measurements and quantum mechanical simulations of the behavior of superconducting two-junction Coulomb-blockade electrometers biased near the superconducting gap. Our quantum model allows coherent superpositions of states with different number of charges on the island. It predicts maximum current modulation /spl delta/I for devices with tunneling resistance R/sub /spl Sigma///spl ap/64/spl pi//spl Delta//spl planck//sup 2/C/sub /spl Sigma///sup 2//(e/sup 6//spl tau/), where /spl tau/ is the time for which the system maintains quantum coherence, C/sub /spl Sigma// is the total island capacitance and /spl Delta/ is the superconducting energy gap. For comparison, we built Al-AlO/sub x/-Al electrometers with R/sub /spl Sigma// from 61 k/spl Omega/ to 1.7 M/spl Omega/ and C/sub /spl Sigma// ranging from 0.9 fF to 8 fF. We find good agreement for /spl tau//spl ap/0.35 nsec.
In view of future macroscopic quantum experiments, we have fabricated prototypes of charge qubits (with tunable Josephson coupling and capacitive gate) provided with capacitively coupled readout single-electron transistor electrometers. The devices are prepared by electron beam direct-writing in conjunction with material deposition by sputtering. All leads are made of Al, and the AlO/sub x/ tunnel barriers are generated by local thermal oxidizing of the surface of the base striplines. The island electrodes are made of Al or Nb in a subsequent deposition step. In the case of Nb it is suitable to protect the barriers by a thin sputtered Al film first. The small-area (100 nm/spl times/100 nm) tunnel junctions have capacitances in the order of a few 10/sup -16/ F; their resistances can be adjusted in a wide range from k/spl Omega/ to M/spl Omega/ with an on-chip spread of less than 10%. The (double) superconducting gap energy was determined to be about 0.4 meV for Al and 1.4 meV for Nb, respectively. Measuring the so-called Coulomb staircase, we have demonstrated the operation of both qubit boxes and sub-e electrometers.
We study the Josephson current through a superconducting grain coupled by two tunnel junctions to macroscopic superconducting leads. As a result of the Coulomb blockade we predict the critical Josephson current to have a threshold behavior when the superconducting gap is suppressed below the charging energy by a magnetic field. This effect is a direct consequence of a discrimination by the superconducting ground state between odd and even number of electrons on the grain. The critical current is periodically modulated by the voltage of a gate electrostatically coupled to the grain. We find a characteristic change in this modulation at the threshold.
We have measured the Cooper pair transistor (CPT) in a tunable electromagnetic environment consisting of four one-dimensional superconducting quantum interference device arrays. The transport properties of the CPT in the high impedance limit, ${Z}_{\mathrm{env}}⪢{R}_{Q}\ensuremath{\simeq}6.45\phantom{\rule{0.3em}{0ex}}\mathrm{k}\ensuremath{\Omega}$, are studied for different ratios of the Josephson coupling energy to the charging energy. As the impedance of the environment is increased, the current-voltage characteristic (IVC) of the CPT develops a Coulomb blockade of Cooper pair tunneling and the measured IVCs agree qualitatively with a theory based on quasicharge dynamics for a CPT. Increasing the impedance of the environment induces a transition in the modulation of the IVC with the gate charge from eee-periodic to 2e2e2e-periodic.
The Cooper-pair tunneling in superconducting charge boxes in tunable electromagnetic environments is experimentally studied using a single-electron-transistor electrometer and via current-voltage characteristics measurement with small excitations. In the low-impedance regime, the environmental effect is quantified with an effective Josephson coupling energy, which is found to decrease as the environment impedance increases. In the high-impedance regime, the Cooper-pair tunneling is blockaded. For impedance above $250\phantom{\rule{0.3em}{0ex}}\mathrm{M}\ensuremath{\Omega}$, Coulomb oscillation of the zero-bias conductance suggests that Cooper-pair tunneling is completely suppressed and subgap quasiparticle tunneling becomes dominant.