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physica status solidi (b)

Fluctuation properties and charge resolution of the superconducting SET electrometer in the regime of cooper‐pair tunneling

A. Hädicke, Wolfram Krech

Published Feb 1, 1996• 0 citations
Publisher

Abstract

Abstract Single‐charge tunneling through a voltage‐biased SSS transistor with a capacitively coupled gate and an electromagnetic environment is considered. The dc Cooper‐pair current in the blockade region of quasiparticle tunneling is studied. Basing on a two‐level approximation, which can be used in the realistic case of low temperatures and small environment resistances, the mean dc Cooperpair current, the noise power spectrum, and the charge resolution are calculated as functions of the driving voltage and the external charge on the island.

DOI
10.1002/pssb.2221930224

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Abstract Single‐charge tunneling through a voltage‐biased SSS transistor with a capacitively coupled gate and an electromagnetic environment is considered. The dc Cooper‐pair current in the blockade region of quasiparticle tunneling is studied. Basing on a two‐level approximation, which can be used in the realistic case of low temperatures and small environment resistances, the mean dc Cooperpair current, the noise power spectrum, and the charge resolution are calculated as functions of the driving voltage and the external charge on the island.
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.
We show how population inversion (PI) occurs in a two-level system (TLS) while measuring its charge using a capacitively coupled superconducting single-electron transistor (SSET), biased in the subgap regime, where the current through the SSET is carried by different cycles involving tunneling of both Cooper pairs and quasiparticles. The PI is directly associated with the resonant nature of the Cooper-pair tunneling. We also show how the SSET may strongly relax the TLS, although there is negligible current flowing through the SSET, i.e. it is turned off. The calculation of the quantum back-action noise is based on a real-time Keldysh approach. We specifically discuss the case of a Cooper Pair Box qubit with the SSET capacitively coupled as read-out device.
We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even-odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasiparticle tunneling rates are comparable to the coherent Cooper pair oscillation frequency. Furthermore, the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.
We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even-odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasiparticle tunneling rates are comparable to the coherent Cooper pair oscillation frequency. Furthermore, the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.
We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures ( T< or =0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e(2) approximately 26 kOmega. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.
We investigate Cooper-pair tunneling in a circuit consisting of two dc-superconducting quantum interference devices in series, with a gate capacitively coupled to the central island. Measurements cover a wide range of values of the ratio between Josephson coupling energy EJ{E}_{J}EJ​ and charging energy EC{E}_{C}EC​. The EJEC\frac{{E}_{J}}{{E}_{C}}EC​EJ​​ ratio dependence of the supercurrent is well described by the orthodox theory provided that strong fluctuations of the Josephson phase due to the electromagnetic environment are taken into account. Our data can be interpreted in terms of squeezing of the charge fluctuations with decreasing EJEC\frac{{E}_{J}}{{E}_{C}}EC​EJ​​ ratio.