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Physica Scripta

Quantum Complementarity for the Superconducting Condensate and the Resulting Electrodynamic Duality

David B. Haviland, 道生 渡部, P. gren, Karin Andersson

Published Jan 1, 2002• 4 citations
Publisher

Abstract

Experiments with small capacitance Josephson junction arrays are described that demonstrate the quantum behavior of the phase of the superconducting condensate. This quantum behavior is based on the complementarity of phase and number for a condensate state of many bosons. A key factor to observation of this quantum behavior is the coupling of the superconducting condensate state to dissipation in the electrodynamic environment of the Josephson junction. It is shown how one-dimensional Josephson junction arrays can be used to design an environment with very weak coupling to dissipation, allowing for measurement of condensate with well defined number. The well defined number is manifest in the Coulomb blockade of Cooper pair tunneling.

DOI
10.1238/physica.topical.102a00062

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Experiments with small capacitance Josephson junction arrays are described that demonstrate the quantum behavior of the phase of the superconducting condensate. This quantum behavior is based on the complementarity of phase and number for a condensate state of many bosons. A key factor to observation of this quantum behavior is the coupling of the superconducting condensate state to dissipation in the electrodynamic environment of the Josephson junction. It is shown how one-dimensional Josephson junction arrays can be used to design an environment with very weak coupling to dissipation, allowing for measurement of condensate with well defined number. The well defined number is manifest in the Coulomb blockade of Cooper pair tunneling.
We review experiments on small-capacitance Josephson junctions. When the Josephson junction is fabricated in the configuration of dc superconducting quantum interference device (SQUID), the Josephson coupling can be tuned IN SITU with an external magnetic field. The electrical transport properties of one-dimensional arrays of small-capacitance dc SQUIDs have been investigated in order to study the superconductor-insulator transition. The arrays have also been used to bias a single Josephson junction, and a clear Coulomb blockade of Cooper-pair tunneling has been observed in the single junction.
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 have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02−−0.6K),(T=0.02--0.6\mathrm{K}),(T=0.02−−0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.
We have investigated how the transport properties of small-Josephson-junction arrays vary depending on a quantum control parameter (the ratio of the Josephson coupling energy E J to the charging energy E C ), the magnitude of dissipation, and the dimensionality d of the system. We found that the arrays show Coulomb blockade behavior when R S is larger than about d R Q ( R Q ≡ h /4 e 2 =6.45 kΩ) and E J / E C is smaller than a threshold depending on the value of R S and the dimensionality. The result is discussed in terms of quantum phase transition induced by the charging effect and the dissipation.
We describe the fabrication and measurement of one-dimensional series arrays of small capacitance Josephson junctions and superconducting quantum interference devices. These arrays exhibit a Coulomb blockade of Cooper pair tunneling when the Josephson coupling energy is the order of the charging energy. The effectiveness of a resistive coaxial cable (ThermocoaxTM made by Philips) for attenuation of high frequency electromagnetic noise is demonstrated. This noise influences the measured dc current–voltage characteristic of the array, having qualitatively the same effect as raising the temperature.
We have measured the current–voltage characteristics of small-capacitance single Josephson junctions at low temperatures T ≤ 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. When the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e 2 ≈ 26 kΩ, a transition to a clear Coulomb blockade of Cooper-pair tunnelling is induced in the single junction. The measured blockade voltage agrees with the theoretical prediction.