Persistent current and voltage in a ring of Josephson junctions

My, Choi

doi:10.1103/physrevb.48.15920

Cited by 10 publications

(14 citation statements)

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“…Experimental studies of linear Josephson junction arrays have advanced at a rapid pace [10][11][12][13][14][15][16]. However, despite considerable theoretical work [17][18][19][20][21][22][23][24][25][26][27] methods for detailed modeling of larger circuit networks are needed to successfully chart the future territory of quantum coherence in networks of increasing size to, e.g., further explore the possibility of topological protection from decoherence [28][29][30][31]. The description presents a considerable challenge to theory due to the combination of several factors: the non-linearity induced by Josephson junctions, the increased number of low energy degrees of freedom, and the peculiar interactions between them induced by flux quantization.…”

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confidence: 99%

Symmetries and Collective Excitations in Large Superconducting Circuits

2013

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In this work, we present theoretical tools suitable for quantitative modeling of large superconducting circuits that include one-dimensional Josephson-junction arrays. The large number of low-energy degrees of freedom and the peculiar interactions between them induced by flux quantization present a considerable challenge to the detailed modeling of such circuits. For the concrete example of the fluxonium device, we show how to address this challenge. Starting from the complete degrees of freedom of the circuit, we employ the relevant collective modes and circuit symmetries to obtain a systematic approximation scheme. Important circuit symmetries include approximate invariance under the symmetric group and lead to considerable simplifications of the theory. Selection rules restrict the possible coupling among different collective modes and help explain the remarkable accuracy of previous simplified models. Using this strategy, we obtain new predictions for the energy spectrum of the fluxonium device that can be tested with current experimental technology.

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confidence: 99%

Symmetries and Collective Excitations in Large Superconducting Circuits

2013

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“…On the other hand, onedimensional (1D) chains of Josephson junctions, where quantum fluctuations should be more important, have been studied mainly in the two limiting cases: the selfcharging model and the nearest-neighbor model where only nearest neighboring charges interact [5,6]. In the 1D system with only self-capacitance, the role of dissipation on the quantum phase transition [7] as well as the persistence current and voltage [8] has also been considered.…”

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confidence: 99%

“…Note that without the off-diagonal term in C −1 ij , the first and the second terms in the action (3) would just be the Villain form of the cosine action along the τ direction [5,8]. To examine the effects of the off-diagonal term, we use the identity exp…”

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Quantum phase transitions in Josephson-junction chains

Choi

et al. 1998

Phys. Rev. B

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We investigate the quantum phase transition in a one-dimensional chain of ultra-small superconducting grains, considering both the self-and junction capacitances. At zero temperature, the system is transformed into a two-dimensional system of classical vortices, where the junction capacitance introduces anisotropy in the interaction between vortices. This leads to the superconductor-insulator transition of the Berezinskii-Kosterlitz-Thouless type, as the ratios of the Josephson coupling energy to the charging energies are varied. It is found that the junction capacitance plays a role similar to that of dissipation and tends to suppress quantum fluctuations; nevertheless the insulator region survives even for arbitrarily large values of the junction capacitance.PACS Numbers: 74.50.+r, 67.40.Db Quantum phase transitions, which are induced by quantum fluctuations at zero temperature, are distinguished from classical phase transitions in several important respects; this has attracted much attention in recent years [1]. In particular, advances in fabrication techniques have made available arrays of ultra-small superconducting grains, where the charging energy dominates the Josephson coupling energy and accordingly, quantum fluctuation effects are of paramount importance. Such Josephson-junction arrays have become a prototype system displaying quantum phase transitions between the superconducting and the insulating phases. In the vicinity of the superconductor-insulator transition, the fluctuation effects depend crucially on the dimensionality of the system. In the case of two-dimensional (2D) arrays, rich effects of quantum fluctuations and resulting phase transitions have been examined for a rather general form of the capacitance matrix, although there still exist unsettled issues in the quantum regime, such as lowtemperature re-entrance [2][3][4]. On the other hand, onedimensional (1D) chains of Josephson junctions, where quantum fluctuations should be more important, have been studied mainly in the two limiting cases: the selfcharging model and the nearest-neighbor model where only nearest neighboring charges interact [5,6]. In the 1D system with only self-capacitance, the role of dissipation on the quantum phase transition [7] as well as the persistence current and voltage [8] has also been considered.This paper investigates the quantum phase transitions in general Josephson-junction chains with both the selfand junction capacitances. At zero temperature, the system is transformed into a two-dimensional system of classical vortices, where the junction capacitance introduces anisotropy in the interaction between vortices. This leads to the superconductor-insulator transition of the Berezinskii-Kosterlitz-Thouless (BKT) type [9,10], as the ratios of the Josephson coupling energy to the charging energies are varied. Interestingly, the junction capacitance here plays a role similar to that of dissipation and tends to suppress quantum fluctuations, enhancing superconductivity. However, the suppression is not strong...

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“…In this Letter we are taking a different approach. When the dynamics of the 2D JJ array is dominated by capacitances of superconducting islands its T = 0 quantum statistical mechanics is equivalent [1,10,14,27,28] to the statistical mechanics of the classical xy spin system in 2 + 1 dimensions at B Figure the effective temperature T * = √ 2JU , with J being the Josephson energy of the junction and U being the charging energy of the superconducting island. The advantage of such a mapping is its suitability for large-scale Monte Carlo (MC) studies.…”

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Persistent current in a 2D Josephson junction array wrapped around a cylinder

Garanin

Chudnovsky

2016

EPL

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We study persistent currents in a Josephson junction array wrapped around a cylinder. The T = 0 quantum statistical mechanics of the array is equivalent to the statistical mechanics of a classical xy spin system in 2+1 dimensions at the effective temperature T * = √ 2JU , with J being the Josephson energy of the junction and U being the charging energy of the superconducting island. It is investigated analytically and numerically on lattices containing over one million sites. For weak disorder and T * J the dependence of the persistent current on disorder and T * computed numerically agrees quantitatively with the analytical result derived within the spin-wave approximation. The high-T * and/or strong-disorder behavior is dominated by instantons corresponding to the vortex loops in 2+1 dimensions. The current becomes destroyed completely at the quantum phase transition into the Cooper-pair insulating phase.

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Persistent current and voltage in a ring of Josephson junctions

Cited by 10 publications

References 14 publications

Symmetries and Collective Excitations in Large Superconducting Circuits

Symmetries and Collective Excitations in Large Superconducting Circuits

Quantum phase transitions in Josephson-junction chains

Persistent current in a 2D Josephson junction array wrapped around a cylinder

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