Superconductor-to-insulator transition in linear arrays of Josephson junctions capacitively coupled to metallic films

We study the decay of superflow of a one-dimensional (1D) superfluid in the presence of a periodic potential. In 1D, superflow at zero temperature can decay via quantum nucleation of phase slips even when the flow velocity is much smaller than the critical velocity predicted by mean-field theories. Applying the instanton method to the O(2) quantum rotor model, we calculate the nucleation rate of quantum phase slips Γ. When the flow momentum p is small, we find that the nucleation rate per unit length increases algebraically with p as Γ/L ∝ p 2K−2 , where L is the system size and K is the Tomonaga-Luttinger parameter. Based on the relation between the nucleation rate and the quantum superfluid-insulator transition, we present a unified explanation on the scaling formulae of the nucleation rate for periodic, disorder, and single-barrier potentials. Using the time-evolving block decimation method, we compute the exact quantum dynamics of the superflow decay in the 1D Bose-Hubbard model at unit filling. From the numerical analyses, we show that the scaling formula is valid for the case of the Bose-Hubbard model, which can quantitatively describe Bose gases in optical lattices.

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“…where the constant c has been determined to be c = 3 in previous work [53]. Notice that scaling formulae similar to Eq.…”

Section: Qualitative Discussion On the Scaling Formulamentioning

confidence: 99%

Quantum phase slips in one-dimensional superfluids in a periodic potential

Danshita

Polkovnikov

2012

Phys. Rev. A

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“…The second implementation exploits the large kinetic inductance of arrays of JJs. Though amenable to design parameters, arrays may also suffer from dissipation due to coupling to internal degrees of freedom [8,9] or to coupling to a dissipative external bath [10]. Indeed, transport measurements on large arrays of JJs show the appearance of a superconducting to insulating transition (SIT) with decreasing Josephson energy E J [11][12][13].…”

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confidence: 99%

Microwave Characterization of Josephson Junction Arrays: Implementing a Low Loss Superinductance

et al. 2012

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We have measured the plasma resonances of an array of Josephson junctions in the regime E(J)>>E(C), up to the ninth harmonic by incorporating it as part of a resonator capacitively coupled to a coplanar waveguide. From the characteristics of the resonances, we infer the successful implementation of a superinductance, an electrical element with a nondissipative impedance greater than the resistance quantum [R(Q)=h/(2e)(2) is approximately equal to 6.5 kΩ] at microwave frequencies. Such an element is crucial for preserving the quantum coherence in circuits exploiting large fluctuations of the superconducting phase. Our results show internal losses less than 20 ppm, self-resonant frequencies greater than 10 GHz, and phase-slip rates less than 1 mHz, enabling direct application of such arrays for quantum information and metrology. Arrays with a loop geometry also demonstrate a new manifestation of flux quantization in a dispersive analog of the Little-Parks effect.

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“…For SC LRO to be stabilized, a finite η > 0 is needed. A selfconsistent equation for η [17][18][19] is obtained by combining (5) with (4). In the limit of λ → 0, a solution with η > 0 exists only for α < 3/2 − 1/(4K) [8].…”

Section: Bosonization Analysis Of the Hard-core Boson Modelmentioning

confidence: 99%

Restoring Long-Range Order in One-Dimensional Superconductivity by Power-Law Hopping

Tezuka

Lobos²,

García-García³

2014

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013)

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Quantum fluctuations destroy phase coherence and thus long-range order in one-dimensional (1D) superconductivity as long as all interactions are short-ranged. Here we discuss the possibility of restoring phase coherence by power-law hopping. A 1D attractive-U Hubbard model with powerlaw hopping having the power-law exponent α is studied by Abelian bosonization and density-matrix renormalization group (DMRG). For 1/2 < α < 3/2, the system has an effective spatial dimensionality d eff > 1. We demonstrate that long-range superconducting order is restored for 1/2 < α < α c , with 5/4 < α c < 3/2. This conclusion is supported by a DMRG analysis of the model.

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Superconductor-to-insulator transition in linear arrays of Josephson junctions capacitively coupled to metallic films

Cited by 15 publications

References 52 publications

Quantum phase slips in one-dimensional superfluids in a periodic potential

Quantum phase slips in one-dimensional superfluids in a periodic potential

Microwave Characterization of Josephson Junction Arrays: Implementing a Low Loss Superinductance

Restoring Long-Range Order in One-Dimensional Superconductivity by Power-Law Hopping

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