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arXiv:cond-mat/0703712 · Journal of Statistical Mechanics Theory and Experiment

Resistively shunted Josephson junctions: quantum field theory predictions versus Monte Carlo results

Sergei L. Lukyanov, Philipp Werner

Published Jun 1, 2007• 24 citations
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Abstract

During the last fourteen years several exact results have been obtained for the so-called boundary sine–Gordon model. In the case of a conformal bulk this 2D boundary quantum field theory describes the universal scaling behaviour of the Caldeira–Leggett model of resistively shunted Josephson junctions. In this work, we use a recently developed Monte Carlo technique to test some of the analytical predictions.

DOI
10.1088/1742-5468/2007/06/p06002

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During the last fourteen years several exact results have been obtained for the so-called boundary sine–Gordon model. In the case of a conformal bulk this 2D boundary quantum field theory describes the universal scaling behaviour of the Caldeira–Leggett model of resistively shunted Josephson junctions. In this work, we use a recently developed Monte Carlo technique to test some of the analytical predictions.
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We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of cluster algorithms and the treatment of long-range interactions. Dissipative quantum spins and resistively shunted Josephson junctions will be considered. Dissipation and decoherence in quantum systems have important practical implications, from stabilizing superconductivity in granular materials, to the loss of information stored in qubits. In all the models we study, energy dissipation is introduced by coupling a quantum mechanical degree of freedom to a bath of suitably
Thermodynamics and transport properties of resistance-shunted Josephson junctions are studied theoretically in the tight-binding limit E C / E J ≪1, where E C and E J are a charging energy and a Josephson coupling energy respectively. Based on a phenomenological harmonic-oscillator model, weak coupling region K = R Q / R ≪1 is analytically studied, where R and R Q = h /(2 e ) 2 are a shunt resistance and the quantum resistance. In addition to an effective bandwidth 2ℏΔeff2 \hbar \Delta_{\rm eff}2ℏΔeff​, we find that this multi-level system genuinely has a novel crossover at lower energy KℏΔeffK \hbar \Delta_{\rm eff}KℏΔeff​ below which the density of states becomes strongly degenerate. These two energy scales control the linear DC responses, optical responses, and nonlinear I - V characteristics. The lower energy crossover indicates the existence of a new class of strongly-correlated phenomena beyond the framework of the Kondo problem.
We have studied both theoretically and experimentally how an LC series circuit connected in parallel to a Josephson junction influences the Josephson dynamics. The presence of the shell circuit introduces two energy scales, which in specific cases, can strongly differ from the plasma frequency of the isolated junction. Josephson junctions were manufactured using the Nb/Al-AlOx/Nb fabrication technology with various on-chip LC shunt circuits. Spectroscopic measurements in the quantum limit show excellent agreement with theory taking into account the shunt inductance and capacitance in the resistively and capacitively shunted junction model. The results clearly show that the dynamics of the system are two-dimensional, resulting in two resonant modes of the system. These findings have important implications for the design and operation of Josephson junction based quantum bits.
Thermodynamics and transport properties of resistance-shunted Josephson junctions are studied theoretically in the tight-binding limit E_C/E_J<<1, where E_C and E_J are a charging energy and a Josephson coupling energy respectively. Based on a phenomenological harmonic-oscillator model, weak coupling region K=R_Q/R<<1 is analytically studied, where R and R_Q=h/(2e)^2 are a shunted resistance and the quantum resistance. In addition to the effective bandwidth, we find that this multi-level system genuinely has a novel crossover at lower energy below which the density of states becomes strongly degenerate. These two energy scales control the linear DC responses, optical responses, and nonlinear I-V characteristics. The lower energy crossover indicates the existence of a new class of strongly-correlated phenomena beyond the framework of the Kondo problem.