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Journal of the Physical Society of Japan

Quantum Effects of Resistance-Shunted Josephson Junctions

Takeo Kato, Masatoshi Imada

Published Jan 1, 2000• 4 citations
Publisher

Abstract

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 \(2 \hbar \Delta_{\rm eff}\), we find that this multi-level system genuinely has a novel crossover at lower energy \(K \hbar \Delta_{\rm eff}\) 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.

DOI
10.1143/jpsj.69.203

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Physical review. B, Condensed matter•Jul 1, 1982•117 citations
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 (2 \hbar \Delta_{\rm eff}), we find that this multi-level system genuinely has a novel crossover at lower energy (K \hbar \Delta_{\rm eff}) 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.
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.
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.
Dynamical simulations and scaling arguments are used to study the current-voltage $(I\ensuremath{-}V)$ characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration ppp are considered, where pc{p}_{c}pc​ is the percolation threshold. For p>pcp>{p}_{c}p>pc​ and zero temperature, the $I\ensuremath{-}V$ curves show power-law behavior above a disorder-dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At pc{p}_{c}pc​ and finite temperature T,T,T, the results show the scaling behavior of a T=0T=0T=0 superconducting transition. The resistance is linear but vanishes for decreasing TTT with an apparent exponential behavior. Crossover to nonlinearity appears at currents proportional to ${T}^{1+{\ensuremath{\nu}}_{T}},$ with a thermal-correlation length exponent ${\ensuremath{\nu}}_{T}$ consistent with the corresponding value for the diluted XY\mathrm{XY}XY model at pc.{p}_{c}.pc​.
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on the magnetic field dependent crossover temperature TcrT_{cr}Tcr​ between the thermal fluctuation and quantum regimes of switching from the superconducting (the zero-voltage) state to a resistive one. In the absence of two-levels systems the crossover temperature shows a smooth decrease with an applied magnetic field characterized by an external flux ΦΦΦ. Beyond that we predict a narrow peak in the dependence of Tcr(Φ)T_{cr}(Φ)Tcr​(Φ) occurring in the intermediate range of ΦΦΦ. The effect becomes more pronounced as the junction size increases. We explain this effect quantitatively by a strong resonant suppression of a potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.
Conventional Josephson metal-insulator-metal devices are inherently underdamped and exhibit hysteretic current-voltage response due to a very high subgap resistance compared to that in the normal state. At the same time, overdamped junctions with single-valued characteristics are needed for most superconducting digital applications. The usual way to overcome the hysteretic behavior is to place an external low-resistance normal-metal shunt in parallel with each junction. Unfortunately, such solution results in a considerable complication of the circuitry design and introduces parasitic inductance through the junction. This paper provides a concise overview of some generic approaches that have been proposed in order to realize internal shunting in Josephson heterostructures with a barrier that itself contains the desired resistive component. The main attention is paid to self-shunted devices with local weak-link transmission probabilities that are so strongly disordered in the interface plane that transmission probabilities are tiny for the main part of the transition region between two super-conducting electrodes, while a small part of the interface is well transparent. We discuss the possibility of realizing a universal bimodal distribution function and emphasize advantages of such junctions that can be considered as a new class of self-shunted Josephson devices promising for practical applications in superconducting electronics operating at 4.2 K.
Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where I0{I}_{0}I0​ is the critical current, CCC is the junction capacitance, and Ls{L}_{s}Ls​ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the LsC{L}_{s}CLs​C resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.