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Scientific Reports

Quadratic Characteristics of Environment Induced Voltage Shot Noise in Josephson Junctions

Jyh-Yang Wang, Tao-Hsiang Chung, Teik‐Hui Lee, Chii‐Dong Chen

Published Jun 9, 2017• 1 citation
Publisher

Abstract

We investigate theoretically and experimentally the environment-induced voltage shot noise in current biased Josephson junctions induced by phase particle tunneling. Quantum mechanical treatment based on the Caldeira-Leggett model with tight-binding formulation in local Wannier bases gives a clear picture of the voltage shot noise. A universal form of the zero-frequency noise spectrum is obtained, which exhibits a quadratic dependence on the mean voltage in small bias region. The quadratic dependence is verified experimentally on junctions covering a wide range of parameters, and is found also in junction arrays of various array sizes.

DOI
10.1038/s41598-017-03790-x

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We investigate theoretically and experimentally the environment-induced voltage shot noise in current biased Josephson junctions induced by phase particle tunneling. Quantum mechanical treatment based on the Caldeira-Leggett model with tight-binding formulation in local Wannier bases gives a clear picture of the voltage shot noise. A universal form of the zero-frequency noise spectrum is obtained, which exhibits a quadratic dependence on the mean voltage in small bias region. The quadratic dependence is verified experimentally on junctions covering a wide range of parameters, and is found also in junction arrays of various array sizes.
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.
The current in a a Coulomb blockaded Josephson junction is sensitive to voltage or phase fluctuations in its electromagnetical environment. This property can be used to detect noise also from non‐Gaussian noise sources. We have experimentally studied IV‐curves of as a function of the shot noise current in a nearby tunnel junction. We observe a linear enhancement of zero‐bias conductance of the Josephson junction as a function of the shot noise power. Furthermore, with increasing shot noise power, the IV‐curves becomes asymmetric with a shift of minimum conductance and the appearance of a local conductance maximum. A quantitative explanation for the asymmetric features due to the non‐Gaussian noise sources is still an open question. There is also motivation to pursue modifications of the current scheme in order to detect individual statistical moments of noise and to connect different noise sources to the Josephson junction.
An experimental investigation is made of the subharmonic Shapiro steps observed on the I-V curves of high-T c superconductor Josephson junctions and on the bias-voltage dependences of the rf noise and detector response when the junctions are subjected to external submillimeter radiation. Structures of this type are ordinarily described by a nonsinusoidal current-phase relation, which is why subharmonic steps appear. Numerical modeling of the processes occurring in a Josephson junction by means of a simple current-phase relation, as in the case of an SNS junction, gives good agreement with experiment. The width of the characteristic Josephson generation line of the junction was estimated on the basis of the noise dependences and the selective detector response. The width can be explained by taking into account the shot noise of the tunneling component of the conductivity. A model of the conductivity of a high-T c superconductor Josephson junction, consisting of a tunnel junction with microshorts possessing metallic conductivity, is discussed.
We have investigated the influence of shot noise on the IV-curves of a single mesoscopic Josephson junction. We find that the blockade of the Cooper pair current is strongly suppressed in the presence of shot noise due to tunnelling in an adjacent SIN junction. Our experimental findings can be accounted for by an extension of the phase correlation theory. Shot-noise effect in a resistive environment R can be characterized by the effective noise temperature T_N = eIR /2 k_B, which means that a Josephson junction can easily detect shot noise from a current well below 1 pA.
Quantum fluctuations of the charge at a current-biased Josephson junction and of the Josephson current couple to the quasiparticle tunneling when the system is at equilibrium in the zero-voltage state. The effect of reducing the capacitance of the junction is studied by means of a model Hamiltonian. When this becomes smaller, charge fluctuations are reduced, but the effective dissipation is also lowered so that the junction displays an underdamped behavior. The Josephson branch is shifted at the voltage e/2C because of charging due to the quasiparticles. A path-integral formulation of the model leads to a high dynamical subgap resistance at I\ensuremath{\rightarrow}0, as recently found experimentally.