Quantum and thermal fluctuations in the dynamics of a RCSJ junction

We theoretically investigate the phase and voltage correlation dynamics, which includes both the deterministic contribution and stochastic fluctuations, under a current noise generated by a resistor including thermal and quantum fluctuations in a resistively and capacitively shunted Josephson junction. An external current is found to shift and intensify the deterministic contributions in phase and voltage. In addition to effects of external current, we observe the relaxation of autocorrelation functions of phase and voltage, which includes the variances due to the current noise, to finite values in the long-time limit. In particular, we find that the asymptotic correlations depend on the resistance as a consequence of quantum effects. We also find an earlier decay of coherence at a higher temperature in which thermal fluctuations dominate over quantum ones. These theoretical predictions can be tested in the next future experiments.We theoretically investigate the phase and voltage correlation dynamics, which includes both the deterministic contribution and stochastic fluctuations, under a current noise generated by a resistor including thermal and quantum fluctuations in a resistively and capacitively shunted Josephson junction. An external current is found to shift and intensify the deterministic contributions in phase and voltage. In addition to effects of external current, we observe the relaxation of autocorrelation functions of phase and voltage, which includes the variances due to the current noise, to finite values in the long-time limit. In particular, we find that the asymptotic correlations depend on the resistance as a consequence of quantum effects. We also find an earlier decay of coherence at a higher temperature in which thermal fluctuations dominate over quantum ones. These theoretical predictions can be tested in the next future experiments.

arXiv:2104.14211Physical review. B./Physical review. BJul 26, 20218 citations

Quantum noise in a current-biased Josephson junction

Yehoshua B. Levinson

Quantum fluctuations in a current-biased Josephson junction, described in terms of the RCSJ model, are considered. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and to calculate the widths of the Josephson radiation lines.Quantum fluctuations in a current-biased Josephson junction, described in terms of the RCSJ model, are considered. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and to calculate the widths of the Josephson radiation lines.

arXiv:cond-mat/0212587Physical review. B, Condensed matterMay 6, 200328 citations

Effect of Noise on the Current-Voltage Characteristics of a Josephson Junction

Patrick A. Lee

The effect of noise on the current-voltage characteristic of a Josephson junction is investigated (1) when the temperature is near the transition temperature of the superconductors and (2) when the junction is driven by an external signal. In case (1) the noise source is the quasiparticle tunneling current but in case (2) there is in addition the noise arising from the finite linewidth of the external signal. This latter noise source is shown to dominate when the junction is operating at high harmonics. We treat the problem in the limits of small and large capacitance and obtain a criterion to determine under what circumstances each limit applies. A solution that includes a first-order correction due to a finite capacitance is given. In the limit of large capacitance the existence and lifetime of hysteresis curves are discussed.The effect of noise on the current-voltage characteristic of a Josephson junction is investigated (1) when the temperature is near the transition temperature of the superconductors and (2) when the junction is driven by an external signal. In case (1) the noise source is the quasiparticle tunneling current but in case (2) there is in addition the noise arising from the finite linewidth of the external signal. This latter noise source is shown to dominate when the junction is operating at high harmonics. We treat the problem in the limits of small and large capacitance and obtain a criterion to determine under what circumstances each limit applies. A solution that includes a first-order correction due to a finite capacitance is given. In the limit of large capacitance the existence and lifetime of hysteresis curves are discussed.

Journal of Applied PhysicsJan 1, 1971104 citations

Noisy quantum phase transitions: an intuitive approach

Emanuele G Dalla Torre, Eugene Demler, Thierry Giamarchi +1 more

Equilibrium thermal noise is known to destroy any quantum phase transition. What are the effects of non-equilibrium noise? In two recent papers we have considered the specific case of a resistively-shunted Josephson junction driven by $1/f$ charge noise. At equilibrium, this system undergoes a sharp quantum phase transition at a critical value of the shunt resistance. By applying a real-time renormalization group (RG) approach, we found that the noise has three main effects: It shifts the phase transition, renormalizes the resistance, and generates an effective temperature. In this paper we explain how to understand these effects using simpler arguments, based on Kirchhoff laws and time-dependent perturbation theory. We also show how these effects modify physical observables and especially the current-voltage characteristic of the junction. In the appendix we describe two possible realizations of the model with ultracold atoms confined to one dimension.Equilibrium thermal noise is known to destroy any quantum phase transition. What are the effects of non-equilibrium noise? In two recent papers we have considered the specific case of a resistively-shunted Josephson junction driven by $1/f$ charge noise. At equilibrium, this system undergoes a sharp quantum phase transition at a critical value of the shunt resistance. By applying a real-time renormalization group (RG) approach, we found that the noise has three main effects: It shifts the phase transition, renormalizes the resistance, and generates an effective temperature. In this paper we explain how to understand these effects using simpler arguments, based on Kirchhoff laws and time-dependent perturbation theory. We also show how these effects modify physical observables and especially the current-voltage characteristic of the junction. In the appendix we describe two possible realizations of the model with ultracold atoms confined to one dimension.

arXiv:1205.3496Physica ScriptaNov 1, 20122 citations

Influence of capacitance and thermal fluctuations on the Josephson diode effect in asymmetric higher-harmonic SQUIDs

G. S. Seleznev, Ya. V. Fominov

Asymmetric two-junction SQUIDs with different current-phase relations in the two Josephson junctions, involving higher Josephson harmonics, demonstrate a flux-tunable Josephson diode effect (asymmetry between currents flowing in the opposite directions, which can be tuned by the magnetic flux through the interferometer loop). We theoretically investigate influence of junction capacitance and thermal fluctuations on performance of such Josephson diodes. Our main focus is on the ``minimal model'' with one junction in the SQUID loop possessing the sinusoidal current-phase relation and the other one featuring additional second harmonic. Capacitance generally weakens the diode effect in the resistive branch (R state) of the current-voltage characteristic (CVC) both in the absence and in the presence of external ac irradiation. At the same time, it leads to qualitatively new features of the Josephson diode effect such as asymmetry of the retrapping currents (which are a manifestation of hysteretic CVC). In particular, the limiting case of the single-sided hysteresis becomes accessible. In its turn, thermal fluctuations are known to lead to nonzero average voltages at any finite current, even below the critical value. We demonstrate that in the diode regime, the fluctuation-induced voltage can become strongly (exponentially) asymmetric. In addition, we find asymmetry of the switching currents arising both due to thermal activation and due to Josephson plasma resonances in the presence of ac irradiation.Asymmetric two-junction SQUIDs with different current-phase relations in the two Josephson junctions, involving higher Josephson harmonics, demonstrate a flux-tunable Josephson diode effect (asymmetry between currents flowing in the opposite directions, which can be tuned by the magnetic flux through the interferometer loop). We theoretically investigate influence of junction capacitance and thermal fluctuations on performance of such Josephson diodes. Our main focus is on the ``minimal model'' with one junction in the SQUID loop possessing the sinusoidal current-phase relation and the other one featuring additional second harmonic. Capacitance generally weakens the diode effect in the resistive branch (R state) of the current-voltage characteristic (CVC) both in the absence and in the presence of external ac irradiation. At the same time, it leads to qualitatively new features of the Josephson diode effect such as asymmetry of the retrapping currents (which are a manifestation of hysteretic CVC). In particular, the limiting case of the single-sided hysteresis becomes accessible. In its turn, thermal fluctuations are known to lead to nonzero average voltages at any finite current, even below the critical value. We demonstrate that in the diode regime, the fluctuation-induced voltage can become strongly (exponentially) asymmetric. In addition, we find asymmetry of the switching currents arising both due to thermal activation and due to Josephson plasma resonances in the presence of ac irradiation.

arXiv:2407.05670Physical review. B./Physical review. BSep 10, 20247 citations

Quantum noise in current-biased Josephson junction

Yehoshua B. Levinson

We consider quantum fluctuations in a current biased overdamped Josephson junction in the regime when the bias current is larger than the critical current. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. Quantum effects are important when the resistor temperature is low compared to the Josephson frequency, even in the case when noise is measured at frequencies lower than the temperature. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and calculate the widths of the Josephson radiation lines.We consider quantum fluctuations in a current biased overdamped Josephson junction in the regime when the bias current is larger than the critical current. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. Quantum effects are important when the resistor temperature is low compared to the Josephson frequency, even in the case when noise is measured at frequencies lower than the temperature. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and calculate the widths of the Josephson radiation lines.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEMay 9, 20033 citations

1/f

charge noise. At equilibrium, this system undergoes a sharp quantum phase transition at a critical value of the shunt resistance. By applying a real-time renormalization group (RG) approach, we found that the noise has three main effects: It shifts the phase transition, renormalizes the resistance, and generates an effective temperature. In this paper we explain how to understand these effects using simpler arguments, based on Kirchhoff laws and time-dependent perturbation theory. We also show how these effects modify physical observables and especially the current-voltage characteristic of the junction. In the appendix we describe two possible realizations of the model with ultracold atoms confined to one dimension.