Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1701.04084 · Physical Review Letters

Quantum Brownian Motion at Strong Dissipation Probed by Superconducting Tunnel Junctions

Berthold Jäck, Jacob Senkpiel, Markus Etzkorn, Joachim Ankerhold, Christian R. Ast, Klaus Kern

Published Oct 4, 2017• 12 citations
arXivHTMLPDF

Abstract

We have investigated the phase dynamics of a superconducting tunnel junction at ultralow temperatures in the presence of high damping, where the interaction with environmental degrees of freedom represents the leading energy scale. In this regime, theory predicts the dynamics to follow a generalization of the classical Smoluchowski description, the quantum Smoluchowski equation, thus, exhibiting overdamped quantum Brownian motion characteristics. For this purpose, we have performed current-biased measurements on the small-capacitance Josephson junction of a scanning tunneling microscope placed in a low impedance environment at milli-Kelvin temperatures. We can describe our experimental findings with high accuracy by using a quantum phase diffusion model based on the quantum Smoluchowski equation. In this way we experimentally demonstrate that overdamped quantum systems follow quasiclassical dynamics with significant quantum effects as the leading corrections.

DOI
10.1103/physrevlett.119.147702

Related papers

Overdamped quantum phase diffusion and charging effects in Josephson junctions

Joachim Ankerhold

By exploiting the recently derived quantum Smoluchowski equation, the classical Ivanchenko-Zil'berman theory for overdamped diffusive phase motion of low-capacitance Josephson junctions is extended to the low-temperature quantum domain where charging effects appear. This formulation allows to derive explicit results for the current-voltage characteristics over a broad range of parameters that reduce to known findings in certain limits. In particular, the transparent analytical approach comprises Coulomb-blockade physics, coherent Cooper-pair transfer, and the precursors of macroscopic quantum tunneling and needs to be supplemented by more sophisticated methods only at very low temperatures.

arXiv:cond-mat/0402516•Europhysics Letters (EPL)•Jul 1, 2004•35 citations

Smoluchowski equation approach for quantum Brownian motion in a tilted periodic potential

William T. Coffey, Yuri P. Kalmykov, С. В. Титов +1 more

Quantum corrections to the noninertial Brownian motion of a particle in a one-dimensional tilted cosine periodic potential are treated in the high-temperature and weak bath-particle coupling limit by solving a quantum Smoluchowski equation for the time evolution of the distribution function in configuration space. The theoretical predictions from two different forms of the quantum Smoluchowski equation already proposed-viz., J. Ankerhold [Phys. Rev. Lett. 87, 086802 (2001)] and W. T. Coffey [J. Phys. A 40, F91 (2007)]-are compared in detail in a particular application to the dynamics of a point Josephson junction. Various characteristics (stationary distribution, current-voltage characteristics, mean first passage time, linear ac response) are evaluated via continued fractions and finite integral representations in the manner customarily used for the classical Smoluchowski equation. The deviations from the classical behavior, discernible in the dc current-voltage characteristics as enhanced current for a given voltage and in the resonant peak in the impedance curve as an enhancement of the Q factor, are, respectively, a manifestation of relatively high-temperature nondissipative tunneling (reducing the barrier height) and dissipative tunneling (reducing the damping of the Josephson oscillations) near the top of a barrier.

Physical Review E•Sep 10, 2008•45 citations

Experimental tests for the quantum behavior of a macroscopic degree of freedom: The phase difference across a Josephson junction

John M. Martinis, Michel Devoret, John L. Clarke

Experiments are described that demonstrate the quantum behavior of a macroscopic degree of freedom, namely the phase difference \ensuremath{\delta} across a current-biased Josephson tunnel junction. The behavior of \ensuremath{\delta} was deduced from measurements of the escape rate \ensuremath{\Gamma} of the junction from its zero-voltage state. The relevant parameters of the junction, that is, its critical current and shunting admittance, were determined in situ in the thermal regime from the dependence of \ensuremath{\Gamma} on bias current and from resonant activation in the presence of microwaves. It was found that the shunting capacitance was dominated by the self-capacitance of the junction while the shunting conductance was dominated by the bias circuitry. For an underdamped junction in the quantum regime, \ensuremath{\Gamma} became independent of temperature at low temperatures with a value that, with no adjustable parameters, was in excellent agreement with predictions for macroscopic quantum tunneling at T=0. When the critical current was reduced with a magnetic field so that the junction remained in the thermal regime at low temperatures, \ensuremath{\Gamma} followed the predictions of the thermal model, thereby showing the influence of extraneous noise to be negligible. In a further series of experiments, the existence of quantized energy levels in the potential well of the junction was demonstrated spectroscopically. The positions of the energy levels agreed quantitatively with quantum-mechanical predictions involving junction parameters measured in the thermal regime. The relative heights and widths of the resonances are in reasonable agreement with the predictions of a simple model.

Physical review. B, Condensed matter•Apr 1, 1987•572 citations

Resolving the effects of frequency-dependent damping and quantum phase diffusion in YBa 2 Cu 3 O 7−x Josephson junctions

D. Stornaiuolo, G. Rotoli, D. Massarotti +4 more

We report on the study of the phase dynamics of high-critical-temperature superconductor Josephson junctions. We realized YBa${}_{2}$Cu${}_{3}$O${}_{7\ensuremath{-}x}$ grain boundary biepitaxial junctions in the submicron scale using low-loss substrates and analyzed their dissipation by comparing the transport measurements with Monte Carlo simulations. The behavior of the junctions can be fitted using a model based on two quality factors, which results in a frequency-dependent damping. Moreover, our devices can be designed to have Josephson energy of the order of the Coulomb energy. In this unusual energy range, phase delocalization strongly influences the device's dynamics, promoting the transition to a quantum phase diffusion regime. We study the signatures of such a transition by combining the outcomes of Monte Carlo simulations with the analysis of the device's parameters, the critical current, and the temperature behavior of the low-voltage resistance ${R}_{0}$.

arXiv:1307.0106•Physical Review B•Apr 25, 2013•33 citations

Quantum Tunneling at Zero Temperature in the Strong Friction Regime

A. O. Bolivar

In the large damping limit we derive a Fokker-Planck equation in configuration space (the so-called Smoluchowski equation) describing a Brownian particle immersed into a thermal environment and subjected to a nonlinear external force. We quantize this stochastic system and survey the problem of escape over a double-well potential barrier. Our finding is that the quantum Kramers rate does not depend on the friction coefficient at low temperatures; i.e., we predict a superfluidity phenomenon in overdamped open systems. Moreover, at zero temperature we show that the quantum escape rate does not vanish in the strong friction regime. This result, therefore, is in contrast with the work by Ankerhold et al. [Phys. Rev. Lett. 87, 086802 (2001)]] in which no quantum tunneling is predicted at zero temperature.

Physical Review Letters•Jan 20, 2005•9 citations

Anomalous Dissipation in Current Biased Josephson Systems

Johannes Hauff, Niklas Gaiser, Joachim Ankerhold +1 more

A new phase diffusive regime in a current biased Josephson junction is theoretically explored which originates from embedding the junction in a circuit environment with anomalous dissipation. This is realized by placing parallel to the junction a resistor in series with a capacitor such that electromagnetic fluctuations effectively couple also to the charge of the junction. This leads to rich Josephson dynamics, in particular for the switching of the junction out of a zero voltage state. Modelled as the escape process of a fictitious phase-particle out of a metastable well, a detailed study reveals that anomalous dissipation has a strong impact at low temperatures when quantum tunneling dominates against thermal activation. As a manifestation, a regime is found, where for realistic circuit parameters the quantum escape process is substantially enhanced, followed by a short voltage pulse and re-trapping with high probability. This class of circuits may be leveraged for detecting microwave photons or dissipative quantum annealing processes. In addition, the analysis provides a general framework for engineering dissipative dynamics in nonlinear systems using anomalous environments.

cond-mat.mes-hallCross-listedarXiv:2607.11647•Jul 14, 2026•0 citations
We have investigated the phase dynamics of a superconducting tunnel junction at ultralow temperatures in the presence of high damping, where the interaction with environmental degrees of freedom represents the leading energy scale. In this regime, theory predicts the dynamics to follow a generalization of the classical Smoluchowski description, the quantum Smoluchowski equation, thus, exhibiting overdamped quantum Brownian motion characteristics. For this purpose, we have performed current-biased measurements on the small-capacitance Josephson junction of a scanning tunneling microscope placed in a low impedance environment at milli-Kelvin temperatures. We can describe our experimental findings with high accuracy by using a quantum phase diffusion model based on the quantum Smoluchowski equation. In this way we experimentally demonstrate that overdamped quantum systems follow quasiclassical dynamics with significant quantum effects as the leading corrections.
By exploiting the recently derived quantum Smoluchowski equation, the classical Ivanchenko-Zil'berman theory for overdamped diffusive phase motion of low-capacitance Josephson junctions is extended to the low-temperature quantum domain where charging effects appear. This formulation allows to derive explicit results for the current-voltage characteristics over a broad range of parameters that reduce to known findings in certain limits. In particular, the transparent analytical approach comprises Coulomb-blockade physics, coherent Cooper-pair transfer, and the precursors of macroscopic quantum tunneling and needs to be supplemented by more sophisticated methods only at very low temperatures.
Quantum corrections to the noninertial Brownian motion of a particle in a one-dimensional tilted cosine periodic potential are treated in the high-temperature and weak bath-particle coupling limit by solving a quantum Smoluchowski equation for the time evolution of the distribution function in configuration space. The theoretical predictions from two different forms of the quantum Smoluchowski equation already proposed-viz., J. Ankerhold [Phys. Rev. Lett. 87, 086802 (2001)] and W. T. Coffey [J. Phys. A 40, F91 (2007)]-are compared in detail in a particular application to the dynamics of a point Josephson junction. Various characteristics (stationary distribution, current-voltage characteristics, mean first passage time, linear ac response) are evaluated via continued fractions and finite integral representations in the manner customarily used for the classical Smoluchowski equation. The deviations from the classical behavior, discernible in the dc current-voltage characteristics as enhanced current for a given voltage and in the resonant peak in the impedance curve as an enhancement of the Q factor, are, respectively, a manifestation of relatively high-temperature nondissipative tunneling (reducing the barrier height) and dissipative tunneling (reducing the damping of the Josephson oscillations) near the top of a barrier.
Experiments are described that demonstrate the quantum behavior of a macroscopic degree of freedom, namely the phase difference \ensuremath{\delta} across a current-biased Josephson tunnel junction. The behavior of \ensuremath{\delta} was deduced from measurements of the escape rate \ensuremath{\Gamma} of the junction from its zero-voltage state. The relevant parameters of the junction, that is, its critical current and shunting admittance, were determined in situ in the thermal regime from the dependence of \ensuremath{\Gamma} on bias current and from resonant activation in the presence of microwaves. It was found that the shunting capacitance was dominated by the self-capacitance of the junction while the shunting conductance was dominated by the bias circuitry. For an underdamped junction in the quantum regime, \ensuremath{\Gamma} became independent of temperature at low temperatures with a value that, with no adjustable parameters, was in excellent agreement with predictions for macroscopic quantum tunneling at T=0. When the critical current was reduced with a magnetic field so that the junction remained in the thermal regime at low temperatures, \ensuremath{\Gamma} followed the predictions of the thermal model, thereby showing the influence of extraneous noise to be negligible. In a further series of experiments, the existence of quantized energy levels in the potential well of the junction was demonstrated spectroscopically. The positions of the energy levels agreed quantitatively with quantum-mechanical predictions involving junction parameters measured in the thermal regime. The relative heights and widths of the resonances are in reasonable agreement with the predictions of a simple model.
We report on the study of the phase dynamics of high-critical-temperature superconductor Josephson junctions. We realized YBa2{}_{2}2​Cu3{}_{3}3​O${}_{7\ensuremath{-}x}$ grain boundary biepitaxial junctions in the submicron scale using low-loss substrates and analyzed their dissipation by comparing the transport measurements with Monte Carlo simulations. The behavior of the junctions can be fitted using a model based on two quality factors, which results in a frequency-dependent damping. Moreover, our devices can be designed to have Josephson energy of the order of the Coulomb energy. In this unusual energy range, phase delocalization strongly influences the device's dynamics, promoting the transition to a quantum phase diffusion regime. We study the signatures of such a transition by combining the outcomes of Monte Carlo simulations with the analysis of the device's parameters, the critical current, and the temperature behavior of the low-voltage resistance R0{R}_{0}R0​.
In the large damping limit we derive a Fokker-Planck equation in configuration space (the so-called Smoluchowski equation) describing a Brownian particle immersed into a thermal environment and subjected to a nonlinear external force. We quantize this stochastic system and survey the problem of escape over a double-well potential barrier. Our finding is that the quantum Kramers rate does not depend on the friction coefficient at low temperatures; i.e., we predict a superfluidity phenomenon in overdamped open systems. Moreover, at zero temperature we show that the quantum escape rate does not vanish in the strong friction regime. This result, therefore, is in contrast with the work by Ankerhold et al. [Phys. Rev. Lett. 87, 086802 (2001)]] in which no quantum tunneling is predicted at zero temperature.
A new phase diffusive regime in a current biased Josephson junction is theoretically explored which originates from embedding the junction in a circuit environment with anomalous dissipation. This is realized by placing parallel to the junction a resistor in series with a capacitor such that electromagnetic fluctuations effectively couple also to the charge of the junction. This leads to rich Josephson dynamics, in particular for the switching of the junction out of a zero voltage state. Modelled as the escape process of a fictitious phase-particle out of a metastable well, a detailed study reveals that anomalous dissipation has a strong impact at low temperatures when quantum tunneling dominates against thermal activation. As a manifestation, a regime is found, where for realistic circuit parameters the quantum escape process is substantially enhanced, followed by a short voltage pulse and re-trapping with high probability. This class of circuits may be leveraged for detecting microwave photons or dissipative quantum annealing processes. In addition, the analysis provides a general framework for engineering dissipative dynamics in nonlinear systems using anomalous environments.