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:1303.5644 · Physical Review A

Effective description of tunneling in a time-dependent potential with applications to voltage switching in Josephson junctions

Christian Kraglund Andersen, Klaus Mølmer

Published May 15, 2013• 16 citations
arXivHTMLPDF

Abstract

We propose to use a time-dependent imaginary potential to describe quantum mechanical tunneling through time-varying potential barriers. We use Gamow solutions for stationary tunneling problems to justify our choice of potential, and we apply our method to describe tunneling of a mesoscopic quantum variable: the phase change across a Josephson junction. The Josephson junction phase variable behaves as the position coordinate of a particle moving in a tilted washboard potential, and our general solution to the motion in such a potential with a time-dependent tilt reproduces a number of features associated with voltage switching in Josephson junctions. Apart from applications as artificial atoms in quantum information studies, the Josephson junction may serve as an electric field sensitive detector, and our studies provide a detailed understanding of how the voltage switching dynamics couples to the electric field amplitude.

DOI
10.1103/physreva.87.052119

Related papers

Running-phase state in a Josephson washboard potential

Gheorghe Sorin Paraoanu

We investigate the dynamics of the phase variable of an ideal underdamped Josephson junction in switching current experiments. These experiments have provided the first evidence for macroscopic quantum tunneling in large Josephson junctions and are currently used for state readout of superconducting qubits. We calculate the shape of the resulting macroscopic wave packet and predict that the propagation of the wave packet long enough after a switching event leads to an average voltage increasing linearly with time.

arXiv:cond-mat/0501280•Physical Review B•Oct 31, 2005•19 citations

Accurate switching currents measurements in quantum washboard potential

Vincenzo Claudio Pierro, Giovanni Filatrella

We tackle the problem of accurate simulations of switching currents arising from tunnel events in the washboard potentials associated to Josephson junctions. The measurements of the probability distribution of the switching currents is essential to determine the quantum character of the device, and therefore is at the core of technological applications, as Josephson junctions, that have been proposed for quantum computers. In particular, we show how to accurately calibrate the parameters of the boundary conditions to avoid spurious reflections of the wavefunction from the finite border of numerical simulations. The proposed approximate numerical scheme exploits a quantum version of a perfect matched layers for the boundary problems associated with this class of potentials. Thus, we employ the analogous of a well established electromagnetic method to deal with radiation in mesoscopic quantum systems. Numerical simulations demonstrate that the known analytic results are well recovered in the appropriated limits of quantum measurements. We also find that a relaxation time shows up in the dynamics of the quantum evolution in between two consecutive measurements.

arXiv:1707.00681•IEEE International Workshop on Metrology for AeroSpace (MetroAeroSpace)•Jun 1, 2016•0 citations

Quantum theory of Josephson junction for a quantum bit

Rachsak Sakdanuphab, Sojiphong Chatraphorn

Josephson junction is one of the promising devices to be used as a quantum bit or known as qubit in a quantum computer. The dynamics of current-bias Josephson junction can be described by using the Resistively and Capacitively Shunted Junction (RCSJ) model which is analogous to the classical motion of a particle in a tilted washboard potential. In this work, quantum theory and approximation methods are used to calculate and explain quantum properties of the Josepson junction. We found that the energy levels in the washboard potential can be quantum mechanically quantized, and thus used as a qubit in quantum computation. The tunneling rate from the n[superscript th] energy level exponentially increases with bias current and the first excited state is three orders of magnitude more than the ground state. The wave function of the state in the potential well is relatively similar to the harmonic oscillator wave function because of the shape of the washboard potential. The transition rate between the energy levels due to an electromagnetic radiation depends on the amplitude and the frequency of microwave current. The period of the oscillation is in the order of nanoseconds. Finally the decoherence time in Josephson junction can be observed by considering the Rabi's oscillation in the presence of current noise. The decoherence time depends on the magnitude of the current noise. This result can be used to determine the feasibility of using Josephson Junction as a qubit

•Jan 1, 2005•0 citations

Switching current distributions in InAs nanowire Josephson junctions

Bum-Kyu Kim, Yong‐Joo Doh

We report on the switching current distributions in nano-hybrid Josephson junctions made of InAs semiconductor nanowires. The temperature dependence of the switching current distribution can be understood through the motion of Josephson phase particles escaping from a tilted washboard potential, and the data could be fitted well by using the macroscopic quantum tunneling, thermal activation or phase diffusion models, depending on temperature. Application of the gate voltage to tune the Josephson coupling strength enable us to adjust the effective temperature for the escape process, and holds promising for developing gate-tunable superconducting phase qubits.

arXiv:1605.03252•Journal of the Korean Physical Society•Aug 1, 2016•3 citations

Nonideal quantum measurement effects on the switching-current distribution of Josephson junctions

Vincenzo Claudio Pierro, Giovanni Filatrella

The quantum character of Josephson junctions is ordinarily revealed through the analysis of the switching currents, i.e., the current at which a finite voltage appears: A sharp rise of the voltage signals the passage (tunnel) from a trapped state (the zero voltage solution) to a running state (the finite voltage solution). In this context, we investigate the probability distribution of the Josephson-junction switching current taking into account the effect of the bias sweeping rate and introducing a simple nonideal quantum measurement scheme. The measurements are modeled as repeated voltage samplings at discrete time intervals, that is, with repeated projections of the time-dependent quantum solutions on the static or the running states, to retrieve the probability distribution of the switching currents. The distribution appears to be immune to the quantum Zeno effect, and it is close to, but distinguishable from, the Wentzel-Kramers-Brillouin approximation. For energy barriers comparable to the quantum fundamental energy state and in the fast bias current ramp rate the difference is neat, and remains sizable in the asymptotic slow rate limit. This behavior is a consequence of the quantum character of the system that confirms the presence of a backreaction of quantum measurements on the outcome of mesoscopic Josephson junctions.

arXiv:1607.03715•Physical Review A•Oct 19, 2016•3 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
We propose to use a time-dependent imaginary potential to describe quantum mechanical tunneling through time-varying potential barriers. We use Gamow solutions for stationary tunneling problems to justify our choice of potential, and we apply our method to describe tunneling of a mesoscopic quantum variable: the phase change across a Josephson junction. The Josephson junction phase variable behaves as the position coordinate of a particle moving in a tilted washboard potential, and our general solution to the motion in such a potential with a time-dependent tilt reproduces a number of features associated with voltage switching in Josephson junctions. Apart from applications as artificial atoms in quantum information studies, the Josephson junction may serve as an electric field sensitive detector, and our studies provide a detailed understanding of how the voltage switching dynamics couples to the electric field amplitude.
We investigate the dynamics of the phase variable of an ideal underdamped Josephson junction in switching current experiments. These experiments have provided the first evidence for macroscopic quantum tunneling in large Josephson junctions and are currently used for state readout of superconducting qubits. We calculate the shape of the resulting macroscopic wave packet and predict that the propagation of the wave packet long enough after a switching event leads to an average voltage increasing linearly with time.
We tackle the problem of accurate simulations of switching currents arising from tunnel events in the washboard potentials associated to Josephson junctions. The measurements of the probability distribution of the switching currents is essential to determine the quantum character of the device, and therefore is at the core of technological applications, as Josephson junctions, that have been proposed for quantum computers. In particular, we show how to accurately calibrate the parameters of the boundary conditions to avoid spurious reflections of the wavefunction from the finite border of numerical simulations. The proposed approximate numerical scheme exploits a quantum version of a perfect matched layers for the boundary problems associated with this class of potentials. Thus, we employ the analogous of a well established electromagnetic method to deal with radiation in mesoscopic quantum systems. Numerical simulations demonstrate that the known analytic results are well recovered in the appropriated limits of quantum measurements. We also find that a relaxation time shows up in the dynamics of the quantum evolution in between two consecutive measurements.
Josephson junction is one of the promising devices to be used as a quantum bit or known as qubit in a quantum computer. The dynamics of current-bias Josephson junction can be described by using the Resistively and Capacitively Shunted Junction (RCSJ) model which is analogous to the classical motion of a particle in a tilted washboard potential. In this work, quantum theory and approximation methods are used to calculate and explain quantum properties of the Josepson junction. We found that the energy levels in the washboard potential can be quantum mechanically quantized, and thus used as a qubit in quantum computation. The tunneling rate from the n[superscript th] energy level exponentially increases with bias current and the first excited state is three orders of magnitude more than the ground state. The wave function of the state in the potential well is relatively similar to the harmonic oscillator wave function because of the shape of the washboard potential. The transition rate between the energy levels due to an electromagnetic radiation depends on the amplitude and the frequency of microwave current. The period of the oscillation is in the order of nanoseconds. Finally the decoherence time in Josephson junction can be observed by considering the Rabi's oscillation in the presence of current noise. The decoherence time depends on the magnitude of the current noise. This result can be used to determine the feasibility of using Josephson Junction as a qubit
We report on the switching current distributions in nano-hybrid Josephson junctions made of InAs semiconductor nanowires. The temperature dependence of the switching current distribution can be understood through the motion of Josephson phase particles escaping from a tilted washboard potential, and the data could be fitted well by using the macroscopic quantum tunneling, thermal activation or phase diffusion models, depending on temperature. Application of the gate voltage to tune the Josephson coupling strength enable us to adjust the effective temperature for the escape process, and holds promising for developing gate-tunable superconducting phase qubits.
The quantum character of Josephson junctions is ordinarily revealed through the analysis of the switching currents, i.e., the current at which a finite voltage appears: A sharp rise of the voltage signals the passage (tunnel) from a trapped state (the zero voltage solution) to a running state (the finite voltage solution). In this context, we investigate the probability distribution of the Josephson-junction switching current taking into account the effect of the bias sweeping rate and introducing a simple nonideal quantum measurement scheme. The measurements are modeled as repeated voltage samplings at discrete time intervals, that is, with repeated projections of the time-dependent quantum solutions on the static or the running states, to retrieve the probability distribution of the switching currents. The distribution appears to be immune to the quantum Zeno effect, and it is close to, but distinguishable from, the Wentzel-Kramers-Brillouin approximation. For energy barriers comparable to the quantum fundamental energy state and in the fast bias current ramp rate the difference is neat, and remains sizable in the asymptotic slow rate limit. This behavior is a consequence of the quantum character of the system that confirms the presence of a backreaction of quantum measurements on the outcome of mesoscopic Josephson junctions.
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.