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:2402.08684

Tale of Tilted Washboards of Potential Energy

Celso L. Ladera, Eduardo Gaião STELLA

Published Jan 3, 2024• 0 citations
arXivHTMLPDF

Abstract

Tilted washboard potentials are periodic functions of potential energy whose graphs remind the profiles of inclined washboards for scrubbing clothes. Practically unknown until the 1970, washboard potentials are at present ubiquitous seminal landscapes across diverse physics researches and technologies now receiving significant attention. However, washboard potentials are still rarely presented to science and engineering undergraduates; perhaps they could hear about those when first studying Josephson junctions. Aiming to promote the presentation of such potentials to undergraduates, we here consider cases of washboard potentials in: classical mechanics, quantum physics and optics. The quantum case is the superconducting Josephson junction whose phase quasi-particle has a tilted washboard potential leading to important applications, e.g. the phase qubit in quantum computation. Optical cases are electro-optical potentials generated with laser beams in which thousands of atom electric dipoles may become confined or evolve, potentials being generated either with laser Bessel beams, or with laser standing waves, whose periodic potential profile is implicitly tilted or may be experimentally adjusted to become tilted. Electro-optical potentials are presently used in fast-paced fundamental research, e.g. Brownian particle motors, atom trapping in optical lattices, optical atomic clocks, protein transport in biological cells, and in condensed matter physics to name a few.

DOI
10.48550/arxiv.2402.08684

Related papers

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

Christian Kraglund Andersen, Klaus Mølmer

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.

arXiv:1303.5644•Physical Review A•May 15, 2013•16 citations

Quantum interference in a driven washboard potential

Quentin Thommen, Jean Claude Garreau, Véronique Zehnlé

The dynamics of a quantum particle in a one-dimensional, tilted (“washboard”) and time-dependent lattice is studied. The approach uses quantum mechanics at the undergraduate level and leads to analytical results that show a rich variety of dynamical behavior and illustrate the fundamental role of interference in quantum systems.

American Journal of Physics•Jul 14, 2004•6 citations

Atomic transport in optical lattices

Henning Hagman

This thesis includes both experimental and theoretical investigations of fluctuation-induced transport phenomena, presented in a series of nine papers, by studies of the dynamics of cold atoms in dissipative optical lattices. With standard laser cooling techniques about 108 cesium atoms are accumulated, cooled to a few μK, and transferred into a dissipative optical lattice. An optical lattice is a periodic light-shift potential, and in dissipative optical lattice the light field is sufficiently close to resonance for incoherent light scattering to be of importance. This provides the system with a diffusive force, but also with a friction through laser cooling mechanisms. In the dissipative optical lattices the friction and the diffusive force will eventually reach a steady state. At steady state, the thermal energy is low enough, compared to the potential depth, for the atoms to be localized close to the potential minima, but high enough for the atoms to occasionally make inter-well flights. This leads to a Brownian motion of the atoms in the optical lattices. In the normal case these random walks average to zero, leading to a symmetric, isotropic diffusion of the atoms. If the optical lattices are tilted, the symmetry is broken and the diffusion will be biased. This leads to a fluctuation-induced drift of the atoms. In this thesis an investigation of such drifts, for an optical lattice tilted by the gravitational force, is presented. We show that even though the tilt over a potential period is small compared to the potential depth, it clearly affect the dynamics of the atoms, and despite the complex details of the system it can, to a good approximation, be described by the Langevin equation formalism for a particle in a periodic potential. The linear drifts give evidence of stop-and-go dynamics where the atoms escape the potential wells and travel over one or more wells before being recaptured. Brownian motors open the possibility of creating fluctuation-induced drifts in the absence of bias forces, if two requirements are fulfilled: the symmetry has to be broken and the system has to be brought out of thermal equilibrium. By utilizing two distinguishable optical lattices, with a relative spatial phase and unequal transfer rates between them, these requirements can be fulfilled. In this thesis, such a Brownian motor is realized, and drifts in arbitrary directions in 3D are demonstrated. We also demonstrate a real-time steering of the transport as well as drifts along pre-designed paths. Moreover, we present measurements and discussions of performance characteristics of the motor, and we show that the required asymmetry can be obtained in multiple ways.

•Jan 1, 2010•1 citation

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

Classical and quantum dissipative dynamics in Josephson junctions: An Arnold problem, bifurcation, and capture into resonance

D. S. Pashin, Сатанин Аркадий Михайлович, Chang Sub Kim

We theoretically study the phase dynamics in Josephson junctions, which maps onto the oscillatory motion of a pointlike particle in the washboard potential. Under appropriate driving and damping conditions, the Josephson phase undergoes intriguing bistable dynamics near a saddle point in the quasienergy landscape. The bifurcation mechanism plays a critical role in superconducting quantum circuits with relevance to nondemolition measurements such as high-fidelity readout of qubit states. We address the question "what is the probability of capture into either basin of attraction?" and answer it concerning both classical and quantum dynamics. Consequently, we derive the Arnold probability and numerically analyze its implementation of the controlled dynamical switching between two steady states under the various nonequilibrium conditions.

arXiv:1803.03743•Physical review. E•Jun 24, 2019•8 citations

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
Tilted washboard potentials are periodic functions of potential energy whose graphs remind the profiles of inclined washboards for scrubbing clothes. Practically unknown until the 1970, washboard potentials are at present ubiquitous seminal landscapes across diverse physics researches and technologies now receiving significant attention. However, washboard potentials are still rarely presented to science and engineering undergraduates; perhaps they could hear about those when first studying Josephson junctions. Aiming to promote the presentation of such potentials to undergraduates, we here consider cases of washboard potentials in: classical mechanics, quantum physics and optics. The quantum case is the superconducting Josephson junction whose phase quasi-particle has a tilted washboard potential leading to important applications, e.g. the phase qubit in quantum computation. Optical cases are electro-optical potentials generated with laser beams in which thousands of atom electric dipoles may become confined or evolve, potentials being generated either with laser Bessel beams, or with laser standing waves, whose periodic potential profile is implicitly tilted or may be experimentally adjusted to become tilted. Electro-optical potentials are presently used in fast-paced fundamental research, e.g. Brownian particle motors, atom trapping in optical lattices, optical atomic clocks, protein transport in biological cells, and in condensed matter physics to name a few.
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.
This thesis includes both experimental and theoretical investigations of fluctuation-induced transport phenomena, presented in a series of nine papers, by studies of the dynamics of cold atoms in dissipative optical lattices. With standard laser cooling techniques about 108 cesium atoms are accumulated, cooled to a few μK, and transferred into a dissipative optical lattice. An optical lattice is a periodic light-shift potential, and in dissipative optical lattice the light field is sufficiently close to resonance for incoherent light scattering to be of importance. This provides the system with a diffusive force, but also with a friction through laser cooling mechanisms. In the dissipative optical lattices the friction and the diffusive force will eventually reach a steady state. At steady state, the thermal energy is low enough, compared to the potential depth, for the atoms to be localized close to the potential minima, but high enough for the atoms to occasionally make inter-well flights. This leads to a Brownian motion of the atoms in the optical lattices. In the normal case these random walks average to zero, leading to a symmetric, isotropic diffusion of the atoms. If the optical lattices are tilted, the symmetry is broken and the diffusion will be biased. This leads to a fluctuation-induced drift of the atoms. In this thesis an investigation of such drifts, for an optical lattice tilted by the gravitational force, is presented. We show that even though the tilt over a potential period is small compared to the potential depth, it clearly affect the dynamics of the atoms, and despite the complex details of the system it can, to a good approximation, be described by the Langevin equation formalism for a particle in a periodic potential. The linear drifts give evidence of stop-and-go dynamics where the atoms escape the potential wells and travel over one or more wells before being recaptured. Brownian motors open the possibility of creating fluctuation-induced drifts in the absence of bias forces, if two requirements are fulfilled: the symmetry has to be broken and the system has to be brought out of thermal equilibrium. By utilizing two distinguishable optical lattices, with a relative spatial phase and unequal transfer rates between them, these requirements can be fulfilled. In this thesis, such a Brownian motor is realized, and drifts in arbitrary directions in 3D are demonstrated. We also demonstrate a real-time steering of the transport as well as drifts along pre-designed paths. Moreover, we present measurements and discussions of performance characteristics of the motor, and we show that the required asymmetry can be obtained in multiple ways.
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.
We theoretically study the phase dynamics in Josephson junctions, which maps onto the oscillatory motion of a pointlike particle in the washboard potential. Under appropriate driving and damping conditions, the Josephson phase undergoes intriguing bistable dynamics near a saddle point in the quasienergy landscape. The bifurcation mechanism plays a critical role in superconducting quantum circuits with relevance to nondemolition measurements such as high-fidelity readout of qubit states. We address the question "what is the probability of capture into either basin of attraction?" and answer it concerning both classical and quantum dynamics. Consequently, we derive the Arnold probability and numerically analyze its implementation of the controlled dynamical switching between two steady states under the various nonequilibrium conditions.
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.