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

Physical Review Letters

Scenario for a quantum phase slip in superfluid He4

S. Burkhart, M. Bernard, Olivier Avenel, Eric Varoquaux

Published Jan 17, 1994• 30 citations
Publisher

Abstract

Slips of the superfluid wave-function phase occur when the flow velocity through an aperture exceeds a critical threshold ${\mathit{v}}_{\mathit{c}}$. We propose a phase slip mechanism in which a microscopic vortex half ring is nucleated at the wall of the aperture. Its subsequent trajectory is described. The properties of the vortex close to the wall are inferred from the Gross-Pitaevskii equation and yield, at T\ensuremath{\sim}0.1 K, a vortex radius at nucleation of 14 \AA{} and a critical velocity of 21 m/s, in agreement with experiment.

DOI
10.1103/physrevlett.72.380

Related papers

Quantum Nucleation of Phase Slips in a 1D Model of a Superfluid

José A. Freire, Daniel P. Arovas, Herbert Levine

We use a 1D model of a superfluid based on the Gross-Pitaevskii Lagrangian to illustrate a general numerical method designed to find quantum tunneling rates in extended bosonic systems. Specifically, we study flow past an obstacle and directly solve the imaginary time dynamics to find the ``bounce'' solution connected with the decay of the metastable laminar state via phase slip nucleation. The action for the tunneling configuration goes to zero at the threshold (in superfluid velocity) for classical production of these slips. Applications to other processes are briefly discussed.

arXiv:cond-mat/9704094•Physical Review Letters•Dec 22, 1997•19 citations

Depinning of a superfluid vortex inside a circular defect

José A. Freire

In this work we study the process of depinning of a quantum of circulation trapped inside a disk by an applied two-dimensional superflow. We use the Gross-Pitaevskii model to describe the neutral superfluid. The collective coordinate dynamics is derived directly from the condensate equation of motion, the nonlinear Schr\"odinger equation, and it is used to obtain an expression for the critical velocity as a function of the defect radius. This expression is compared with a numerical result obtained from the time-independent nonlinear Schr\"odinger equation. Below the critical velocity, we obtain the dependence of the semiclassical nucleation rate with the flow velocity at infinity. Above the critical velocity, the classical vortex depinning is illustrated with a numerical simulation of the time-dependent nonlinear Schr\"odinger equation.

arXiv:cond-mat/0107090•Physical review. B, Condensed matter•May 1, 2000•0 citations

Vortex-induced phase slip dissipation in a torioidal Bose-Einstein condensate flowing through a barrier

Lee A. Collins

We study the phase slips superfluid dissipation mechanism with a BEC flowing through a repulsive barrier inside a torus. The barrier is adiabatically raised across the annulus while the condensate is flowing with a finite quantized angular momentum. We found that, at a critical height, a vortex reaches the barrier moving radially from the inner region to eventually circulate along the annulus. At a slightly higher barrier, an anti-vortex also enters into the annulus from the outward region. The vortex and anti-vortex decrease the total angular momentum by leaving behind their respective paths a 2{pi} phase slip. When they collide or orbit along the same loop, the condensate suffers a global 2{pi} phase slip and the total angular momentum decreases by one quantum. The analysis is based on numerical simulations of the dynamical Gross-Pitaevskii equation both in two- and three-dimensions, the latter with the experimental parameters of the torus trap recently created at the NIST institute.

Physical Review Letters•Jan 1, 2009•0 citations

Quantum phase slips in one-dimensional superfluids in a periodic potential

Ippei Danshita, Anatoli Polkovnikov

We study the decay of superflow of a one-dimensional (1D) superfluid in the presence of a periodic potential. In 1D, superflow at zero temperature can decay via quantum nucleation of phase slips even when the flow velocity is much smaller than the critical velocity predicted by mean-field theories. Applying the instanton method to the O(2) quantum rotor model, we calculate the nucleation rate of quantum phase slips $\ensuremath{\Gamma}$. When the flow momentum $p$ is small, we find that the nucleation rate per unit length increases algebraically with $p$ as $\ensuremath{\Gamma}/L\ensuremath{\propto}{p}^{2K\ensuremath{-}2}$, where $L$ is the system size and $K$ is the Tomonaga-Luttinger parameter. Based on the relation between the nucleation rate and the quantum superfluid-insulator transition, we present a unified explanation on the scaling formulas of the nucleation rate for periodic, disorder, and single-barrier potentials. Using the time-evolving block decimation method, we compute the exact quantum dynamics of the superflow decay in the 1D Bose-Hubbard model at unit filling. From the numerical analyses, we show that the scaling formula is valid for the case of the Bose-Hubbard model, which can quantitatively describe Bose gases in optical lattices.

arXiv:1110.4306•Physical Review A•Feb 29, 2012•26 citations

Vortex nucleation in uniform superfluid flow past a flat solid wall

Dale I. Pullin, John Elie Sader

The flow of a superfluid past a solid boundary can generate vortices, with a key criterion being that the local flow speed reaches the speed of sound (Landau). However, the physical mechanism underlying this vortex generation remains unresolved. We consider the canonical problem of uniform flow past an impenetrable planar wall, to examine the vortex nucleation process generated by a solid obstruction moving through a superfluid. A linear stability analysis is conducted of this uniform two-dimensional flow governed by the Gross–Pitaevskii equation (GPE). This shows that the flow is marginally stable to two-dimensional, normal-mode perturbations. Direct numerical solutions of the GPE confirm this finding for small perturbations of finite amplitude. They also reveal the existence of a critical amplitude above which instabilities, in the form of vortices, are nucleated at the solid wall in finite time. Once nucleated, these vortices convect away from the solid wall with infinite initial speed. The physical mechanism underlying this nonlinear phenomenon is discussed, and a proposal is advanced to deepen its understanding.

Journal of Fluid Mechanics•Jul 17, 2026•0 citations

Nucleation and kinematics of vortices in stirred Bose Einstein condensates

Jonas Rønning, Luiza Angheluta

We apply the Halperin-Mazenco formalism within the Gross-Pitaevskii theory to characterise the kinematics and nucleation of quantum vortices in a two-dimensional stirred Bose Einstein condensate. We introduce a smooth defect density field measuring the superfluid vorticity and is a topologically conserved quantity. We use this defect density field and its associated current density to study the precursory pattern formations that occur inside the repulsive potential of an obstacle and determine the onset of vortex nucleation and shedding. We demonstrate that phase slips form inside hard potentials even in the absence of vortex nucleation, whereas for soft potentials they occur only above a critical stirring velocity leading to vortex nucleation. The Halperin-Mazenco formalism provides an elegant and accurate method of deriving the point vortex dynamic directly from the Gross-Pitaevskii equation.

arXiv:2210.14620•Oct 26, 2022•0 citations
Slips of the superfluid wave-function phase occur when the flow velocity through an aperture exceeds a critical threshold vc{\mathit{v}}_{\mathit{c}}vc​. We propose a phase slip mechanism in which a microscopic vortex half ring is nucleated at the wall of the aperture. Its subsequent trajectory is described. The properties of the vortex close to the wall are inferred from the Gross-Pitaevskii equation and yield, at T\ensuremath{\sim}0.1 K, a vortex radius at nucleation of 14 \AA{} and a critical velocity of 21 m/s, in agreement with experiment.
We use a 1D model of a superfluid based on the Gross-Pitaevskii Lagrangian to illustrate a general numerical method designed to find quantum tunneling rates in extended bosonic systems. Specifically, we study flow past an obstacle and directly solve the imaginary time dynamics to find the ``bounce'' solution connected with the decay of the metastable laminar state via phase slip nucleation. The action for the tunneling configuration goes to zero at the threshold (in superfluid velocity) for classical production of these slips. Applications to other processes are briefly discussed.
In this work we study the process of depinning of a quantum of circulation trapped inside a disk by an applied two-dimensional superflow. We use the Gross-Pitaevskii model to describe the neutral superfluid. The collective coordinate dynamics is derived directly from the condensate equation of motion, the nonlinear Schr\"odinger equation, and it is used to obtain an expression for the critical velocity as a function of the defect radius. This expression is compared with a numerical result obtained from the time-independent nonlinear Schr\"odinger equation. Below the critical velocity, we obtain the dependence of the semiclassical nucleation rate with the flow velocity at infinity. Above the critical velocity, the classical vortex depinning is illustrated with a numerical simulation of the time-dependent nonlinear Schr\"odinger equation.
We study the phase slips superfluid dissipation mechanism with a BEC flowing through a repulsive barrier inside a torus. The barrier is adiabatically raised across the annulus while the condensate is flowing with a finite quantized angular momentum. We found that, at a critical height, a vortex reaches the barrier moving radially from the inner region to eventually circulate along the annulus. At a slightly higher barrier, an anti-vortex also enters into the annulus from the outward region. The vortex and anti-vortex decrease the total angular momentum by leaving behind their respective paths a 2{pi} phase slip. When they collide or orbit along the same loop, the condensate suffers a global 2{pi} phase slip and the total angular momentum decreases by one quantum. The analysis is based on numerical simulations of the dynamical Gross-Pitaevskii equation both in two- and three-dimensions, the latter with the experimental parameters of the torus trap recently created at the NIST institute.
We study the decay of superflow of a one-dimensional (1D) superfluid in the presence of a periodic potential. In 1D, superflow at zero temperature can decay via quantum nucleation of phase slips even when the flow velocity is much smaller than the critical velocity predicted by mean-field theories. Applying the instanton method to the O(2) quantum rotor model, we calculate the nucleation rate of quantum phase slips $\ensuremath{\Gamma}$. When the flow momentum ppp is small, we find that the nucleation rate per unit length increases algebraically with ppp as $\ensuremath{\Gamma}/L\ensuremath{\propto}{p}^{2K\ensuremath{-}2}$, where LLL is the system size and KKK is the Tomonaga-Luttinger parameter. Based on the relation between the nucleation rate and the quantum superfluid-insulator transition, we present a unified explanation on the scaling formulas of the nucleation rate for periodic, disorder, and single-barrier potentials. Using the time-evolving block decimation method, we compute the exact quantum dynamics of the superflow decay in the 1D Bose-Hubbard model at unit filling. From the numerical analyses, we show that the scaling formula is valid for the case of the Bose-Hubbard model, which can quantitatively describe Bose gases in optical lattices.
The flow of a superfluid past a solid boundary can generate vortices, with a key criterion being that the local flow speed reaches the speed of sound (Landau). However, the physical mechanism underlying this vortex generation remains unresolved. We consider the canonical problem of uniform flow past an impenetrable planar wall, to examine the vortex nucleation process generated by a solid obstruction moving through a superfluid. A linear stability analysis is conducted of this uniform two-dimensional flow governed by the Gross–Pitaevskii equation (GPE). This shows that the flow is marginally stable to two-dimensional, normal-mode perturbations. Direct numerical solutions of the GPE confirm this finding for small perturbations of finite amplitude. They also reveal the existence of a critical amplitude above which instabilities, in the form of vortices, are nucleated at the solid wall in finite time. Once nucleated, these vortices convect away from the solid wall with infinite initial speed. The physical mechanism underlying this nonlinear phenomenon is discussed, and a proposal is advanced to deepen its understanding.
We apply the Halperin-Mazenco formalism within the Gross-Pitaevskii theory to characterise the kinematics and nucleation of quantum vortices in a two-dimensional stirred Bose Einstein condensate. We introduce a smooth defect density field measuring the superfluid vorticity and is a topologically conserved quantity. We use this defect density field and its associated current density to study the precursory pattern formations that occur inside the repulsive potential of an obstacle and determine the onset of vortex nucleation and shedding. We demonstrate that phase slips form inside hard potentials even in the absence of vortex nucleation, whereas for soft potentials they occur only above a critical stirring velocity leading to vortex nucleation. The Halperin-Mazenco formalism provides an elegant and accurate method of deriving the point vortex dynamic directly from the Gross-Pitaevskii equation.