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. B, Condensed matter

Vortex-pair state in rotating superfluid A3 at low temperatures

Kazumi Maki, X. Zotos

Published Jan 1, 1985• 13 citations
Publisher

Abstract

An earlier analysis of the vortex-pair state is extended to lower temperatures. It is shown that the circular-hyperbolic pair describes both the observed transverse satellite frequency and intensity quite well. However, it appears rather difficult to distinguish the radial-hyperbolic pair from the circular-hyperbolic pair. We also predict that the distance between vortices in a pair increases rapidly as the temperature decreases, which can be tested by ultrasonic attenuation.

DOI
10.1103/physrevb.31.177

Related papers

Vortex pairs in rotating A3 in a tilted magnetic field

Kazumi Maki, X. Zotos

We extend our analysis of Seppaaumllaauml-Volovik vortices in rotating $^{3}\mathit{A}$ in a high magnetic field to the configuration where the magnetic field is tilted from the rotation axis. We find that the distance between vortices in a vortex pair decreases as the tilting angle increases from 0 to \ensuremath{\pi}/2. While the transverse NMR satellite frequency is quite insensitive to tilting except at lower temperature, the intensity of the resonance increases by almost 30% when ${\ensuremath{\theta}}_{0}$=\ensuremath{\pi}/2 compared to that for ${\ensuremath{\theta}}_{0}$=0 (${\ensuremath{\theta}}_{0}$ is the tilting angle) at T/${T}_{c}$\ensuremath{\simeq}0.75. This is quite consistent with the recent experimental result of Seppaaumllaauml et al.

Physical review. B, Condensed matter•Mar 1, 1985•5 citations

Experiments on Vortices in Rotating Superfluid He3 - A

Pertti Juhani Hakonen, Olli T. Ikkala, S. T. Islander

A satellite peak has been observed in the NMR spectrum of rotating $^{3}\mathrm{He}$-$A$; the peak intensity depends linearly on $\ensuremath{\Omega}$ at the high angular velocities, $\ensuremath{\Omega}=0.6\ensuremath{-}1.5$ rad/s, needed to resolve it. The frequency shift of the satellite is independent of $\ensuremath{\Omega}$. These results strongly suggest the existence of vortices in rotating $^{3}\mathrm{He}$-$A$ with the vortex density proportional to $\ensuremath{\Omega}$. Another satellite peak also has been observed which probably is due to solitons.

Physical Review Letters•Oct 25, 1982•108 citations

Vortex lattices in rapidly rotating Bose-Einstein condensates: Modes and correlation functions

Gordon Baym

After delineating the physical regimes that vortex lattices encounter in rotating Bose-Einstein condensates as the rotation rate $\ensuremath{\Omega}$ increases, we derive the normal modes of the vortex lattice in two dimensions at zero temperature. Taking into account effects of the finite compressibility, we find an inertial mode of frequency $\ensuremath{\geqslant}2\ensuremath{\Omega}$, and a primarily transverse Tkachenko mode, whose frequency goes from being linear in the wave vector in the slowly rotating regime, where $\ensuremath{\Omega}$ is small compared with the lowest compressional mode frequency, to quadratic in the wave vector in the opposite limit. We calculate the correlation functions of vortex displacements and phase, density and superfluid velocities, and find that the zero-point excitations of the soft quadratic Tkachenko modes lead in a large system to a loss of long-range phase correlations, growing logarithmically with distance, and hence lead to a fragmented state at zero temperature. The vortex positional ordering is preserved at zero temperature, but the thermally excited Tkachenko modes cause the relative positional fluctuations to grow logarithmically with separation at finite temperature. The superfluid density, defined in terms of the transverse velocity autocorrelation function, vanishes at all temperatures. Finally we construct the long-wavelength single-particle Green's function in the rotating system and calculate the condensate depletion as a function of temperature.

arXiv:cond-mat/0308342•Physical Review A•Apr 27, 2004•51 citations

Spatial Distribution of Superfluid Vortices

D. Scott Shenk, James B. Mehl

We report accurate measurements of the increase, due to rotation, of the attenuation of second sound in an annulus. The measurements can be explained in detail by a vortex-free-region model in close agreement with theory, assuming a vortex-core parameter of 10 \AA{} at 1.65 K. The range of agreement extends from the vorticity threshold to relatively high angular velocities.

Physical Review Letters•Dec 20, 1971•13 citations

Slow Vortex Formation in Applied Flow: the Precursor to Superfluid Turbulence

Antti Finne, V. B. Eltsov, Georg Eska +5 more

The dynamics of quantized vortices in rotating $^3$He-B is investigated in the low density (single-vortex) regime as a function of temperature. An abrupt transition is observed at $0.5 T_{\rm c}$. Above this temperature the number of vortex lines remains constant, as they evolve to their equilibrium positions. Below this temperature the number of vortices increases linearly in time until the vortex density has grown sufficiently for turbulence to switch on. On the basis of numerical calculations we suggest a mechanism responsible for vortex formation at low temperatures and identify the mutual friction parameter which governs its abrupt temperature dependence.

arXiv:cond-mat/0502119•Feb 4, 2005•0 citations

Vortex states in rotating A3 in a weak magnetic field

X. Zotos, Kazumi Maki

We study theoretically the phase diagram of vortex states in $^{3}\mathit{A}$ in a weak magnetic field H\ensuremath{\sim}${H}_{0}$(30 Oe). We find that the lattice of 2\ensuremath{\pi} analytic vortices proposed by Fujita et al. has the lowest free energy for H\ensuremath{\ll}${H}_{0}$, while for H\ensuremath{\gg}${H}_{0}$ the lattice of vortex pairs (Sepp\"al\"a-Volovik vortices) is more favorable. In the vicinity of the transition temperature (T>0.8${T}_{c}$) the lattice of dipole-locked vortex pairs appears between the above two configurations in a magnetic field H\ensuremath{\sim}0.5${H}_{0}$ and for a rotation speed \ensuremath{\Omega}\ensuremath{\lesssim}0.04 rad/sec.

Physical review. B, Condensed matter•Jun 1, 1985•11 citations
An earlier analysis of the vortex-pair state is extended to lower temperatures. It is shown that the circular-hyperbolic pair describes both the observed transverse satellite frequency and intensity quite well. However, it appears rather difficult to distinguish the radial-hyperbolic pair from the circular-hyperbolic pair. We also predict that the distance between vortices in a pair increases rapidly as the temperature decreases, which can be tested by ultrasonic attenuation.
We extend our analysis of Seppaaumllaauml-Volovik vortices in rotating 3A^{3}\mathit{A}3A in a high magnetic field to the configuration where the magnetic field is tilted from the rotation axis. We find that the distance between vortices in a vortex pair decreases as the tilting angle increases from 0 to \ensuremath{\pi}/2. While the transverse NMR satellite frequency is quite insensitive to tilting except at lower temperature, the intensity of the resonance increases by almost 30% when ${\ensuremath{\theta}}_{0}$=\ensuremath{\pi}/2 compared to that for ${\ensuremath{\theta}}_{0}$=0 (${\ensuremath{\theta}}_{0}$ is the tilting angle) at T/Tc{T}_{c}Tc​\ensuremath{\simeq}0.75. This is quite consistent with the recent experimental result of Seppaaumllaauml et al.
A satellite peak has been observed in the NMR spectrum of rotating 3He^{3}\mathrm{He}3He-AAA; the peak intensity depends linearly on $\ensuremath{\Omega}$ at the high angular velocities, $\ensuremath{\Omega}=0.6\ensuremath{-}1.5$ rad/s, needed to resolve it. The frequency shift of the satellite is independent of $\ensuremath{\Omega}$. These results strongly suggest the existence of vortices in rotating 3He^{3}\mathrm{He}3He-AAA with the vortex density proportional to $\ensuremath{\Omega}$. Another satellite peak also has been observed which probably is due to solitons.
After delineating the physical regimes that vortex lattices encounter in rotating Bose-Einstein condensates as the rotation rate $\ensuremath{\Omega}$ increases, we derive the normal modes of the vortex lattice in two dimensions at zero temperature. Taking into account effects of the finite compressibility, we find an inertial mode of frequency $\ensuremath{\geqslant}2\ensuremath{\Omega}$, and a primarily transverse Tkachenko mode, whose frequency goes from being linear in the wave vector in the slowly rotating regime, where $\ensuremath{\Omega}$ is small compared with the lowest compressional mode frequency, to quadratic in the wave vector in the opposite limit. We calculate the correlation functions of vortex displacements and phase, density and superfluid velocities, and find that the zero-point excitations of the soft quadratic Tkachenko modes lead in a large system to a loss of long-range phase correlations, growing logarithmically with distance, and hence lead to a fragmented state at zero temperature. The vortex positional ordering is preserved at zero temperature, but the thermally excited Tkachenko modes cause the relative positional fluctuations to grow logarithmically with separation at finite temperature. The superfluid density, defined in terms of the transverse velocity autocorrelation function, vanishes at all temperatures. Finally we construct the long-wavelength single-particle Green's function in the rotating system and calculate the condensate depletion as a function of temperature.
The dynamics of quantized vortices in rotating 3^33He-B is investigated in the low density (single-vortex) regime as a function of temperature. An abrupt transition is observed at 0.5Tc0.5 T_{\rm c}0.5Tc​. Above this temperature the number of vortex lines remains constant, as they evolve to their equilibrium positions. Below this temperature the number of vortices increases linearly in time until the vortex density has grown sufficiently for turbulence to switch on. On the basis of numerical calculations we suggest a mechanism responsible for vortex formation at low temperatures and identify the mutual friction parameter which governs its abrupt temperature dependence.
We study theoretically the phase diagram of vortex states in 3A^{3}\mathit{A}3A in a weak magnetic field H\ensuremath{\sim}H0{H}_{0}H0​(30 Oe). We find that the lattice of 2\ensuremath{\pi} analytic vortices proposed by Fujita et al. has the lowest free energy for H\ensuremath{\ll}H0{H}_{0}H0​, while for H\ensuremath{\gg}H0{H}_{0}H0​ the lattice of vortex pairs (Sepp\"al\"a-Volovik vortices) is more favorable. In the vicinity of the transition temperature (T>0.8Tc{T}_{c}Tc​) the lattice of dipole-locked vortex pairs appears between the above two configurations in a magnetic field H\ensuremath{\sim}0.5H0{H}_{0}H0​ and for a rotation speed \ensuremath{\Omega}\ensuremath{\lesssim}0.04 rad/sec.