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:cond-mat/0401251 · Physical Review A

Nambu-Goldstone mode in a rotating dilute Bose-Einstein condensate

Masahito Ueda, Tatsuya Nakajima

Published Apr 7, 2006• 21 citations
arXivHTMLPDF

Abstract

The Nambu-Goldstone mode (NGM), associated with vortex nucleation in a harmonically confined, two-dimensional dilute Bose-Einstein condensate is studied. We argue, based on exact diagonalization calculations, that the NGM manifests in the lowest-lying envelope of the quasidegenerate spectrum that emerges as the vortex is about to enter the condensate. The quasidegenerate states constitute a series of octupole-mode branches that originate primarily from pairwise repulsive interactions between octupole excitations and are distinguished by the number of admixed quadrupolar excitations. As the vortex approaches the center of the condensate and the system's axisymmetry is restored, the NGM becomes massive due to its coupling to higher rotational bands. We clarify the mechanism of this mass acquisition by using a newly developed projection-operator method.

DOI
10.1103/physreva.73.043603

Related papers

Two Nambu-Goldstone zero modes for rotating Bose-Einstein condensates

Rodney Polkinghorne, Tapio Simula

We consider rotating finite-size vortex arrays in Bose-Einstein condensates that are confined by cylindrically symmetric external potentials. We show that such systems possess two exact Nambu-Goldstone zero modes associated with two spontaneously broken continuous symmetries of the system. We verify our analytical result via direct numerical diagonalizations of the Bogoliubov--de Gennes equations. We conclude by comparing rotating vortex lattices in superfluids to supersolids and discrete time crystals.

arXiv:2109.04648•Physical Review A•Dec 8, 2021•7 citations

Nambu-Goldstone modes in segregated Bose-Einstein condensates

Hiromitsu Takeuchi, Kenichi Kasamatsu

Nambu-Goldstone modes in immiscible two-component Bose-Einstein condensates are studied theoretically. In a uniform system, a flat domain wall is stabilized and then the translational invariance normal to the wall is spontaneously broken in addition to the breaking of two U(1) symmetries in the presence of two complex order parameters. We clarify the properties of the low-energy excitations and identify that there exist two Nambu-Goldstone modes: an in-phase phonon with a linear dispersion and a ripplon with a fractional dispersion. The signature of the characteristic dispersion can be verified in segregated condensates in a harmonic potential.

arXiv:1309.3224•Physical Review A•Oct 9, 2013•32 citations

Breathing Modes in Rotating Bose-Condensed Gas: An Exact Diagonalization Study

Mohd. Imran, M. A. H. Ahsan

We present an exact diagonalization study of the breathing mode collective excitations for a rotating Bose-Einstein condensate of \(N = 10\) spinless bosons interacting via repulsive finiterange Gaussian potential and harmonically confined in quasi-two-dimension. The yrast state and the low-lying excited states are variationally obtained in given subspaces of the quantized total angular momentum \(L\) employing the beyond lowest Landau level approximation in slowly rotating regime with \(0\le L< 2N\). For a given \(L\), the low-energy eigenspectra (bands) are obtained in weakly to moderately interacting regime. Further, for a given interaction, the split in low-lying eigenenergies with increasing \(L\) is the precursor to spontaneous symmetry breaking of the axisymmetry associated with the entry of the first vortex. With increase in repulsive interaction, the value of the first breathing mode increases for stable total angular momentum states \(L = 0\) and \(N\), but decreases for intermediate \(0 < L < N\) metastable states. The position of the observed first breathing modes in the eigenspectrum remains unchanged as the interaction is varied over several orders of magnitude.

arXiv:1508.02202•Journal of Atomic Molecular Condensate and Nano Physics•Dec 4, 2015•2 citations

Applications of rotational excitations in Bose-Einstein condensates

Anssi Collin

This thesis contains theoretical studies of weakly interacting, trapped Bose-Einstein condensed gases. The main emphasis is on the rotational properties of these systems. A typical Bose-Einstein condensate reacts to external rotation by forming singly quantized vortices. By the word ”typical” we refer to a condensate with repulsive interparticle interactions and with a frozen spin degree of freedom. However, there are some atomic species for which the low-energy interactions are attractive. Moreover, the tuning of different condensate properties is relatively easy. For example, there are ways to experimentally change the effective interaction from repulsive to attractive. For an attractively interacting condensate the vortex is not the only possible rotational state but the sample may also experience rotation through its center of mass. In the first part of the thesis, we analyze some properties of a rotating attractive Bose gas at the zero temperature limit. First, we note that in order to maintain energetical stability, the gas has to be rotated in an external trap which is steeper than a harmonic trap. We study the system in an anharmonic quadratic + quartic potential. The rotating ground state phase-space is determined with analytical and numerical methods. If the interactions are strong enough, the rotating ground state appears to be a state with the rotating center of mass. On the other hand, at the limit of weak interactions the system experiences rotation by forming a multiply quantized vortex. We also determine the spectrum of elementary excitations for these quantum many-particle states. We find that the broken symmetry of the center of mass rotating state induces an additional zero-energy (Goldstone) mode and that the small oscillations of the ground state exhibit the decoupling between the center of mass and relative motions. If the spin of the atoms is allowed to change freely, a rich variety of topological excitations in condensates can be studied. External rotation is one of the tools for examining the excitations in spinor condensates. In a spinless scalar condensate the appearance of a quantized vortex is manifested by the vortex line in which the condensate density vanishes. In the plane perpendicular to the vortex line, one speaks of the vortex core for the density minimum. We study the properties of slowly rotated F = 1 spinor condensates and show that for ferromagnetic interactions the ground state is a coreless vortex. While the individual spin components may carry ordinary vortices the overall density of the system is coreless. We also study a method to create a point-like monopole structure in a ferromagnetic condensate by suitably imprinting vortices and solitons for different spin components of the condensate.

Työväentutkimus Vuosikirja•Mar 1, 2006•0 citations

Quasi-Nambu-Goldstone Modes in Bose-Einstein Condensates

Shun Uchino, Michikazu Kobayashi, Muneto Nitta +1 more

We show that quasi-Nambu-Goldstone (NG) modes, which play prominent roles in high energy physics but have been elusive experimentally, can be realized with atomic Bose-Einstein condensates. The quasi-NG modes emerge when the symmetry of a ground state is larger than that of the Hamiltonian. When they appear, the conventional vacuum manifold should be enlarged. Consequently, topological defects that are stable within the conventional vacuum manifold become unstable and decay by emitting the quasi-NG modes. Contrary to conventional wisdom, however, we show that the topological defects are stabilized by quantum fluctuations that make the quasi-NG modes massive, thereby suppressing their emission.

arXiv:1010.2864•Physical Review Letters•Dec 3, 2010•52 citations

Conformal symmetry of trapped Bose-Einstein condensates and massive Nambu-Goldstone modes

Keisuke Ohashi, Toshiaki Fujimori, Muneto Nitta

The Gross-Pitaevskii or nonlinear Schr\"odinger equation relevant to ultracold atomic gaseous Bose-Einstein condensates possesses a modified Schr\"odinger symmetry in two spatial dimensions, in the presence of a harmonic trapping potential, an (artificial) constant magnetic field (or rotation), and an (artificial) electric field of a quadratic electrostatic potential. We find that a variance and a center of a trapped gas with or without a vorticity can be regarded as massive Nambu-Goldstone (NG) modes associated with spontaneous breaking of the modified Schr\"odinger symmetry. We show that the Noether theorem for the modified Schr\"odinger symmetry gives universal equations of motion which describe exact time evolutions of the trapped gases such as a harmonic oscillation, a cyclotron motion, and a breathing oscillation with frequencies determined by the symmetry independent of the details of the system. We further construct an exact effective action for all the NG modes.

arXiv:1705.09118•Physical Review A•Nov 7, 2017•20 citations
The Nambu-Goldstone mode (NGM), associated with vortex nucleation in a harmonically confined, two-dimensional dilute Bose-Einstein condensate is studied. We argue, based on exact diagonalization calculations, that the NGM manifests in the lowest-lying envelope of the quasidegenerate spectrum that emerges as the vortex is about to enter the condensate. The quasidegenerate states constitute a series of octupole-mode branches that originate primarily from pairwise repulsive interactions between octupole excitations and are distinguished by the number of admixed quadrupolar excitations. As the vortex approaches the center of the condensate and the system's axisymmetry is restored, the NGM becomes massive due to its coupling to higher rotational bands. We clarify the mechanism of this mass acquisition by using a newly developed projection-operator method.
We consider rotating finite-size vortex arrays in Bose-Einstein condensates that are confined by cylindrically symmetric external potentials. We show that such systems possess two exact Nambu-Goldstone zero modes associated with two spontaneously broken continuous symmetries of the system. We verify our analytical result via direct numerical diagonalizations of the Bogoliubov--de Gennes equations. We conclude by comparing rotating vortex lattices in superfluids to supersolids and discrete time crystals.
Nambu-Goldstone modes in immiscible two-component Bose-Einstein condensates are studied theoretically. In a uniform system, a flat domain wall is stabilized and then the translational invariance normal to the wall is spontaneously broken in addition to the breaking of two U(1) symmetries in the presence of two complex order parameters. We clarify the properties of the low-energy excitations and identify that there exist two Nambu-Goldstone modes: an in-phase phonon with a linear dispersion and a ripplon with a fractional dispersion. The signature of the characteristic dispersion can be verified in segregated condensates in a harmonic potential.
We present an exact diagonalization study of the breathing mode collective excitations for a rotating Bose-Einstein condensate of N=10N = 10N=10 spinless bosons interacting via repulsive finiterange Gaussian potential and harmonically confined in quasi-two-dimension. The yrast state and the low-lying excited states are variationally obtained in given subspaces of the quantized total angular momentum LLL employing the beyond lowest Landau level approximation in slowly rotating regime with 0≤L<2N0\le L< 2N0≤L<2N. For a given LLL, the low-energy eigenspectra (bands) are obtained in weakly to moderately interacting regime. Further, for a given interaction, the split in low-lying eigenenergies with increasing LLL is the precursor to spontaneous symmetry breaking of the axisymmetry associated with the entry of the first vortex. With increase in repulsive interaction, the value of the first breathing mode increases for stable total angular momentum states L=0L = 0L=0 and NNN, but decreases for intermediate 0<L<N0 < L < N0<L<N metastable states. The position of the observed first breathing modes in the eigenspectrum remains unchanged as the interaction is varied over several orders of magnitude.
This thesis contains theoretical studies of weakly interacting, trapped Bose-Einstein condensed gases. The main emphasis is on the rotational properties of these systems. A typical Bose-Einstein condensate reacts to external rotation by forming singly quantized vortices. By the word ”typical” we refer to a condensate with repulsive interparticle interactions and with a frozen spin degree of freedom. However, there are some atomic species for which the low-energy interactions are attractive. Moreover, the tuning of different condensate properties is relatively easy. For example, there are ways to experimentally change the effective interaction from repulsive to attractive. For an attractively interacting condensate the vortex is not the only possible rotational state but the sample may also experience rotation through its center of mass. In the first part of the thesis, we analyze some properties of a rotating attractive Bose gas at the zero temperature limit. First, we note that in order to maintain energetical stability, the gas has to be rotated in an external trap which is steeper than a harmonic trap. We study the system in an anharmonic quadratic + quartic potential. The rotating ground state phase-space is determined with analytical and numerical methods. If the interactions are strong enough, the rotating ground state appears to be a state with the rotating center of mass. On the other hand, at the limit of weak interactions the system experiences rotation by forming a multiply quantized vortex. We also determine the spectrum of elementary excitations for these quantum many-particle states. We find that the broken symmetry of the center of mass rotating state induces an additional zero-energy (Goldstone) mode and that the small oscillations of the ground state exhibit the decoupling between the center of mass and relative motions. If the spin of the atoms is allowed to change freely, a rich variety of topological excitations in condensates can be studied. External rotation is one of the tools for examining the excitations in spinor condensates. In a spinless scalar condensate the appearance of a quantized vortex is manifested by the vortex line in which the condensate density vanishes. In the plane perpendicular to the vortex line, one speaks of the vortex core for the density minimum. We study the properties of slowly rotated F = 1 spinor condensates and show that for ferromagnetic interactions the ground state is a coreless vortex. While the individual spin components may carry ordinary vortices the overall density of the system is coreless. We also study a method to create a point-like monopole structure in a ferromagnetic condensate by suitably imprinting vortices and solitons for different spin components of the condensate.
We show that quasi-Nambu-Goldstone (NG) modes, which play prominent roles in high energy physics but have been elusive experimentally, can be realized with atomic Bose-Einstein condensates. The quasi-NG modes emerge when the symmetry of a ground state is larger than that of the Hamiltonian. When they appear, the conventional vacuum manifold should be enlarged. Consequently, topological defects that are stable within the conventional vacuum manifold become unstable and decay by emitting the quasi-NG modes. Contrary to conventional wisdom, however, we show that the topological defects are stabilized by quantum fluctuations that make the quasi-NG modes massive, thereby suppressing their emission.
The Gross-Pitaevskii or nonlinear Schr\"odinger equation relevant to ultracold atomic gaseous Bose-Einstein condensates possesses a modified Schr\"odinger symmetry in two spatial dimensions, in the presence of a harmonic trapping potential, an (artificial) constant magnetic field (or rotation), and an (artificial) electric field of a quadratic electrostatic potential. We find that a variance and a center of a trapped gas with or without a vorticity can be regarded as massive Nambu-Goldstone (NG) modes associated with spontaneous breaking of the modified Schr\"odinger symmetry. We show that the Noether theorem for the modified Schr\"odinger symmetry gives universal equations of motion which describe exact time evolutions of the trapped gases such as a harmonic oscillation, a cyclotron motion, and a breathing oscillation with frequencies determined by the symmetry independent of the details of the system. We further construct an exact effective action for all the NG modes.