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:1310.6989 · Physical Review A

Goldstone-mode instability leading to fragmentation in a spinor Bose-Einstein condensate

Yuki Kawaguchi

Published Mar 20, 2014• 18 citations
arXivHTMLPDF

Abstract

We apply the number-conserving Bogoliubov theory to spinor Bose-Einstein condensates and show that the Goldstone magnon causes instability leading to fragmentation. Unlike the dynamical instability, where modes with complex eigenfrequencies grow exponentially, here the zero-energy mode exhibits algebraic growth. We also point out that a small fraction of thermally excited atoms enhances the fragmentation dynamics.

DOI
10.1103/physreva.89.033627

Related papers

Dynamic fragmentation of a spinor Bose-Einstein condensate

Özgür Esat Müstecaplıoğlu, Mei Zhang, S. Yi +2 more

We investigate dynamical behavior of fragmentation of a spinor Bose-Einstein condensate in both the semiclassical and quantum regimes. We show that an unfragmented condensate can become fragmented at later times due to the inherent interactions of elastic atomic collisions, when a certain phase relationship exists among the state amplitudes in different components initially. A close relationship between the fragmentation and population dynamics of atomic distributions within different spin components is found for certain initial states with zero magnetization. The type of fragmentation regime is characterized via atom-number fluctuations. We also address complications of our study when the condensate spatial mode function is different for each spin component.

Physical Review A•Dec 23, 2003•18 citations

Quantum Mass Acquisition in Spinor Bose-Einstein Condensates

Nguyen Thanh Phuc, Yuki Kawaguchi, Masahito Ueda

Quantum mass acquisition, in which a massless (quasi)particle becomes massive due to quantum corrections, is predicted to occur in several subfields of physics. However, its experimental observation remains elusive since the emergent energy gap is too small. We show that a spinor Bose-Einstein condensate is an excellent candidate for the observation of such a peculiar phenomenon as the energy gap turns out to be 2 orders of magnitude larger than the zero-point energy. This extraordinarily large energy gap is a consequence of the dynamical instability. The propagation velocity of the resultant massive excitation mode is found to be decreased by the quantum corrections as opposed to phonons.

arXiv:1404.5685•Physical Review Letters•Dec 2, 2014•7 citations

Splitting instability of a multiply charged vortex in a Bose-Einstein condensate

Yuki Kawaguchi, Tetsuo Ohmi

We consider the splitting mechanism of a multiply charged vortex into singly charged vortices in a Bose-Einstein condensate confined in a harmonic potential at zero temperature. The Bogoliubov equations support unstable modes with complex eigenfrequencies (CE modes), which cause the splitting instability without the influence of thermal atoms. The investigation of the excitation spectra shows that the negative-energy (NE) mode plays an important role in the appearance of the CE modes. The configuration of vortices in splitting is determined by the angular momentum of the associated NE mode. This structure has also been confirmed by the numerical simulation of the time-dependent Gross-Pitaevskii equation.

arXiv:cond-mat/0402553•Physical Review A•Oct 11, 2004•112 citations

Beliaev Theory of Spinor Bose-Einstein Condensates and Its Applications

Thanh Phuc Nguyen

Due to the coexistence of phase coherence and magnetic order, Bose-Einstein condensates with internal degrees of freedom, i.e., spinor BECs, are considered to serve as an ideal table-top playground for the studies of various phenomena in different fields of physics.They have been widely used in studying spin textures and topological defects, coherent spin dynamics, quantum symmetry breaking, quantum phase transitions, etc.However, the theoretical framework used in these works is based on the mean-field theory in which the effects of quantum fluctuations are ignored.Despite the success of the mean-field theory in the description of spinor BECs, there are particular features whose account must rely on a beyond-mean-field theory as the effects of quantum fluctuations become significant.In this thesis, we develop the Beliaev theory, which is a Green's function approach beyond the Bogoliubov theory, for spinor BECs to study the effects of quantum fluctuations on the condensates' phase structures, elementary excitations, stabilities, and phase transitions.First, we point out that the Bogoliubov theory fails to capture the metastable states associated with first-order quantum phase transitions in spin-2 BECs.In fact, we show that these metastable states are induced by quantum fluctuations, and only by going to the next-order approximation, i.e., the Beliaev theory, can we show that they indeed appear around the phase boundaries.Besides the fluctuation-induced metastability, we find another important class of first-order quantum phase transitions in both spin-1 and spin-2 BECs.In this class, there is no metastable state to all orders of approximation since it is prohibited by a high symmetry of the Hamiltonian at the phase boundary, resulting in a characteristic flat energy landscape.Despite being first-order phase transitions, the flat energy landscape leads to the criticality in the dynamics of the condensate through these transitions in a manner similar to second-order phase transitions.Second, we succeed in deriving the analytic expression for the energy gap of the so-called quasi-Nambu-Goldstone (quasi-NG) modes, which are excitations not generated by spontaneous symmetry breaking, in the nematic phase of spin-2 BECs.Although quasi-NG modes are gapless at the mean-field level, we prove that with quantum corrections they acquire a nonzero energy gap.From the obtained magnitude of the energy gap, we can evaluate the critical temperature above which a topological defect such as a vortex of spin nematicity would decay by emitting thermally excited quasi-NG modes.We also study how the propagation of quasi-NG modes in space is affected by the particle-number density fluctuations of the condensate.Third, we calculate the damping rates of various types of quasiparticles in a spin-2 BEC including phonons, magnons, and quasi-NG modes.They actually have finite lifetime and decay via numerous channels of collision with the condensate atoms.Using either the Fermi's golden rule or the spinor Beliaev theory, we obtain the analytic expressions for the damping rates of phonons and magnons, from which the power-law dependence of the damping rates on the momentum is deduced.In contrast, the damping of quasi-NG modes is suppressed due to the energy conservation.

•Mar 24, 2014•0 citations

Relationship Between Dynamical Instability and Zero Modes for Dark Soliton in Bose–Einstein Condensate

Junichi Takahashi, Yusuke Nakamura, Y. Yamanaka

Investigating the Bogoliubov-de Gennes equation, widely used in the analysis of Bose-Einstein condensate in neutral atomic gases, we reveal some aspect of the interplay between the zero and complex modes. The complex mode implies that the system is dynamically unstable. The zero modes originate from the spontaneous symmetry breakdown, but their roles are not clear because they cause the infrared divergence. In this paper, we deal with the system of a dark soliton in Bose-Einstein condensate which has two zero modes corresponding to the spontaneously broken U(1) gauge and translational symmetries, and show that the zero and its adjoint modes, associated with the spontaneous breakdown of translational symmetry, turn into pure imaginary modes under the perturbation which explicitly breaks translational symmetry.

Asia Pacific Physics Conference (APPC)•Mar 19, 2014•0 citations

Full-time dynamics of modulational instability in spinor Bose-Einstein condensates

Evgeny V. Doktorov, Vassilis M. Rothos, Yuri S. Kivshar

We describe the full-time dynamics of modulational instability in $F=1$ spinor Bose-Einstein condensates for the case of the integrable three-component model associated with the matrix nonlinear Schr\"odinger equation. We obtain an exact homoclinic solution of this model by employing the dressing method which we generalize to the case of the higher-rank projectors. This homoclinic solution describes the development of modulational instability beyond the linear regime, and we show that the modulational instability demonstrates the reversal property when the growth of the modulated amplitude is changed by its exponential decay.

arXiv:0704.2280•Physical Review A•Jul 27, 2007•22 citations
We apply the number-conserving Bogoliubov theory to spinor Bose-Einstein condensates and show that the Goldstone magnon causes instability leading to fragmentation. Unlike the dynamical instability, where modes with complex eigenfrequencies grow exponentially, here the zero-energy mode exhibits algebraic growth. We also point out that a small fraction of thermally excited atoms enhances the fragmentation dynamics.
We investigate dynamical behavior of fragmentation of a spinor Bose-Einstein condensate in both the semiclassical and quantum regimes. We show that an unfragmented condensate can become fragmented at later times due to the inherent interactions of elastic atomic collisions, when a certain phase relationship exists among the state amplitudes in different components initially. A close relationship between the fragmentation and population dynamics of atomic distributions within different spin components is found for certain initial states with zero magnetization. The type of fragmentation regime is characterized via atom-number fluctuations. We also address complications of our study when the condensate spatial mode function is different for each spin component.
Quantum mass acquisition, in which a massless (quasi)particle becomes massive due to quantum corrections, is predicted to occur in several subfields of physics. However, its experimental observation remains elusive since the emergent energy gap is too small. We show that a spinor Bose-Einstein condensate is an excellent candidate for the observation of such a peculiar phenomenon as the energy gap turns out to be 2 orders of magnitude larger than the zero-point energy. This extraordinarily large energy gap is a consequence of the dynamical instability. The propagation velocity of the resultant massive excitation mode is found to be decreased by the quantum corrections as opposed to phonons.
We consider the splitting mechanism of a multiply charged vortex into singly charged vortices in a Bose-Einstein condensate confined in a harmonic potential at zero temperature. The Bogoliubov equations support unstable modes with complex eigenfrequencies (CE modes), which cause the splitting instability without the influence of thermal atoms. The investigation of the excitation spectra shows that the negative-energy (NE) mode plays an important role in the appearance of the CE modes. The configuration of vortices in splitting is determined by the angular momentum of the associated NE mode. This structure has also been confirmed by the numerical simulation of the time-dependent Gross-Pitaevskii equation.
Due to the coexistence of phase coherence and magnetic order, Bose-Einstein condensates with internal degrees of freedom, i.e., spinor BECs, are considered to serve as an ideal table-top playground for the studies of various phenomena in different fields of physics.They have been widely used in studying spin textures and topological defects, coherent spin dynamics, quantum symmetry breaking, quantum phase transitions, etc.However, the theoretical framework used in these works is based on the mean-field theory in which the effects of quantum fluctuations are ignored.Despite the success of the mean-field theory in the description of spinor BECs, there are particular features whose account must rely on a beyond-mean-field theory as the effects of quantum fluctuations become significant.In this thesis, we develop the Beliaev theory, which is a Green's function approach beyond the Bogoliubov theory, for spinor BECs to study the effects of quantum fluctuations on the condensates' phase structures, elementary excitations, stabilities, and phase transitions.First, we point out that the Bogoliubov theory fails to capture the metastable states associated with first-order quantum phase transitions in spin-2 BECs.In fact, we show that these metastable states are induced by quantum fluctuations, and only by going to the next-order approximation, i.e., the Beliaev theory, can we show that they indeed appear around the phase boundaries.Besides the fluctuation-induced metastability, we find another important class of first-order quantum phase transitions in both spin-1 and spin-2 BECs.In this class, there is no metastable state to all orders of approximation since it is prohibited by a high symmetry of the Hamiltonian at the phase boundary, resulting in a characteristic flat energy landscape.Despite being first-order phase transitions, the flat energy landscape leads to the criticality in the dynamics of the condensate through these transitions in a manner similar to second-order phase transitions.Second, we succeed in deriving the analytic expression for the energy gap of the so-called quasi-Nambu-Goldstone (quasi-NG) modes, which are excitations not generated by spontaneous symmetry breaking, in the nematic phase of spin-2 BECs.Although quasi-NG modes are gapless at the mean-field level, we prove that with quantum corrections they acquire a nonzero energy gap.From the obtained magnitude of the energy gap, we can evaluate the critical temperature above which a topological defect such as a vortex of spin nematicity would decay by emitting thermally excited quasi-NG modes.We also study how the propagation of quasi-NG modes in space is affected by the particle-number density fluctuations of the condensate.Third, we calculate the damping rates of various types of quasiparticles in a spin-2 BEC including phonons, magnons, and quasi-NG modes.They actually have finite lifetime and decay via numerous channels of collision with the condensate atoms.Using either the Fermi's golden rule or the spinor Beliaev theory, we obtain the analytic expressions for the damping rates of phonons and magnons, from which the power-law dependence of the damping rates on the momentum is deduced.In contrast, the damping of quasi-NG modes is suppressed due to the energy conservation.
Investigating the Bogoliubov-de Gennes equation, widely used in the analysis of Bose-Einstein condensate in neutral atomic gases, we reveal some aspect of the interplay between the zero and complex modes. The complex mode implies that the system is dynamically unstable. The zero modes originate from the spontaneous symmetry breakdown, but their roles are not clear because they cause the infrared divergence. In this paper, we deal with the system of a dark soliton in Bose-Einstein condensate which has two zero modes corresponding to the spontaneously broken U(1) gauge and translational symmetries, and show that the zero and its adjoint modes, associated with the spontaneous breakdown of translational symmetry, turn into pure imaginary modes under the perturbation which explicitly breaks translational symmetry.
We describe the full-time dynamics of modulational instability in F=1F=1F=1 spinor Bose-Einstein condensates for the case of the integrable three-component model associated with the matrix nonlinear Schr\"odinger equation. We obtain an exact homoclinic solution of this model by employing the dressing method which we generalize to the case of the higher-rank projectors. This homoclinic solution describes the development of modulational instability beyond the linear regime, and we show that the modulational instability demonstrates the reversal property when the growth of the modulated amplitude is changed by its exponential decay.