arXiv subjects

Makoto Tsubota

Publications and source records attributed to Makoto Tsubota.

At least 127 records · Page 7Linked to original sources

arXiv2006

Phase Separation of a Fast Rotating Boson-Fermion Mixture in the Lowest-Landau-Level Regime

By minimizing the coupled mean-field energy functionals, we investigate the ground-state properties of a rotating atomic boson-fermion mixture in a two-dimensional parabolic trap. At high angular frequencies in the mean-field-lowest-Landau-level regime, quantized vortices enter the bosonic condensate, and a finite number of degenerate fermions form the maximum-density-droplet state. As the boson-fermion coupling constant increases, the maximum density droplet develops into a lower-density state associated with the phase separation, revealing characteristics of a Landau-level structure.

cond-mat.mes-hall↗

arXiv2006

Self-Organization of Vortex Length Distribution in Quantum Turbulence: An Approach from the Barabasi-Albert Model

The energy spectrum of quantum turbulence obeys Kolmogorov's law. The vortex length distribution (VLD), meaning the size distribution of the vortices, in Kolmogorov quantum turbulence also obeys a power law. We propose here an innovative idea to study the origin of the power law of the VLD. The nature of quantized vortices allows one to describe the decay of quantum turbulence with a simple model that is similar to the Barabasi-Albert model of large networks. We show here that such a model can reproduce the power law of the VLD well.

cond-mat.other↗

arXiv2006

Kolmogorov Spectrum of Quantum Turbulence

There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of stable topological defects called quantized vortices, and thus quantum turbulence provides a simpler prototype of turbulence than classical turbulence. In this paper, we investigate the dynamics and statistics of quantized vortices in quantum turbulence by numerically solving a modified Gross-Pitaevskii equation. First, to make decaying turbulence, we introduce a dissipation term that works only at scales below the healing length. Second, to obtain steady turbulence through the balance between injection and decay, we add energy injection at large scales. The energy spectrum is quantitatively consistent with the Kolmogorov law in both decaying and steady turbulence. Consequently, this is the first study that confirms the inertial range of quantum turbulence.

cond-mat.other↗

arXiv2005

Quantum Phase Transition from Superfluid to Localized Condensates of Bose Fluid in a Confined Potential

We develop a model of a strongly correlated Bose fluid model in a confined potential for the purpose of analyzing the localization of Bose-Einstein condensation and the disappearance of superfluidity. This work is motivated by the recent observation of a quantum phase transition in liquid $^4$He in porous glass at high pressures. By introducing a pressure-dependent localization length of the localized condensates, we could make a new analytical criterion for the localization of the condensate. Without introducing any free parameters, the resulting critical pressure of the transition from superfluid to localization is shown to be quantitatively consistent with observations.

cond-mat.dis-nn↗

arXiv2005

Inertial Range and the Kolmogorov Spectrum of Quantum Turbulenc

Quantum turbulence is numerically studied by solving the Gross-Pitaevskii equation. Introducing both the energy dissipation at small scales and the energy injection at large scales, we succeed in obtaining the steady turbulence made by the balance of the injection and the dissipation of the energy. The inertial range takes the Kolmogorov spectrum and the energy flux is consistent with the energy dissipation rate at small scales. These results confirm the properties of the inertial range of quantum turbulence, proposing a prototype of turbulence much simpler than conventional classical turbulence.

cond-mat.stat-mech↗

arXiv2005

Localization of Bose-Einstein Condensation and Disappearance of Superfluidity of Strongly Correlated Bose Fluid in a Confined Potential

We develop a Bose fluid model in a confined potential to consider the new quantum phase due to the localization of Bose-Einstein condensation and disappearance of superfluidity which is recently observed in liquid 4He in porous glass at high pressures. A critical pressure of the transition to this phase can be defined by our new analytical criterion of supposing the size of localized Bose-Einstein condensate becomes comparable to the scale of confinement. The critical pressure is quantitatively consistent with observations without free parameters.

cond-mat.dis-nn↗

arXiv2005

Spin textures in rotating two-component Bose-Einstein condensates

We investigate two kinds of coreless vortices with axisymmetric and nonaxisymmetric configurations in rotating two-component Bose-Einstein condensates. Starting from the Gross-Pitaevskii energy functional in a rotating frame, we derive a nonlinear sigma model generalized to the two-component condensates. In terms of a pseudospin representation, an axisymmetric vortex and a nonaxisymmetric one correspond to spin textures referred to as a "skyrmion" and a "meron-pair", respectively. A variational method is used to investigate the dependence of the sizes of the stable spin textures on system parameters, and the optimized variational function is found to reproduce well the numerical solution. In the SU(2) symmetric case, the optimal skyrmion and meron-pair are degenerate and transform to each other by a rotation of the pseudospin. An external rf-field that couples coherently the hyperfine states of two components breaks the degeneracy in favor of the meron-pair texture due to an effective transverse pseudomagnetic field. The difference between the intracomponent and intercomponent interactions yields a longitudinal pseudomagnetic field and a ferromagnetic or an antiferromagnetic pseudospin interaction, leading to a meron-pair texture with an anisotropic distribution of vorticity.

cond-mat.mes-hall↗

arXiv2005

Vortices in multicomponent Bose-Einstein condensates

We review the topic of quantized vortices in multicomponent Bose-Einstein condensates of dilute atomic gases, with an emphasis on that in two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross-Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose-Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose-Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.

cond-mat.other↗

arXiv2005

Three-dimensional dynamics of vortex lattice formation in Bose-Einstein condensates

We numerically study the dynamics of vortex lattice formation in a rotating cigar-shaped Bose-Einstein condensate. The study is a three-dimensional simulation of the Gross-Pitaevskii equation with a phenomenological dissipation term. The simulations reveal previously unknown dynamical features of the vortex nucleation process, in which the condensate undergoes a strongly turbulent stage and the penetrating vortex lines vibrate rapidly. The vibrations arise from spontaneous excitation of Kelvin waves on the proto-vortices during a surface wave instability, caused by an inhomogeneity of the condensate density along the elongated axial direction.

cond-mat.other↗

arXiv2004

Vortex molecules in coherently coupled two-component Bose-Einstein condensates

A vortex molecule is predicted in rotating two-component Bose-Einstein condensates whose internal hyperfine states are coupled coherently by an external field. A vortex in one component and that in the other are connected by a domain wall of the relative phase, constituting a "vortex molecule", which features a nonaxisymmetric (pseudo)spin texture with a pair of merons. The binding mechanism of the vortex molecule is discussed based on a generalized nonlinear sigma model and a variational ansatz. The anisotropy of vortex molecules is caused by the difference in the scattering lengths, yielding a distorted vortex-molecule lattice in fast rotating condensates.

cond-mat.mes-hall↗

arXiv2004

Multiple domain formation induced by modulation instability in two-component Bose-Einstein condensates

The dynamics of multiple domain formation caused by the modulation instability of two-component Bose-Einstein condensates in an axially symmetric trap are studied by numerically integrating the coupled Gross-Pitaevskii equations. The modulation instability induced by the intercomponent mean-field coupling occurs in the out-of-phase fluctuation of the wave function and leads to the formation of multiple domains that alternate from one domain to another, where the phase of one component jumps across the density dips where the domains of the other exist. This behavior is analogous to a soliton train, which explains the origin of the long lifetime of the spin domains observed by Miesner {it et al.} [Phys. Rev. Lett. {bf 82}, 2228 (1999)].

cond-mat.soft↗

arXiv2003

Chaotic Quantum Vortexes In A Weakly Non Ideal Bose Gas. Thermodynamic Equilibrium And Turbulence

We study the stochastic behavior of a set of chaotic vortex loops appeared in imperfect Bose gas. Dynamics of Bose-gas is supposed to obey Gross-Pitaevskii equation with additional noise satisfying fluctuation-dissipation relation. The corresponding Fokker-Planck equation for probability functional has solution ${\cal P}(\{ψ({\bf r})\})={\cal N}\exp (-H\{ψ({\bf r)}\} /T),$ where $H\{ψ({\bf r})\} $ is the Ginzburg-Landau free energy. Considering vortex filaments as topological defects of field $ψ({\bf r})$ we derive a Langevin-type equation of motion of the line with the correspondingly transformed stirring force. The respective Fokker-Planck equation for probability functional ${\cal P}(\{{\bf s}(ξ)\})$ in vortex loop configuration space is shown to have a solution in the form of ${\cal P}(\{{\bf s}(ξ)\})={\cal N}\exp (-H\{{\bf s}\} /T),$ where ${\cal N}$ is the normalizing factor and $H\{{\bf s}\} $ is energy of vortex line configurations. Analyzing this result we discuss possible reasons for destruction of the thermodynamic equilibrium and follow the mechanisms of transition to the turbulent state

cond-mat.soft↗

arXiv2003

Vortex phase diagram in rotating two-component Bose-Einstein condensates

We investigate the structure of vortex states in rotating two-component Bose-Einstein condensates with equal intracomponent but varying intercomponent coupling constants. A phase diagram in the intercomponent-coupling versus rotation-frequency plane reveals rich equilibrium structures of vortex states. As the ratio of intercomponent to intracomponent couplings increases, the interlocked vortex lattices undergo phase transitions from triangular to square, to double-core lattices, and eventually develop interwoven "serpentine" vortex sheets with each component made up of chains of singly quantized vortices.

cond-mat↗

arXiv2003

Dynamics of quantized vortices in superfluid helium and rotating Bose-Einstein condensates

In this article, we review the research on the dynamics of quantized vortices in superfluid helium and rotating Bose-Einstein condensates. First, after briefly reviewing the earlier research and describing the current problems on quantized vortices in superfluid $^4$He, we focus our review on superfluid turbulence and vortex filament dynamics. Superfluid turbulence was recently shown to have an energy spectrum consistent with the Kolmogorov law, which is an important statistical law in fully developed classical turbulence. We describe the diffusion of an inhomogeneous vortex tangle with relation to the observed decay of vortices at very low temperatures. We also describe the vortex states that appear in a rotating channel with counterflow. The competition between rotational effects and counterflow effects makes a new state of "a polarized vortex tangle". Next, we discuss recent numerical analysis of the Gross-Pitaevskii equation in the specific field of atomic-gas Bose-Einstein condensation. Consistent with observations, the simulated condensate starts an elliptic oscillation after the rotation is turned on, which induces the surface-mode excitations. The vortices develop from these surface excitations and then enter the bulk condensate, eventually forming a vortex lattice. When a condensate is held in a quadratic-plus-quartic combined potential, the fast rotation makes "a giant vortex" in which most vortices are absorbed into a central density hole.

cond-mat↗

arXiv2003

Quadrupole-scissors modes and nonlinear mode coupling in trapped two-component Bose-Einstein condensates

We theoretically investigate quadrupolar collective excitations in two-component Bose-Einstein condensates and their nonlinear dynamics associated with harmonic generation and mode coupling. Under the Thomas-Fermi approximation and the quadratic polynomial ansatz for density fluctuations, the linear analysis of the superfluid hydrodynamic equations predicts excitation frequencies of three normal modes constituted from monopole and quadrupole oscillations, and those of three scissors modes. We obtain analytically the resonance conditions for the second harmonic generation in terms of the trap aspect ratio and the strength of intercomponent interaction. The numerical simulation of the coupled Gross-Pitaevskii equations vindicates the validity of the analytical results and reveals the dynamics of the second harmonic generation and nonlinear mode coupling that lead to nonlinear oscillations of the condensate with damping and recurrence reminiscent of the Fermi-Pasta-Ulam problem.

cond-mat↗

arXiv2003

A Kelvin-wave cascade on a vortex in superfluid $^4$He at a very low temperature

A study by computer simulation is reported of the behaviour of a quantized vortex line at a very low temperature when there is continuous excitation of low-frequency Kelvin waves. There is no dissipation except by phonon radiation at a very high frequency. It is shown that non-linear coupling leads to a net flow of energy to higher wavenumbers and to the development of a simple spectrum of Kelvin waves that is insensitive to the strength and frequency of the exciting drive. The results are likely to be relevant to the decay of turbulence in superfluid $^4$He at very low temperatures.

cond-mat↗

arXiv2003

Instability of vortex array and transitions to turbulent states in rotating helium II

We consider superfluid helium inside a container which rotates at constant angular velocity and investigate numerically the stability of the array of quantized vortices in the presence of an imposed axial counterflow. This problem was studied experimentally by Swanson {\it et al.}, who reported evidence of instabilities at increasing axial flow but were not able to explain their nature. We find that Kelvin waves on individual vortices become unstable and grow in amplitude, until the amplitude of the waves becomes large enough that vortex reconnections take place and the vortex array is destabilized. The eventual nonlinear saturation of the instability consists of a turbulent tangle of quantized vortices which is strongly polarized. The computed results compare well with the experiments. Finally we suggest a theoretical explanation for the second instability which was observed at higher values of the axial flow.

cond-mat.soft↗

arXiv2003

Rotating Superfluid Turbulence

Almost all studies of vortex states in helium II have been concerned with either ordered vortex lattices or disordered vortex tangles. This work studies numerically what happens in the presence of both rotation (which induces order) and thermal counterflow (which induces disorder). We find a new statistically steady state in which the vortex tangle is polarized along the rotational axis. Our results are used to interpret an instability which was discovered experimentally by Swanson et al. years ago but has been unexplained until now.

cond-mat↗