We apply the theory of the inhomogeneous Kibble-Zurek mechanism to understand the quench dynamics in the transition from a Mott insulator to a superfluid in a cold Bose gas confined in both a two-dimensional optical lattice and a harmonic trap. The local quench time and the resulting Kibble-Zurek diabatic-adiabatic boundary take a nontrivial positional dependence due to the Mott-lobe structure of the ground-state phase diagram of the Bose-Hubbard model. We demonstrate the quench dynamics through the time-dependent Gutzwiller simulations, revealing inhomogeneous properties of the growth of the superfluid order parameter. The inhomogeneous Kibble-Zurek theory is applicable to the shallow harmonic trap.

Quantum droplets are ultradilute liquid states that emerge from the competitive interplay of two Hamiltonian terms, the mean-field energy and beyond-mean-field correction, in a weakly interacting binary Bose gas. We relate the formation of droplets in symmetric and asymmetric two-component one-dimensional boson systems to the modulational instability of a spatially uniform state driven by the beyond-mean-field term. Asymmetry between the components may be caused by their unequal populations or unequal intra-component interaction strengths. Stability of both symmetric and asymmetric droplets is investigated. Robustness of the symmetric solutions against symmetry-breaking perturbations is confirmed.

We study transverse instability and disintegration dynamics of a domain wall
of a relative phase in two-component Bose-Einstein condensates with a coherent
Rabi coupling. We obtain analytically the stability phase diagram of the
stationary solution of the domain wall for the one-dimensional coupled
Gross-Pitaevskii equations in the plane of the Rabi frequency and the
intercomponent coupling constant. Outside the stable region, the domain wall is
dynamically unstable for the transverse modulation along the direction
perpendicular to the phase kink. The nonlinear evolution associated with the
instability is demonstrated through numerical simulations for both the domain
wall without edges and that with edges formed by the quantized vortices.

Superfluid He-3-B possesses three locally stable vortices known as a normal-core vortex (o vortex), an A-phasecore vortex (v vortex), and a double-core vortex (d vortex). In this work, we study the effects of a magnetic field (less than or similar to 0.1 T) parallel or perpendicular to the vortex axis on these structures by solving the two-dimensional Ginzburg-Landau equation for two different sets of strong coupling correction. The energies of the v and d vortices have nontrivial dependence on the magnetic field. As the parallel magnetic field increases, the v vortex is energetically unstable even at high pressures and the d vortex becomes energetically most stable at all possible pressures. In perpendicular magnetic field, the energy of the v vortex is lower than that of the d vortex in the high pressure regime. In addition, the orientation of the double cores in the d vortex prefers to be parallel to the magnetic field at low pressures, while the d vortex with the double cores perpendicular to the magnetic field is allowed to continuously deform into the v vortex with increasing pressure.

We study numerically the structure of a vortex lattice in rotating two-component Bose-Einstein condensates with equal atomic masses and equal intra- and intercomponent coupling strengths. The numerical simulations of the Gross-Pitaevskii equation show that the quantized vortices in this situation form lattice configuration accompanying vortex stripes, honeycomb lattices, and their complexes. This is a result of the degeneracy of the system for the SU(2) symmetric operation, which causes a continuous transformation between the above structures. In terms of the pseudospin representation, the complex lattice structures are identified as a hexagonal lattice of doubly winding half skyrmions.

We revisit the fundamental problem of the splitting instability of a doubly quantized vortex in uniform singlecomponent superfluids at zero temperature. We analyze the system-size dependence of the excitation frequency of a doubly quantized vortex through large-scale simulations of the Bogoliubov-de Gennes equation, and find that the system remains dynamically unstable even in the infinite-system-size limit. Perturbation and semi-classical theories reveal that the splitting instability radiates a damped oscillatory phonon as an opposite counterpart of a quasi-normal mode.

We present a theoretical study of quantum simulations of (1+1)-dimensional U(1) lattice gauge-Higgs models, which contain a compact U(1) gauge field and a Higgs matter field, by using ultracold bosonic gases on a one-dimensional optical lattice. Starting from the extended Bose-Hubbard model with on-site and nearest-neighbor interactions, we derive the U(1) lattice gauge-Higgs model as a low-energy effective theory. The derived gauge-Higgs model exhibits nontrivial phase transitions between the confinement and Higgs phases, and we discuss the relation with the phase transition in the extended Bose-Hubbard model. Finally, we study the real-time dynamics of an electric flux by the Gross-Pitaevskii equations and the truncated Wigner approximation. The dynamics is governed by a bosonic analog of the Schwinger mechanism - i.e., the shielding of an electric flux by a condensation of Higgs fields, which occurs differently in the Higgs and the confinement phases. These results, together with the obtained phase diagrams, shall guide experimentalists in designing quantum simulations of the gauge-Higgs models by using cold gases.

In this paper, we study theoretically atomic quantum simulations of a U(1) gauge-Higgs model on a three-dimensional (3D) spatial lattice by using an extended Bose-Hubbard model with intersite repulsions on a 3D optical lattice. Here, the phase and density fluctuations of the boson variable on each site of the optical lattice describe the vector potential and the electric field on each link of the gauge-model lattice, respectively. The target gauge model is different from the standard Wilson-type U(1) gauge-Higgs model because it has plaquette and Higgs interactions with asymmetric couplings in the space-time directions. Nevertheless, the corresponding quantum simulation is still important as it provides us with a platform to study unexplored time-dependent phenomena characteristic of each phase in the general gauge-Higgs models. To determine the phase diagram of the gauge-Higgs model at zero temperature, we perform Monte Carlo simulations of the corresponding 3+1-dimensional U(1) gauge-Higgs model, and obtain the confinement and Higgs phases. To investigate the dynamical properties of the gauge-Higgs model, we apply the Gross-Pitaevskii equations to the extended Bose-Hubbard model. We simulate the time evolution of an electric flux that initially is put on a straight line connecting two external point charges. We also calculate the potential energy between this pair of charges and obtain the string tension in the confinement phase. Finally, we propose a feasible experimental setup for the atomic simulations of this quantum gauge-Higgs model on the 3D optical lattice. These results may serve as theoretical guides for future experiments.

study vortex dynamics in trapped two-component Bose-Einstein condensates with a laser-induced spin-orbit coupling using the numerical analysis of the Gross-Pitaevskii equation. The spin-orbit coupling leads to three distinct ground-state phases, which depend on some experimentally controllable parameters. When a vortex is put in one or both of the two-component condensates, the vortex dynamics exhibits very different behaviors in each phase, which can be observed in experiments. These dynamical behaviors can be understood by clarifying the stable vortex structure realized in each phase.

Lattice gauge theory has provided a crucial non-perturbative method in studying canonical models in high-energy physics such as quantum chromodynamics. Among other models of lattice gauge theory, the lattice gauge-Higgs model is a quite important one because it describes a wide variety of phenomena/models related to the Anderson-Higgs mechanism, such as superconductivity, the standard model of particle physics, and the inflation process of the early Universe. In this paper, we first show that atomic description of the lattice gauge model allows us to explore real-time dynamics of the gauge variables by using the Gross-Pitaevskii equations. Numerical simulations of the time development of an electric flux reveal some interesting characteristics of the dynamic aspect of the model and determine its phase diagram. Next, to realize a quantum simulator of the U(1) lattice gauge-Higgs model on an optical lattice filled by cold atoms, we propose two feasible methods: (i) Wannier states in the excited bands and (ii) dipolar atoms in a multilayer optical lattice. Wepay attention to the constraint of Gauss's law and avoid nonlocal gauge interactions.

We have previously discussed the design of a neutral atom quantum computer with an on-demand interaction [E. Hosseini Lapasar et al., J. Phys. Soc. Jpn. 80, 114003 ( 2011)]. In this contribution, we propose an experimental method to demonstrate a selective two-qubit gate operation that is less demanding than our original proposal, although the gate operation is limited to act between two neighboring atoms. We evaluate numerically the process of a two-qubit gate operation that is applied to a selected pair of nearest-neighbor, trapped atoms and we estimate the upper bound of the gate operation time and corresponding gate fidelity. The proposed scheme is scalable and, though challenging, is feasible with current experimental capabilities.

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. © 2013 American Physical Society.

In certain field theoretical models, composite solitons consisting of a domain wall and vortex lines attached to the wall have been referred to as 'D-brane solitons'. We show that similar composite solitons can be realized in phase-separated two-component Bose-Einstein condensates. We discuss the similarities and differences between topological solitons in the Abelian-Higgs model and those in two-component Bose-Einstein condensates. On the basis of the formulation of gauge theory, we introduce the 'boojum charge' to characterize the D-brane soliton in Bose-Einstein condensates. © 2013 IOP Publishing Ltd.

Recently, the possibility of quantum simulation of dynamical gauge fields was pointed out by using a system of cold atoms trapped on each link in an optical lattice. However, to implement exact local gauge invariance, fine-tuning the interaction parameters among atoms is necessary. In the present Letter, we study the effect of violation of the U(1) local gauge invariance by relaxing the fine-tuning of the parameters and showing that a wide variety of cold atoms is still a faithful quantum simulator for a U(1) gauge-Higgs model containing a Higgs field sitting on sites. The clarification of the dynamics of this gauge-Higgs model sheds some light upon various unsolved problems, including the inflation process of the early Universe. We study the phase structure of this model by Monte Carlo simulation and also discuss the atomic characteristics of the Higgs phase in each simulator. © 2013 American Physical Society.

We study composite solitons, consisting of domain walls and vortex lines attaching to the walls in two-component Bose-Einstein condensates. When the total density of the two components is homogeneous, the system can be mapped to the O(3) nonlinear sigma model for the pseudospin representing the two-component order parameter, and the analytical solutions of the composite solitons can be obtained. Based on the analytical solutions, we discuss the detailed structure of the composite solitons in two-component condensates by employing the generalized nonlinear s model, where all degrees of freedom of the original Gross-Pitaevskii theory are active. The domain wall pulled by a vortex is logarithmically bent as a membrane pulled by a pin. It bends more flexibly than the domain wall in the sigma model, because the density inhomogeneity results in a reduction of the domain wall tension from that in the sigma model limit. We find, however, that the curvature of the wall bending pulled by a vortex is still greater than that expected from the reduced tension due to only the density inhomogeneity. Finally, we study the composite soliton structure for actual experimental situations with trapped immiscible condensates under rotation, through numerical simulations of the coupled Gross-Pitaevskii equations.

We review recent important topics in quantized vortices and quantum turbulence in atomic Bose–Einstein condensates (BECs). They have previously been studied for a long time in superfluid helium. Quantum turbulence is currently one of the most important topics in low-temperature physics. Atomic BECs have two distinct advantages over liquid helium for investigating such topics: quantized vortices can be directly visualized and the interaction parameters can be controlled by the Feshbach resonance. A general introduction is followed by a description of the dynamics of quantized vortices, hydrodynamic instability, and quantum turbulence in atomic BECs.

In brane cosmology, the Big Bang is hypothesized to occur by the annihilation of the brane-anti-brane pair in a collision, where the branes are threedimensional objects in a higher-dimensional Universe. Spontaneous symmetry breaking accompanied by the formation of lower-dimensional topological defects, e.g. cosmic strings, is triggered by the so-called 'tachyon condensation', where the existence of tachyons is attributable to the instability of the brane-anti-brane system. Here, we discuss the closest analogue of the tachyon condensation in atomic Bose-Einstein condensates. We consider annihilation of domain walls, namely branes, in strongly segregated two-component condensates, where one component is sandwiched by two domains of the other component. In this system, the process of the brane annihilation can be projected effectively as ferromagnetic ordering dynamics onto a twodimensional space. Based on this correspondence, three-dimensional formation of vortices from a domain-wall annihilation is considered to be a kink formation due to spontaneous symmetry breaking in the two-dimensional space. We also discuss a mechanism to create a 'vorton' when the sandwiched component has a vortex string bridged between the branes. We hope that this study motivates experimental researches to realize this exotic phenomenon of spontaneous symmetry breaking in superfluid systems. © Springer Science+Business Media, LLC 2012.

We consider a selective two-qubit gate operation in a neutral atom quantum computer. In this proposal neutral atoms are trapped by an array of near field Fresnel diffraction (NFFD) light with variable aperture size, by which the position of an atom can be controlled in a direction perpendicular to the aperture. Two-qubit gate operation between an arbitrary pair of atoms is implemented by sending these atoms to a one-dimensional optical lattice and then colliding a particular set of quantum states of these atoms. We analyze the two-qubit gate implementation in detail and obtain an upper bound of the gate operation time 7.87 ms with the corresponding fidelity 0.886.

We briefly review the theoretical formulation of bosons in an optical lattice subject to a effective magnetic field. Starting from the Bose-Hubbard Hamiltonian, we can reduce the problem into the classical frustrated system in the two limiting cases, i.e., the Josephson junction regime and the hard-core limit at finite temperatures. The former can be described by the uniformly frustrated XY model, which is accessible in usual BEC experiments in a deep optical lattice. The latter introduces the extended XY model with the fluctuation of the amplitude of pseudospins, referred to as the gauged CP1 model. The common features of the two systems are that the thermodynamic properties are sensitive to the magnetic flux piecing the plaquette. We show the results of the Monte Carlo simulations for the nontrivial latter case. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated XY model, where only the phase is a dynamical variable.

We show theoretically that a domain-wall annihilation in two-component Bose-Einstein condensates causes tachyon condensation accompanied by spontaneous symmetry breaking in a two-dimensional subspace. Three-dimensional vortex formation from domain-wall annihilations is considered a kink formation in subspace. Numerical experiments reveal that the subspatial dynamics obey the dynamic scaling law of phase-ordering kinetics. This model is experimentally feasible and provides insights into how the extra dimensions influence subspatial phase transition in higher-dimensional space. DOI: 10.1103/PhysRevLett.109.245301

We study a mechanism to create a vorton or three-dimensional skyrmion in phase-separated two-component BECs with the order parameters Psi(1) and Psi(2) of the two condensates. We consider a pair of a domain wall (brane) and an antidomain wall (antibrane) stretched by vortices (strings), where the Psi(2) component with a vortex winding is sandwiched by two domains of the Psi(1) component. The vortons appear when the domain wall pair annihilates. Experimentally, this can be realized by preparing the phase separation in the order Psi(1), Psi(2), and Psi(1) components, where the nodal plane of a dark soliton in Psi(1) component is filled with the Psi(2) component with vorticity. By selectively removing the filling Psi(2) component gradually with a resonant laser beam, the collision of the brane and antibrane can be made, creating vortons.

We study finite-temperature phase structures of hard-core bosons in a two-dimensional optical lattice subject to an effective magnetic field by employing the gauged CP1 model. Based on the extensive Monte Carlo simulations, we study their phase structures at finite temperatures for several values of the magnetic flux per plaquette of the lattice and mean particle density. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated XY model, with only the phase as a dynamical variable. This suggests that cold-atom simulators of the frustrated XY model are available irrespective of the particle filling at each site. © 2012 American Physical Society.

We study finite-temperature phase structures of hard-core bosons in a two-dimensional optical lattice subject to an effective magnetic field by employing the gauged CP1 model. Based on the extensive Monte Carlo simulations, we study their phase structures at finite temperatures for several values of the magnetic flux per plaquette of the lattice and mean particle density. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated XY model, with only the phase as a dynamical variable. This suggests that cold-atom simulators of the frustrated XY model are available irrespective of the particle filling at each site.

We study the dynamical properties of bosons in an optical lattice subject to a synthetic magnetic field at zero temperature. First, we consider a superfluid regime where the nearest-neighbor hopping is much larger than the on-site repulsion and a large number of bosons are occupied in each site. Then, the dynamics is well described by the discrete nonlinear Schrodinger equation. Second, we study the dynamics of hard-core bosons as a limit of the strong interparticle interaction by solving the truncated Green's functions for the boson and density operators. We discuss the evolution of the density and the vorticity, which are clearly distinct between two regimes.

We study the dynamics of vortex nucleation and lattice formation in a Bose-Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross-Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by R. A. Williams, especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency. © 2011 American Physical Society.

We study the dynamics of vortex nucleation and lattice formation in a Bose-Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross-Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by R. A. Williams et al. [Phys. Rev. Lett. 104, 050404 (2010)], especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency.

We propose a scalable neutral atom quantum computer with an on-demand interaction through a selective two-qubit gate operation. Atoms are trapped by a lattice of near field Fresnel diffraction lights so that each trap captures a single atom. One-qubit gate operation is implemented by a gate control laser beam which is applied to an individual atom. Two-qubit gate operation between an arbitrary pair of atoms is implemented by sending these atoms to a state-dependent optical lattice and making them collide so that a particular two-qubit state acquires a dynamical phase. We give numerical evaluations corresponding to these processes, from which we estimate the upper bound of a two-qubit gate operation time and corresponding gate fidelity. Our proposal is feasible within currently available technology developed in cold atom gas, MEMS, nanolithography, and various areas in optics.

We have studied a Bose-Einstein condensate of Rb-87 atoms under an oscillatory excitation. For a fixed frequency of excitation, we have explored how the values of amplitude and time of excitation must be combined in order to produce quantum turbulence in the condensate. Depending on the combination of these parameters different behaviors are observed in the sample. For the lowest values of time and amplitude of excitation, we observe a bending of the main axis of the cloud. Increasing the amplitude of excitation we observe an increasing number of vortices. The vortex state can evolve into the turbulent regime if the parameters of excitation are driven up to a certain set of combinations. If the value of the parameters of these combinations is exceeded, all vorticity disappears and the condensate enters into a different regime which we have identified as the granular phase. Our results are summarized in a diagram of amplitude versus time of excitation in which the different structures can be identified. We also present numerical simulations of the Gross-Pitaevskii equation which support our observations. (C) 2011 by Astro Ltd. Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA

We study the asymptotic interaction between two half-quantized vortices in two-component Bose-Einstein condensates. When two vortices in different components are placed at distance 2R, the leading order of the force between them is found to be (ln R/xi - 1/2)/R-3,in contrast to 1/R between vortices placed in the same component. We derive it analytically using the Abrikosov ansatz and the profile functions of the vortices, confirmed numerically with the Gross-Pitaevskii model. We also find that the short-range cutoff of the intervortex potential linearly depends on the healing length.

We theoretically study the vortex formation from the collision of the domain walls in phase-separated two-component Bose-Einstein condensates. The collision process mimics the tachyon condensation for the annihilation of D-brane and anti-D-brane in string theory. A pair annihilation leaves the quantized vortices with superflow along their core, namely superflowing cosmic strings. It is revealed that the line density and the core size of the vortices depend on the initial distance between the walls.

Dynamical instabilities at the interface between two Bose-Einstein condensates that are moving relative to each other are investigated using mean-field and Bogoliubov analyses. Kelvin-Helmholtz instability is dominant when the interface thickness is much smaller than the wavelength of the unstable interface mode, whereas the counter-superflow instability becomes dominant in the opposite case. These instabilities emerge not only in an immiscible system but also in a miscible system where an interface is produced by external potential. Dynamics caused by these instabilities are numerically demonstrated in rotating trapped condensates. © 2010 The American Physical Society.

Dynamical instabilities at the interface between two Bose-Einstein condensates that are moving relative to each other are investigated using mean-field and Bogoliubov analyses. Kelvin-Helmholtz instability is dominant when the interface thickness is much smaller than the wavelength of the unstable interface mode, whereas the counter-superflow instability becomes dominant in the opposite case. These instabilities emerge not only in an immiscible system but also in a miscible system where an interface is produced by external potential. Dynamics caused by these instabilities are numerically demonstrated in rotating trapped condensates.

We demonstrate theoretically that analogues of D-branes in string theory can be realized in rotating, phase-separated, two-component Bose-Einstein condensates and that they are observable using current experimental techniques. This study raises the possibility of simulating D-branes in the laboratory.

We theoretically study the Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates using the Gross-Pitaevskii and Bogoliubov-de Gennes models. A flat interface between the two condensates is shown to deform into sawtooth or Stokes-type waves, leading to the formation of singly quantized vortices on the peaks and troughs of the waves. This scenario of interface instability in quantum fluids is quite different from that in classical fluids.

We theoretically study Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates with shear flow at T=0. The stability of the shear flow state is investigated with the Gross-Pitaevskii and the Bogoliubov-de Gennes models, compared with a hydrodynamic model. The dynamics of the instability is revealed by numerically solving the Gross-Pitaevskii equation. In the nonlinear development, singly-quantized vortices are released from the interface between the two condensates.

We study interfacial topological defects called boojums, a vortex ending or a connecting point of two kinds of vortex cores, in rotating two-component Bose-Einstein condensates. First, we show that the boojum exists at a vortex ending that connects to the interface of the strongly phase-separated condensates. Next, we study various boojums appearing between two phases characterized by different vortex structures, where the intercomponent s-wave scattering lengths are spatially varied. Using three-dimensional simulations of the Gross-Pitaevskii equations, we reveal the detailed structure of the boojums by visualizing its density distribution and effective superflow vorticity.

We propose a different type of Landau instability in trapped Bose-Einstein condensates by a helically moving environment. In the presence of quantized vortices, the instability can cause spontaneous radiation and amplification of Kelvin waves. This study gives a microscopic understanding of the Donnelly-Glaberson instability which was known as the hydrodynamic instability in superfluid helium. The Donnelly-Glaberson instability can be a powerful tool for observing the dispersion relation of Kelvin waves, vortex reconnections, and quantum turbulence in atomic Bose-Einstein condensates.

We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained. © 2009 The American Physical Society.

We derive a uniformly frustrated XY model that describes two-dimensional Josephson-junction arrays consisting of rotating Bose-Einstein condensates trapped by both a harmonic trap and a corotating deep optical lattice. The harmonic trap makes the coupling constant of the model have a nonuniform parabolic dependence. We study the ground state through Monte Carlo simulations in a wide range of the frustration parameter f, revealing a rich variety of vortex patterns.

We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained.

In this review, we give an overview of the experimental and theoretical advances in the physics of quantised vortices in dilute atomic gas Bose-Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantised vortices by directly visualising vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilised by a rotating potential created by a laser beam, magnetic field and thermal gas. Finite-size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate. © 2009 Elsevier B.V.

We investigate the ground state structure of two-dimensional Josephson junction arrays consisting of Bose-Einstein condensates trapped by both a rotating harmonic potential and a corotating deep optical lattice with square symmetry. Monte Carlo simulations of the uniformly frustrated XY model in a wide range of the frustration parameter f reveal that the stable configuration of vortices for a simple fractional number f is a staircase structure, consisting of diagonal chains of vortices with periodic lattice of unit cells.

We consider theoretically static and dynamic properties of multicomponent Bose-Einstein condensates (BECs) composed of a mixture of Yb-174 and Yb-176 atoms. The condensate of Yb-176 atoms has an attractive interaction, collapsing above a certain critical particle number. This criterion is modified by the presence of another repulsive condensate of Yb-174 atoms. We discuss the stability condition of this condensate mixture and collapsing dynamics due to the instability.

We investigate the effect of rotation for two-dimensional Josephson junction arrays consisting of atomic Bose-Einstein condensates trapped by both a harmonic trap and an optical lattice. This system is analogous to the superconducting Josephson junction array to which a transverse magnetic field is applied, being described by the uniformly frustrated XY model. The frustration parameter f, defined by the rotation frequency of the condensate and the lattice constant of the optical lattice, is an important parameter to determine the ground state. The numerical simulations of the Gross-Pitaevskii equation reveal that for f = 1/2 the ground state possesses the checkerboard pattern of vortices, and for f < 1/2 the vortex configuration is characterized by the staircase form.

We present simulation results of the vortex dynamics in a trapped Bose-Einstein condensate in the presence of a rotating optical lattice. Changing the potential amplitude and the relative rotation frequency between the condensate and the optical lattice, we find a rich variety of dynamical phases of vortices. In particular, when the optical lattice rotates faster than the condensate, the competition between the pinning force and the interactions by nucleated interstitial vortices leads to the melting of vortex lattice, yielding a vortex liquid phase.

We present simulation results of the vortex dynamics in a trapped Bose-Einstein condensate in the presence of a rotating optical lattice. Changing the potential amplitude and the relative rotation frequency between the condensate and the optical lattice, we find a rich variety of dynamical phases of vortices. The onset of these different phases is described by the force balance of a driving force, a pinning force, and vortex-vortex interactions. In particular, when the optical lattice rotates faster than the condensate, an incommensurate effect leads to a vortex-liquid phase supported by the competition between the driving force and the dissipation.

We investigate nonlinear dynamics induced by the modulation instability of a two-component mixture in an atomic Bose-Einstein condensate. The nonlinear dynamics is examined using numerical simulations of the time-dependent coupled Gross-Pitaevskii equations. The unstable modulation grows from initially miscible condensates into various types of vector solitary waves, depending on the combinations of the sign of the coupling constants (intracomponent and intercomponent). We discuss the detailed features of the modulation instability, dynamics of solitary wave formation, and an analogy with the collapsing dynamics in a single-component condensate with attractive interactions.

We investigate nonlinear dynamics induced by the modulation instability of a two-component mixture in an atomic Bose-Einstein condensate. The nonlinear dynamics is examined using numerical simulations of the time-dependent coupled Gross-Pitaevskii equations. The unstable modulation grows from initially miscible condensates into various types of vector solitary waves, depending on the combinations of the sign of the coupling constants (intracomponent and intercomponent). We discuss the detailed features of the modulation instability, dynamics of solitary wave formation, and an analogy with the collapsing dynamics in a single-component condensate with attractive interactions. © 2006 The American Physical Society.

We investigate numerically stable structures of vortex states in rotating two-component Bose-Einstein condensates (BECs) in a quadratic plus quartic potential. We discover various new vortex structures by changing the intracomponent coupling constants, the intercomponent coupling constant and the rotation frequency.

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 protovortices during a surface wave instability, caused by an inhomogeneity of the condensate density along the elongated axial direction.

We review the topic of quantized vortices in multicomponent Bose-Einstein condensates of dilute atomic gases, with an emphasis on the 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. © World Scientific Publishing Company.

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.

We investigate the dynamics of pattern formation caused by the modulation instability of two-component Bose-Einstein condensates in trapping potentials based on the numerical analysis of 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. We especially focus on the dimensional dependence of the dynamics by varying the aspect ratio of the trapping potential, finding the two-step dynamic process of the pattern formation due to the different time scales of the instability in the different spatial dimensions. © 2005 Springer Science+Business Media, Inc.

We study theoretically and numerically the dynamics of quantized vortices in superfluid helium and rotating Bose-Einstein condensates. After reviewing briefly the recent motivation, we discuss these topics with the emphasis on the research done by our group. One of the modern important problems is how superfluid turbulence relates to classical turbulence. First, we show that superfluid turbulence consisting of a vortex tangle has an energy spectrum consistent with the Kolmogorov law. Second, we discuss the vortex states that appear in a rotating channel with counterflow. In the field of atomic-gas Bose-Einstein condensation, the dramatic observations of quantized vortices were made for rotating condensates. By solving numerically the Gross-Pitaevskii equation, we found a whole story of the vortex lattice formation consistent with the observations. © 2005 Springer Science+Business Media, Inc.

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 one 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.

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 et al. [Phys. Rev. Lett. 82, 2228 (1999)].

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. These six modes are bifurcated into in-phase and out-of-phase modes by the intercomponent interaction, yielding the nonlinear dynamics that are absent in a single-component condensate. 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.

The quadrupole and scissors modes of two-component Bose-Einstein condensates (BEC) were investigated. The nonlinear dynamics associated with the second harmonic generation of the quadrupole and scissors modes and mode coupling were also studied. The Thomas-Fermi approximation and quadratic polynomial ansatz for density fluctuations were used for the linear analysis of the superfluid hydrodynamic equations. It was found that the excitation frequencies of three normal modes constituted from monopole and quadrupole oscillations and those of three scissors modes. The condition of the second harmonic generation was obtained as functions of the aspect ratio of a trapping potential and intercomponent interaction strength.

In this paper, we describe two kinds of characteristic nonlinear dynamics in two-component Bose-Einstein condensates. For two overlapping components, we analyzed the collective modes and a variety of nonlinear mode couplings, which were then confirmed by numerical simulation of the time-dependent Gross-Pitaevskii equations. Next, we consider the nonlinear dynamics of two condensates after abruptly turning on the intercomponent coupling strength. For strong intercomponent interactions the out-of-phase density wave of the condensates became unstable, leading to multiple domain formation.

We study the equilibrium structure of vortex states in rotating two-component Bose-Einstein condensates. Each component forms respectively a vortex state and the intercomponent coupling makes a rich variety of structures combining these two vortex states. We show a phase diagram of stable vortex states in the intercomponent-coupling versus rotation-frequency. As the intercomponent coupling and the rotation frequency increase, the interlocked vortex lattices undergo structural transition from a triangular lattice to a square one. In a strongly phase-separated regime, vortex cores in each component overlap, forming double-core vortex lattices and serpentine vortex sheets. We also discuss the effect of Josephson coupling between two components on the vortex states.

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.

We study the dynamics of vortex lattice formation of a rotating trapped Bose-Einstein condensate by numerically solving the two-dimensional Gross-Pitaevskii equation with a dissipative term. The condensate trapped in a quadratic potential forms a triangle lattice of quantized vortices, following the damped elliptic oscillation of the condensate and the excitation of surface waves, which is consistent with the experimental results of an ENS group. A fast rotating condensate confined in a quadratic-plus-quartic potential generates a giant vortex absorbing all phase defects into a single density hole, where a quasi-one-dimensional circular superflow is realized. (C) 2003 Elsevier Science B.V. All rights reserved.

We investigate numerically the structure of vortex lattices in rotating two-component Bose-Einstein condensates with equal intraspecies interaction strengths g(11) = g(22). The stationary solutions of the coupled Gross-Pitaevskii equations with a centrifugal term show various non-trivial patterns of vortex lattices, depending on the interspecies interaction strength g(12). For rootg(11)g(22) > g(12) the vortices in each condensate form a vortex lattice, and one lattice is shifted from the other to reduce the overlap of the condensates. For rootg(11)g(22) < g(12) when the phase separation of the condensate occurs, the vortex lattices are destroyed, forming the vortex sheet structure. The dynamics of vortex lattice formation is also discussed. (C) 2003 Elsevier Science B.V. All rights reserved.

We study the response of a trapped Bose-Einstein condensate to a sudden turn on of a rotating drive by numerically solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by a quasiparticle projection method. In a quadrupolar resonant regime, which depends on the trap anisotropy, simple periodic oscillations in surface-mode populations disappear and the system exhibits stochastic dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.

A fast rotating Bose-Einstein condensate confined in a quadratic-plus-quartic potential is found to dynamically generate a "giant vortex" that absorbs all phase singularities into a central low density hole, thereby sustaining a quasi-one-dimensional circular superflow at a supersonic speed.

We study the dynamics of vortex lattice formation of a rotating trapped Bose-Einstein condensate by numerically solving the two-dimensional Gross-Pitaevskii equation. and find that the condensate undergoes elliptic deformation, followed by unstable surface-mode excitations before forming a quantized vortex lattice. The origin of the peculiar surface-mode excitations is identified to be phase fluctuations at the low-density surface regime. The obtained dependence of a distortion parameter on time and that on the driving frequency agree with the recent experiments by Madison et al, [Phys. Rev. Lett. 86, 4443 (2001)].

We show theoretically the existence of the metastable state and study the decay through the macroscopic quantum tunneling in two-component Bose-Einstein condensates. The numerical analysis of the coupled Gross-Pitaevskii equations clarifies the metastable states whose configuration preserves or breaks the symmetry of the trapping potential, depending on the interspecies interaction and the particle number. We calculate the tunneling decay rate of the metastable state by using the collective coordinate approximation and the bounce technique. It is found that the macroscopic quantum tunneling is observable in a wide range of the particle number.

We study the dynamics of vortex lattice formation of a rotating trapped Bose-Einstein condensate by numerically solving the two-dimensional Gross-Pitaevskii equation, and find that the condensate undergoes elliptic deformaton, followed by unstable surface-mode excitations before forming a quantized vortex lattice. The dependence of the number of vortices on the rotation frequency is obtained.

We study theoretically the generation of cyclic supercurrent among three superfluids coupled by the Josephson junctions. Depending on the initial relative phases between superfluids. Josephson current flows cyclically through the superfluids to create a quantized vortex. Reducing the coupling strength changes the motion from periodic to chaotic, thus suppressing the cyclic current. Applying this result to the Kibble-Zurek mechanism, the probability of the vortex generation via this mechanism is modified from the simple estimate,given by the geodesic rule. We compare our results with the Lancaster, Grenoble and Helsinki experiments.

We show theoretically the existence of a metastable state and the possibility of decay to the ground state through macroscopic quantum tunneling in two-component Bose-Einstein condensates with repulsive interactions. Numerical analysis of the coupled Gross-Pitaevskii equations clarifies the metastable states whose configuration preserves or breaks the symmetry of the trapping potential, depending on the interspecies interaction and the particle number. We calculate the tunneling decay rate of the metastable state by using the collective coordinate method under the WKB approximation. Then the height of the energy barrier is estimated by the saddle point solution. It is found that macroscopic quantum tunneling is observable in a wide range of particle numbers. Macroscopic quantum coherence between two distinct states is discussed this might give an additional coherent property of two-component Bose condensed systems. Thermal effects on the decay rate are estimated. © 2001 The American Physical Society.

The Josephson effect in three cyclically coupled superfluids is studied theoretically. We analyze the simultaneous Gross-Pitaevskii equations with coupling terms between condensates. Depending on the initial phase differences between the condensates, Josephson current flows cyclically to make a vortex. Reducing the coupling between the superfluids suppresses the cyclic current, and generates a self-maintained imbalance of particle population. (C) 2000 Elsevier Science B,V. All rights reserved.

The Josephson effect in cyclically coupled Bose-Einstein condensates is studied theoretically. We analyze the simultaneous Gross-Pitaevskii equations with coupling terms between adjacent condensates. Depending on the initial relative phases between condensates, Josephson current flows cyclically to create a quantized vortex. Reducing the coupling between condensates changes the motion from periodic to chaotic, thus suppressing the cyclic current. The relation to the Kibble-Zurek mechanism is discussed; the density of the generated vortices is less than that predicted by this mechanism.

極低温での中性希薄原子気体ボーズ・アインシュタイン凝縮体のダイナミクスはグロス-ピタエフスキー方程式で記述される。最近、回転系における量子渦生成の問題に対して、 M.Loboらや、Parkerらは数値シミュレーションの結果から、散逸のない系でも量子渦が生成されるだけでなく渦糸格子まで形成されるという主張をおこなっている。散逸のないグロス-ピタエフスキー方程式のシミュレーションでは高波数のモードが順次生成され、乱流状態が起こり、その後に渦糸格子が形成される。我々はこれらの数値シミュレーションを詳しく解析することで、渦糸格子が形成される機構とこの数値シミュレーションの問題点を指摘する。

2成分Bose-Einstein凝縮体におけるパターン形成の問題、特にマルチドメイン構造形成と量子渦状態に関する最近の我々の研究について報告する。相互位相変調の不安定性による相分離のダイナミクスをGross-Pitaevskii方程式の数値解析により調べ、2成分凝縮体が交互に配列したマルチドメイン構造を形成する事を明らかにした。回転ポテンシャル中の2成分凝縮体は、異成分原子間相互作用と回転振動数に依存して、四角格子、渦シートなどの多彩な渦状態を形成する事が明らかとなった。

この論文は国立情報学研究所の電子図書館事業により電子化されました。

研究代表者中原は，前年度までの科研費「リー代数を用いた非断熱量子制御の研究」で開発した量子位相を非断熱的に印可する方法を用いて，新たなトポロジカル励起の生成を研究した．まず，3次元光トラップに閉じ込められたスピン１ポーラー相のボース凝縮体（以下BEC）において，3次元4重極磁場と軸方向の強い一様磁場を非断熱制御の処方に従って時間的に変化させる．すると非断熱制御が厳密に成り立つ点の半径を制御することにより，任意のHopfチャージを持ったリンク構造が生じることを示した．の構造は2次元球面の3次ホモトピー群で分類される．次にスピン2のBECのサイクリック相およびバイアキシャル・ネマティック相において非断熱を用いた3次元Skyrmionの生成を研究した．これ等のオーダーパラメターは3次元球の3次のホモトピー群で分類されるが，複雑な対称性を反映して，Skyrmionは24や16の大きな写像度を持つことを示した．また，BECにおいて一様な運動量密度を持つ波束を生成するポテンシャルを増田，中村らによって開発された「早送り理論」を用いて導出し，その非自明なスケーリング則を研究した． 分担者高木は平行平板中超流動ヘリウム3-A相での半整数量子渦について，実験家と共同研究を行った． 分担者笠松は擬2次元一様系におけるBEC中の巻き数2の量子渦の安定性を理論的に調べた．システムサイズが十分大きくなると，不安定性を引き起こす素励起の振動数の虚部が有限の値に収束し，一様系において多重量子渦は動的に不安定であることを明らかにした．また，有限磁場下における超流動ヘリウム3--B相の渦芯構造と相図を研究した．

本応募課題では、人工的に造られた磁場(ゲージ場)下における冷却原子気体で実現する量子相および非平衡ダイナミクスを弱相関および強相関の両方の視点から理論的に研究する。最近実現した人工ゲージ場は冷却原子気体の物理に新しい方向性をもたらし、磁場中の多体粒子系の量子シミュレーターの実現ならびにスピン軌道相互作用をもつボース凝縮という新しい概念を生み出した。本研究ではこの系の非平衡ダイナミクスに焦点をあて、可換および非可換人工ゲージ場の強さに依存して起こるボース粒子系の新奇量子現象の解明を行う。粒子間の相関の強さは系に挿入する光格子の強さを変えることで調整する。理論解析は実験を強く意識して行い、実験との詳細な比較や新しい実験の提案をする事を目的とする。

光学格子上の冷却原子系を用いてU(1)格子ゲージ・ヒッグスモデルを量子シミュレーションする方法を提案し，実験で期待される結果を予想した。この方法は1,2,3次元いずれの光学格子にも適用可能で，サイト間密度-密度相互作用を持つ拡張ボースハバードモデルと異方的相互作用を持つU(1)ゲージ・ヒッグスモデルの対応を与える。また，実験での指針を得るため，ゲージモデルの相構造を数値シミュレーションで求め，原子系のパラメータで相構造を表した。さらに，グロス・ピタエフスキー方程式を用いて系の時間発展を解析した。1次元系に対しては，電気力線の力学に関するシュウインガー機構の動的版と見なせる現象を観測した。

本研究の目的は主に計算機を用いた数値実験的研究手法によりゲージ理論の相構造と低エネルギー励起等を明らかし、関連する量子多体現象を解明することにある。特に近年発展が著しい極低温原子系や強相関多体系に焦点を当てている。その中で極低温原子系は物理的に興味がある種々の系やモデルを実際の原子系でシミュレートし、その動力学を解明する手法として注目を集めている。本研究においては、格子ゲージ理論に対して量子シミュレートする処方および実験的なセットアップを提唱し、期待される観測結果を‘古典’数値シミュレーションにより求めた。また人工磁場の導入により可能となったHaldaneモデル等の研究も行った。

超流動ヘリウム、冷却原子気体を対象に、これらを統括的に扱い、量子流体力学の展開を目指す。これらの系では、その最小の構成要素としての量子渦が出現し、その物性や流体力学的性質を決める上で重要な役割を果たす。本年度に得られた主な成果は以下の通り。1. 超流動ヘリウム4の熱カウンター乱流を対象に、full Biot-Savartの渦糸モデルによる数値計算を初めて行い、渦間相互作用を完全に取り入れる事で、乱流の統計的定常状態が得られる事を示した。得られた状態の実験結果との一致も良い。2. 相分離した2成分ボース凝縮体における量子渦の物理に関して以下の新しい知見を得た。(1)回転ポテンシャル中の安定状態は2成分の境界に量子渦が一次元的に配列した渦シート構造となることを明らかにした。特徴的な長さのスケールはドメインの表面張力と渦による運動エネルギーのつり合いで決まることを示した。(2)相分離した2成分BECの勇断流に対する安定性を調べた。これは古典流体ではKelvin-Helmholtz不安定性として知られる現象と頬似のものであるが,BECは粘性をもたない超流動性と渦の循環が量子化されるという特有の性質を持ち,新たな流体現象が期待できる。我々は界面の不安定化により,量子渦の生成を伴った特徴的なパターン形成のダイナミクスを明らかにした。

原子気体Bose-Einstein凝縮体(BEC)における新たな量子相の発見とその動的な現象に関して研究を進めているが、本年度は以下の内容を明らかにした。1, 相分離した2成分BECの剪断流に対する安定性を調べた。これは古典流体ではKelvin-Helmholtz不安定性として知られる現象と類似のものであるが,BECは粘性をもたない超流動性と渦の循環が量子化されるという特有の性質を持ち,新たな流体現象が期待できる。我々は界面の不安定化により,量子渦の生成を伴った特徴的なパターン形成のダイナミクスを明らかにした。2, 2成分BECでドメインウォールと渦が結合した複合ソリトンの構造を調べた。2成分BECは場の理論で知られる非線形シグマ模型で記述することができ,複合ソリトンの解析解を求める事ができた。渦とウォールの接合部はモノポールで結ばれており,これはBoojumとして知られる界面に存在する点欠陥であることを示した。また,この複合ソリトンは弦理論で「D-brane」として知られる物体に相当し,実験室で実現するD-braneを提唱した。これにより原子気体と弦理論を結びつける新たな研究の方向性を提唱する事ができた。3, 有効磁場中の光格子ポテンシャルに閉じ込められたハードコアボソンの基底状態の相図をCP1模型のモンテカルロシミュレーションにより調べた。この模型は各サイトの粒子数の揺ら...

超流動ヘリウム、中性原子気体ボース凝縮系(BEC)といった低温の量子凝縮系を対象に、量子流体力学の構築を行った。これらの系の流体力学は量子力学に支配され、その最小の構成要素としての量子渦が出現する。超流動ヘリウムでは、量子乱流と古典乱流の対比、振動物体が引き起こす量子乱流遷移などを明らかにした。原子気体BECでは、量子乱流の生成方法を提示し、スピノールBECの磁気共鳴などを明らかにした。

本研究ではナノケルビンの超低温まで冷却された中性原子気体のボース・アインシュタイン凝縮体(以下BECと略す)で起こる超流動現象と原子間相互作用の効果によって生じる非線形現象に関しての理論的研究を行った.2成分のBECの原子間相互作用によって起こる相分離の不安定性による種々のパターン形成の非線形ダイナミクスを明らかにした.またBECに存在し,超流動性に深く関与する特異な渦の構造を明らかにした.

本研究は,探究活動を授業に取り入れることにより,学生たちの認知能力の向上が促進される可能性を探る,というものであった。そのために高専1年生基礎数学のための教材集『数ナビで数学を探しにいこう』を作成し,その具体的な活用についてT3Japan年会において定期的に発表を行ってきた。また,研究成果のまとめとしてテクノロジーの活用に関するシンポジウム(2009 年3 月)を開き,今後の研究継続に関する提案を行った。