Masahiro Takahashi

We have observed and characterized the nonequilibrium spatial dynamics of a two-component Rb-87 Bose-Einstein condensate (BEC) that is controllable switched back and forth between the miscible and immiscible phases of the phase separation transition by changing the internal states of the Rb-87 atoms. The subsequent evolution exhibits large scale oscillations of the spatial structure that involve component mixing and separation. We show that the larger total energy of the miscible system results in a higher oscillation frequency. This investigation introduces a new technique to control the miscibility and the spatial degrees of freedom in atomic BECs.

We investigate the dynamic properties of bouncing and penetration in colliding binary and ternaryBose-Einstein condensates comprised of different Zeeman or hyperfine states of Rb-87. Through the application ofmagnetic field gradient pulses, two-or three-component condensates in an optical trap are spatially separated and then made to collide. The subsequent evolutions are classified into two categories: repeated bouncing motion and mutual penetration after damped bounces. We experimentally observed mutual penetration for immiscible condensates, bouncing between miscible condensates, and domain formation for miscible condensates. From numerical simulations of the Gross-Pitaevskii equation, we find that the penetration time can be tuned by slightly changing the atomic interaction strengths.

We study a system of interacting spinless fermions in one dimension that, in the absence of interactions, reduces to the Kitaev chain [Kitaev, Phys. Usp. 44, 131 (2001)]. In the noninteracting case, a signal of topological order appears as zero-energy modes localized near the edges. We show that the exact ground states can be obtained analytically even in the presence of nearest-neighbor repulsive interactions when the on-site (chemical) potential is tuned to a particular function of the other parameters. As with the noninteracting case, the obtained ground states are twofold degenerate and differ in fermionic parity. We prove the uniqueness of the obtained ground states and show that they can be continuously deformed to the ground states of the noninteracting Kitaev chain without gap closing. We also demonstrate explicitly that there exists a set of operators each of which maps one of the ground states to the other with opposite fermionic parity. These operators can be thought of as an interacting generalization of Majorana edge zero modes.

We examine the possible phase diagram in an H-T plane for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a two-band Pauli-limiting superconductor. We here demonstrate that, as a result of the competition of two different modulation lengthscales, the FFLO phase is divided into two phases by the first-order transition: the Q(1)- and Q(2)-FFLO phases at the higher and lower fields. The Q(2)-FFLO phase is further divided by successive first order transitions into an infinite family of FFLO subphases with rational modulation vectors, forming a devil's staircase structure for the field dependences of the modulation vector and paramagnetic moment. The critical magnetic field above which the FFLO is stabilized is lower than that in a single-band superconductor. However, the tricritical Lifshitz point L at T-L is invariant under two-band parameter changes.

Multiband effects on Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states of a Pauli-limiting two-band superconductor are studied theoretically in the wide range of parameters, based on the Bogoliubov-de Gennes equation. First, we examine the phase diagrams of two-band systems with a passive band in which the intraband pairing interaction is absent and superconductivity is induced by a Cooper pair tunneling from an active band. The critical field of Bardeen-Cooper-Schrieffer to FFLO states becomes lower than the Lifshitz point with increasing the interband tunneling strength. We also study the thermodynamics of Pauli-limiting two-band superconductors with nonzero intraband pairing interactions. As a consequence of a competing effect between two bands, the FFLO phase is divided into two phases: Q(1)- and Q(2)-FFLO phases. In a particular case, the latter is further subdivided into a family of FFLO states with rational modulation lengths, where the spatial structure of the pair potential is approximately describable with sinusoidal functions with multiple modulation wave numbers. The resultant phase diagram is qualitatively different from that in a single-band superconductor and gives rise to a devil's staircase structure in the field dependence of physical quantities.

We study stationary states for the nonlinear Schrodinger equation on Fibonacci lattices, which are expected to be realized by Bose-Einstein condensates loaded into an optical lattice. When the model does not have a nonlinear term, the wavefunctions and the spectrum are known to show fractal structures. Such wavefunctions are termed critical. We present a phase diagram of the energy spectrum for varying the nonlinearity. It consists of three portions: a forbidden region, the spectrum of critical states and the spectrum of stationary solitons. We show that the energy spectrum of critical states remains intact, irrespective of the nonlinearity in the large number of stationary solitons.

We have computed phase diagrams for rotating spin-1 Bose-Einstein condensates with long-range magnetic dipoledipole interactions. Spin textures including vortex sheets, staggered half-quantum- and skyrmion vortex lattices and higher order topological defects have been found. These systems exhibit both superfluidity and magnetic crystalline ordering and they could be realized experimentally by imparting angular momentum in the spinor condensate.

We have solved numerically the ground states of a Bose-Einstein condensate in the presence of dipolar interparticle forces using a semiclassical approach. Our motivation is to model, in particular, the spontaneous spin textures emerging in quantum gases with large dipole moments, such as Cr-52 or Dy condensates, or ultracold gases consisting of polar molecules. For a pancake-shaped harmonic ( optical) potential, we present the ground-state phase diagram spanned by the strength of the nonlinear coupling and dipolar interactions. In an elongated harmonic potential, we observe a helical spin texture. The textures calculated according to the semiclassical model in the absence of external polarizing fields are predominantly analogous to previously reported results for a ferromagnetic F = 1 spinor Bose-Einstein condensate, suggesting that the spin textures arising from the dipolar forces are largely independent of the value of the quantum number F or the origin of the dipolar interactions.

We theoretically investigate the low-lying excitation spectra of coreless vortex states in Bose-Einstein condensates (BECs) with F = 2 hyperfine spin degrees of freedom. Here, we extend the previous work in F = 1 spinor BEC. In addition to the dynamical instabilities in F = 1 coreless vortex states, we find an another set of dynamical instabilities due to different hyperfine spin interaction. The calculation is carried out in the possible parameter space of the F = 2 Rb-87 atom. This study assists interpretation of experimental data and presents a general characteristics of the dynamical instability of F = 2 hyperfine spin system. whether the ground state of the spin interaction is in the cyclic or polar phase. Our study can encourages the experiments to examine our results.

We show that the effective theory of long wavelength low energy behavior of a dipolar Bose-Einstein condensate(BEC) with large dipole moments (treated as a classical spin) can be modeled using an extended non-linear sigma model (NLSM) like energy functional with an additional non-local term that represents long ranged anisotropic dipole-dipole interaction. Minimizing this effective energy functional we calculate the density and spin-profile of the dipolar Bose-Einstein condensate in the mean-field regime for various trapping geometries. The resulting configurations show strong intertwining between the spin and mass density of the condensate, transfer between spin and orbital angular momentum in the form of Einstein-de Hass effect, and novel topological properties. We have also described the theoretical framework in which the collective excitations around these mean field solutions can be studied and discuss some examples qualitatively.

The low-lying excitations of coreless vortex states in F=1 spinor Bose-Einstein condensates (BECs) are theoretically investigated using the Gross-Pitaevskii and Bogoliubov-de Gennes equations. The spectra of the elementary excitations are calculated for different spin-spin interaction parameters and ratios of the number of particles in each sublevel. There exist dynamical instabilities of the vortex state which are suppressed by ferromagnetic interactions, and, conversely, enhanced by antiferromagnetic interactions. In both of the spin-spin interaction regimes, we find vortex-splitting instabilities in analogy with scalar BECs. In addition, a phase-separating instability is found in the antiferromagnetic regime.

We investigate the dynamical stability of the coreless vortex state in F = 1 spinor Bose-Einstein condensates, by numerically solving the Gross-Pitaevskii and Bogoliubov-de Gennes equations. We cover both ferromagnetic and antiferromagnetic interaction regions and the magnetizations per particle M from -1 to +1. It is found that the coreless vortex state is dynamically stable in large parameter regions of magnetization M. At M = -1, the hyperfine spin component with vortex winding 2 is dominant, and hence the coreless vortex can spontaneously decay even without dissipation. However, it is found that in the ferromagnetic case, the spin-spin interactions tend to stabilize the state. In the antiferromagnetic case, we find new dynamical instability modes which are not obtained in the ferromagnetic interaction region. In the antiferromagnetic interaction region, the spin-spin interactions can stimulate dynamical instabilities, while there still remains a large stability area in the parameter M. This is because of certain restrictions in inducing dynamical instability.

In Fermionic superfluids with a vortex, at T=0, the depletion of the atomic density appears in the core region, which is strongly associated with the discreteness of the core-bound state, called the Caroli-de Gennes-Matricon state. In imbalanced superfluid, however, it is found by the microscopic study based on the Bogoliubov-de Gennes approximation that this quantum depletion is progressively filled out in majority spin species as population imbalance increases. In contrast, the minority species keeps the depletion, which enables the direct observation of "superfluidity", because the quantized vortex is a hallmark of superfluidity.

Quantized vortex-core structure is theoretically investigated in fermion superfluids with population imbalance for two atom species of neutral atom clouds near a Feshbach resonance. In contrast with the vortex core in balance case where the quantum depletion makes a vortex visible through the density profile measurement, the vortex core is filled in and becomes less visible because the quantized discrete bound states are occupied exclusively by the majority species. Yet it is shown that the core can be visible through the minority density profile experiment using phase contrast imaging, revealing an interesting opportunity to examine low-lying fermionic core bound states unexplored so far.