Yuki Kawaguchi, Muneto Nitta, Masahito Ueda
We show that knots of spin textures can be created in the polar phase of a spin-1 Bose-Einstein condensate, and discuss experimental schemes for their generation and probe, together with their lifetime.
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We theoretically propose and numerically realize spin echo in a spinor Bose--Einstein condensate (BEC). We investigate the influence on the spin echo of phase separation of the condensate. The equation of motion of the spin density exhibits two relaxation times. We use two methods to separate the relaxation times and hence demonstrate a technique to reveal magnetic dipole--dipole interactions in spinor BECs.
We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schrödinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision …
We show that a spin-1 Bose-Einstein condensate with ferromagnetic interactions spontaneously generates a topological spin texture, in which the m = \pm 1 components of the magnetic sublevels form vortices with opposite circulations. This phenomenon originates from an interplay between ferromagnetic interactions and spin conservation.
We demonstrate the existence of the helical vortex solution in two-component Bose-Einstein condensates which can be identified as a twisted vorticity flux. Based on this we argue that the recently proposed knot in two-component Bose-Einstein condensates can be interpreted as a vorticity knot, a vortex ring made of the helical vortex. This picture shows that the knot is made of two quantized vorticity fluxes linked together, whose topology $π_3(S^2)$ is fixed by the linking number of two vorticity fluxes. Due to the helical structure the knot has both topological and dynamical stability. We est…
Magnetization dynamics of a half-quantum vortex in a spin-1 Bose-Einstein condensate with a ferromagnetic interaction are investigated by mean-field and Bogoliubov analyses. The transverse magnetization is shown to break the axisymmetry and form threefold domains. This phenomenon originates from the topological structure of the half-quantum vortex and spin conservation.
We study soliton solutions for the Gross--Pitaevskii equation of the spinor Bose--Einstein condensates with hyperfine spin F=2 in one-dimension. Analyses are made in two ways: by assuming single-mode amplitudes and by generalizing Hirota's direct method for multi-components. We obtain one-solitons of single-peak type in the ferromagnetic, polar and cyclic states, respectively. Moreover, twin-peak type solitons both in the ferromagnetic and the polar state are found.
We theoretically investigate the effect of an anisotropic trap on the instability of the polar $(m_F=0)$ phase of a spin-1 Bose-Einstein condensate. By considering rigorously the spatial quantization, we show that the growth of the nascent ferromagnetic phase at short times becomes anisotropic with stronger oscillations in the magnetization correlation function along the unconfined direction.
We classify all possible fractional charge vortices of charge less than unity in spin-1 and spin-2 polar and cyclic Bose-Einstein condensates (BECs) with zero magnetization. Statics and dynamics of these vortices in quasi-two-dimensional spinor BECs are studied employing accurate numerical solution and a Lagrange variational approximation. The results for density and collective-mode oscillation are illustrated using fractional-charge BEC vortex of $^{23}$Na and $^{87}$Rb atoms with realistic interaction and trapping potential parameters.
Magnon excitation in a spinor Bose-Einstein condensate by a driven magnetic field is shown to have a close analogy with the dynamical Casimir effect. A time-dependent external magnetic field amplifies quantum fluctuations in the magnetic ground state of the condensate, leading to magnetization of the system. The magnetization occurs in a direction perpendicular to the magnetic field breaking the rotation symmetry. This phenomenon is numerically demonstrated and the excited quantum field is shown to be squeezed.
We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. A modified Landau-Lifshitz equation is derived and exact magnetic soliton solutions are obtained analytically. Our results show that the time-oscillation of the soliton size can be controlled in practical experiment by adjusting of the light-induced dipole-dipole interaction. Moreover, the elastic collision of two solitons is investigated.
We studied the static and dynamic domain wall solutions of spinor Bose-Einstein condensates trapped in an optical lattice. The single and double domain wall solutions are constructed analytically. Our results show that the magnetic field and light-induced dipolar interactions play an important role for both the formation of different domain walls and the adjusting of domain wall width and velocity. Moreover, these interactions can drive the motion of domain wall of Bose ferromagnet systems similar to that driven by the external magnetic field or the spin-polarized current in fermion ferromagne…
Motivated by a recent experiment, we study non-equilibrium quantum phenomena taking place in the quench of a spinor Bose-Einstein condensate through the zero-temperature phase transition separating the polar paramagnetic and planar ferromagnetic phases. We derive the typical spin domain structure (correlations of the effective magnetization) created by the quench arising due to spin-mode quantum fluctuations, and establish a sample-size scaling law for the creation of spin vortices, which are topological defects in the transverse magnetization.
It is well known that both a particle with spin and a quantum field in a Bianchi type IX Universe are both related to the quantum mechanical top. In this paper we will combine these insights to show that the dynamics of a cold gas of noninteracting atoms with total momentum F=1 may be used to explore the behavior of quantum matter near a cosmological singularity.
The achievement in cooling alkali atomic gases, such as $^{87}$Rb, $^{23}$Na and $^{7}$Li, to quantum degeneracy opens up a way to study magnetism in spinor bosons, because these constituent atoms usually have a hyperfine spin degree of freedom. This article reviews several basic problems related to the ferromagnetic phase transition in spinor atomic Bose gases from a theoretical perspective. After a brief discussion on various possible origins of the ferromagnetic interaction, the phase diagram of the ferromagnetically coupled spinor bosons is investigated. It is found that the ferromagnetic …
We investigate the non-Abelian Josephson effect in spinor Bose-Einstein condensates with double optical traps. We propose, for the first time, a real physical system which contains non-Abelian Josephson effects. The collective modes of this weak coupling system have very different density and spin tunneling characters comparing to the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps respectively, which are a crucial feature of the non-Abelian Josephson effects. We also give an experimental protocol to observe this novel effect in fu…
The generation of the population oscillation of the multicomponent spinor Bose-Einstein condensate is demonstrated in this paper. We observe and examine the nonsynchronous decreasing processes of the magnetic fields generated between quadrupole coils and Ioffe coils during the switch-off of the quadrupole-Ioffe-configuration trap, which is considered to induce a nonadiabatic transition. Starting from the two-level Schrödinger equation, we have done some numerical fitting and derived an analytical expression identical to the results of E. Majorana and C. Zener, of which both the results well ma…
We demonstrate theoretically that using standard external magnetic fields, one can imprint point-like topological defects to the spin texture of a dilute Bose-Einstein condensate. Symmetries of the condensate order parameter render this topological defect to be accompanied with a vortex filament corresponding to the Dirac string of a magnetic monopole. The vorticity in the condensate coincides with the magnetic field of a magnetic monopole, providing an ideal analogue to the monopole studied by Dirac.
We report on a study of the spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interactions. By solving the non-local Gross-Pitaevskii equations for this system, we find three ground-state phases. Moreover, we show that a substantial orbital angular momentum accompanied by chiral symmetry breaking emerges spontaneously in a certain parameter regime. We predict that all these phases can be observed in the spin-1 $^{87}$Rb condensate by changing the number of atoms or the trap frequency.
The ground state of a spinor Bose liquid is ferromagnetic, while the softest excitation above the ground state is the magnon mode. The dispersion relation of the magnon in a one-dimensional liquid is periodic in the wavenumber q with the period 2πn, determined by the density n of the liquid. Dynamic correlation functions, such as e.g. spin-spin correlation function, exhibit power-law singularities at the magnon spectrum, $ω\toω_m(q,n)$. Without using any specific model of the inter-particle interactions, we relate the corresponding exponents to independently measurable quantities $\partialω_m/…
We investigate magnetic properties of Mott-insulating phases of ultracold Bose and Fermi spinor gases in optical lattices. We consider in particular the F=2 Bose gas, and the F=3/2 and F=5/2 Fermi gases. We derive effective spin Hamiltonians for one and two atoms per site and discuss the possibilities of manipulating the magnetic properties of the system using optical Feshbach resonances. We discuss low temperature quantum phases of a 87Rb gas in the F=2 hyperfine state, as well as possible realizations of high spin Fermi gases with either 6Li or 132Cs atoms in the F=3/2 state, and with 173Yb …
Magnetic dipole-dipole interaction dominated Bose-Einstein condensates are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from large spin limit to obtain an effective minimal Hamiltonian; a version extended from a non-linear sigma model. By solving the Gross-Pitaevskii equation we find several novel spin textures where the mass density and spin density are strongly coupled, depending upon trap geometries due to the long-range and anisotropic natures of the dipole-dipole interaction.
Manipulation of the quantum state by the Majorana transition in spinor BEC system has been realized by altering the rotation frequency of the magnetic field's direction. This kind of manipulation method has no limitation on the transition speed in principle and the system is well closed, which provides a new and superior tool to manipulate quantum states. Using this methord on pulsed atom laser, multicomponent spinor atom laser is generated. We demonstrate that the experiment results are agreed with the theoretical predication.
Weak dipolar effects in atomic Bose-Einstein condensates (BECs) have recently been predicted to develop spin textures. However, observation of these effects requires magnetic field as low as $\sim 10 μ$G for spin-1 alkali BECs, so that they are not washed out by the Zeeman effect. We present a scheme to observe the magnetic dipole-dipole interaction in alkali BECs under a realistic magnetic field of $\sim 100$ mG. Our scheme enables us to extract genuine dipolar effects and should apply also to $^{52}$Cr BECs.
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 Schroedinger 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 modulation amplitude is ch…
We demonstrate a precision magnetic microscope based on direct imaging of the Larmor precession of a $^{87}$Rb spinor Bose-Einstein condensate. This magnetometer attains a field sensitivity of 8.3 pT/Hz$^{1/2}$ over a measurement area of 120 $μ$m$^2$, an improvement over the low-frequency field sensitivity of modern SQUID magnetometers. The corresponding atom shot-noise limited sensitivity is estimated to be 0.15 pT/Hz$^{1/2}$ for unity duty cycle measurement. The achieved phase sensitivity is close to the atom shot-noise limit suggesting possibilities of spatially resolved spin-squeezed magne…
We analyze the spinor dynamics of a Rb-87 F=2 condensate initially prepared in the m_F=0 Zeeman sublevel. We show that this dynamics, characterized by the creation of correlated atomic pairs in m_F=+/-1, presents an intriguing multi-resonant magnetic field dependence induced by the trap inhomogeneity. This dependence is directly linked to the most unstable Bogoliubov spin excitations of the initial m_F = 0 condensate, showing that, in general, even a qualitative understanding of the pair creation efficiency in a spinor condensate requires a careful consideration of the confinement.
We show that a degenerate gas of two-species bosonic atoms interacting through a p-wave Feshbach resonance (as realized in, e.g., a 85Rb-87Rb mixture) exhibits a finite-momentum atomic-molecular superfluid (AMSF), sandwiched by a molecular p-wave (orbital spinor) superfluid and by an s-wave atomic superfluid at large negative and positive detunings, respectively. The magnetic field can be used to tune the modulation wave vector of the AMSF state, as well as to drive quantum phase transitions in this rich system.
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 instab…
The spinor Bose-Einstein condensate of atomic gases has been experimentally realized by a number of groups. Further, theoretical proposals of the possible vortex states have been sugessted. This paper studies the effects of the quadratic Zeeman energy on the vortex states. This energy was ignored in previous theoretical studies, although it exists in experimental systems. We present phase diagrams of various vortex states taking into account the quadratic Zeeman energy. The vortex states are calculated by the Gross-Pitaevskii equations. Several new kinds of vortex states are found. It is also …
We study spin-polarized states and their stability in anti-ferromagnetic states of spinor (F=1) quasi-one-dimensional Bose-Einstein condensates. Using analytical approximations and numerical methods, we find various types of polarized states, including: patterns of the Thomas-Fermi type; structures with a pulse-shape in one component inducing a hole in the other components; states with holes in all three components; and domain walls. A Bogoliubov-de Gennes analysis reveals that families of these states contain intervals of a weak oscillatory instability, except for the domain walls, which are …
We present an exact analytical solution of the fundamental system of quasi-one-dimensional spin-1 bosons with infinite delta-repulsion. The eigenfunctions are constructed from the wave functions of non-interacting spinless fermions, based on Girardeau's Fermi-Bose mapping, and from the wave functions of distinguishable spins. We show that the spinor bosons behave like a compound of non-interacting spinless fermions and non-interacting distinguishable spins. This duality is especially reflected in the spin densities and the energy spectrum. We find that the momentum distribution of the eigensta…
We point out that the internal spin symmetry of the order parameter manifests itself at the core of a fractional vortex in real space without spin-orbit coupling. Such symmetry breaking arises from a topological constraint and the commensurability between spin symmetries of the order parameters inside and outside the core. Our prediction can be applied to probe the cyclic order parameter in a rotating spin-2 $^{87}$Rb condensate as a non-circular vortex core in a biaxial nematic state.
We consider the effect of thermal fluctuations on rotating spinor F=1 condensates in axially-symmetric vortex phases, when all the three hyperfine states are populated. We show that the relative phase among different components of the order parameter can fluctuate strongly due to the weakness of the interaction in the spin channel. These fluctuations can be significant even at low temperatures. Fluctuations of relative phase lead to significant fluctuations of the local transverse magnetization of the condensate. We demonstrate that these fluctuations are much more pronounced for the antiferro…
We study the zero temperature phase diagram of the disordered spin-1 Bose-Hubbard model in a 2-dimensional square lattice. To this aim, we use a mean field Gutzwiller ansatz and a probabilistic mean field perturbation theory. The spin interaction induces two different regimes corresponding to a ferromagnetic and antiferromagnetic order. In the ferromagnetic case, the introduction of disorder reproduces analogous features of the disordered scalar Bose-Hubbard model, consisting in the formation of a Bose glass phase between Mott insulator lobes. In the antiferromagnetic regime the phase diagram …
We investigate the long-term dynamics of spin textures prepared by cooling unmagnetized spinor gases of F=1 $^{87}$Rb to quantum degeneracy, observing domain coarsening and a strong dependence of the equilibration dynamics on the quadratic Zeeman shift $q$. For small values of $|q|$, the textures arrive at a configuration independent of the initial spin-state composition, characterized by large length-scale spin domains, and the establishment of easy-axis (negative $q$) or easy-plane (positive $q$) magnetic anisotropy. For larger $|q|$, equilibration is delayed as the spin-state composition of…
We report on the spin textures produced by cooling unmagnetized $^{87}$Rb F=1 spinor gases into the regime of quantum degeneracy. At low temperatures, magnetized textures form that break translational symmetry and display short-range periodic magnetic order characterized by one- or two-dimensional spatial modulations with wavelengths much smaller than the extent of the quasi-two-dimensional degenerate gas. Spin textures produced upon cooling spin mixtures with a non-zero initial magnetic quadrupole moment also show ferromagnetic order that, at low temperature, coexists with the spatially modul…
We investigate the dynamics of bright matter wave solitons in spin-1 Bose-Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross-Pitaevskii (3-GP) equations using Hirota's method involving a non-standard bilinearization. The similarity transformations are developed to construct the soliton solutions of non-autonomous 3-GP system. The non-autonomous solitons admit different density profiles. An interesting phenomenon of soliton compression is identified for kink-like nonlinearity coefficient with Hermite-Gaussian-like…
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