In this work, we derive the equations of motion governing the hydrodynamics of spin-F spinor condensates. We pursue a description based on standard physical variables (total density and superfluid velocity), alongside 2F `spin-nodes': unit vectors that describe the spin F state, and also exhibit the point-group symmetry of a spinor condensate's mean-field ground state. The hydrodynamic equations of motion consist of a mass continuity equation, 2F Landau-Lifshitz equations for the spin-nodes, and a modified Euler equation. In particular, we provide a generalization of the Mermin-Ho relation to spin one, and find an analytic solution for the skyrmion texture in the incompressible regime of a spin-half condensate. These results exhibit a beautiful geometrical structure that underlies the dynamics of spinor condensates.
In this paper we study the linearized dynamics of spinor condensates using the spin-node formalism developed in arXiv:0812.3403. We provide a general method to linearize the equations of motion based on the symmetry of the mean-field ground state using the local stereographic projection of the spin nodes. We also provide a simple construction to extract the collective modes from symmetry considerations alone akin to the analysis of vibrational excitations of polyatomic molecules. Finally, we will present a mapping between the spin-wave modes, and the wave functions of electrons in atoms, where…
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 present measurements and a theoretical model for the interplay of spin dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features like quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a F=1 $^{87}$Rb Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to thermal equilibration.
We characterize fluctuations in atom number and spin populations in F=1 sodium spinor condensates. We find that the fluctuations enable a quantitative measure of energy dissipation in the condensate. The time evolution of the population fluctuations shows a maximum. We interpret this as evidence of a dissipation-driven separatrix crossing in phase space. For a given initial state, the critical time to the separatrix crossing is found to depend exponentially on the magnetic field and linearly on condensate density. This crossing is confirmed by tracking the energy of the spinor condensate as we…
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 have mapped out a detailed phase diagram that shows the ground state structure of a spin-1 condensate with magnetic dipole-dipole interactions. We show that the interplay between the dipolar and the spin-exchange interactions induces a rich variety of quantum phases that exhibit spontaneous magnetic ordering in the form of intricate spin textures.
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.
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 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 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 study the semiclassical dynamics of a spinor condensate with the magnetic dipole-dipole interaction included. The time evolution of the population imbalance and the relative phase among different spin components depends greatly on the relative strength of interactions as well as on the initial conditions. The interplay of spin exchange and dipole-dipole interaction makes it possible to manipulate the atomic population on different components, leading to the phenomena of spontaneous magnetization and Macroscopic Quantum Self Trapping. Simple estimate demonstrates that these effects are acces…
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 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.
We consider a spinor condensate of $^{87}$Rb atoms in F=1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in $m_F=0$ component we find that the system evolves towards a state of thermal equilibrium with kinetic energy equally distributed among all magnetic components. We show that this process is dominated by the dipolar interaction of magnetic spins rather than spin mixing contact potential. Our results show that because of a dynamical separation of magnetic components the spin mixing dynamics in $^{87}$Rb condensate is governed by dipolar interaction which pla…
We show that the newly discovered $^{52}$Cr Bose condensate in zero magnetic field can be a spin nematic of the following kind: A "maximum" polar state, a "co-linear" polar state, or a biaxial nematic ferromagnetic state. We also present the phase diagram with a magnetic field in the interaction subspace containing the Chromium condensate. It contains many uniaxial and biaxial spin nematic phases, which often but not always break time reversal symmetry, and can exist with or without spontaneous magnetization.
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 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.
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.
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 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…
We study the energetics of vortices and vortex lattices produced by rotation in the cyclic phase of F=2 spinor Bose condensates. In addition to the familiar triangular lattice predicted by Tkachenko for $^4$He, many more complex lattices appear in this system as a result of the spin degree of freedom. In particular, we predict a magnetic-field-driven transition from a triangular lattice to a honeycomb lattice. Other transitions and lattice geometries are driven at constant field by changes in the temperature-dependent ratio of charge and spin stiffnesses, including a transition through an aper…
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 study the mechanisms and the limits of pumping vorticity into a spinor condensate through manipulations of magnetic (B-) fields. We discover a fundamental connection between the geometrical properties of the magnetic fields and the quantized circulation of magnetically trapped atoms, a result which generalizes several recent experimental and theoretical studies. The optimal procedures are devised that are capable of continuously increasing or decreasing a condensate's vorticity by repeating certain two step B-field manipulation protocols. We carry out detailed numerical simulations that sup…
We propose to the create vortices in spin-1 condensates via magnetic dipole-dipole interaction. Starting with a polarized condensate prepared under large axial magnetic field, we show that by gradually inverting the field, population transfer among different spin states can be realized in a controlled manner. Under optimal condition, we generate a doubly quantized vortex state containing nearly all atoms in the condensate. The resulting vortex state is a direct manifestation of the dipole-dipole interaction and spin textures in spinor condensates. We also point out that the whole process can b…
We show that an effective quadratic Zeeman effect can be generated in $^{52}$Cr by proper laser configurations, and in particular by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, can be used to induce topological defects by controllably quenching across transitions between phases of different symmetries, allows for the observability of the Einstein-de Haas effect for relatively large magnetic fields, and may be employed to create $S=1/2$ systems with spinor dynamics. Similar ideas could be explored in other atomic species opening an exc…
We study the ground state and classify its phase diagram for a mixture of two spin-1 condensates in the absence of external magnetic (B-) field according to atomic parameters for intra- and inter-species spin exchange coupling and singlet pairing interaction. Ignoring the inter-species singlet pairing interaction, the ground state phases are found analytically. Numerical approach of simulated annealing is adopted when the singlet pairing interaction is present. Our results on the phase diagram and the boundaries between phases allow for easy identifications of quantum phase transitions, that c…
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 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…
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.
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.
We consider a spinor condensate of 87Rb atoms in its F=1 hyperfine state at finite temperatures. Putting initially all atoms in m_F=0 component we find that the system evolves into the state of thermal equilibrium. This state is approached in a step-like process and when established it manifests itself in distinguishable ways. The atoms in states m_F=+1 and m_F=-1 start to rotate in opposite directions breaking the chiral symmetry and showing highly regular spin textures. Also the coherence properties of the system changes dramatically. Depending on the strength of spin-changing collisions the…
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.
Condensates of atoms with spins can have vortices of several types; these are related to the symmetry group of the atoms' ground state. We discuss how, when a condensate is placed in a small magnetic field that breaks the spin symmetry, these vortices may form bound states. Using symmetry classification of vortex-charge and rough estimates for vortex interactions, one can show that some configurations that are stable at zero temperature can decay at finite temperatures by crossing over energy barriers. Our focus is cyclic spin 2 condensates, which have tetrahedral symmetry.
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.
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.
The magnetic radiation of the fully-condensed states of $^{23}$Na condensates have been studied. A narrow characteristic spectral line with a wave length proportional to N^(-2/5) (N is the number of particles) and with a probability of transition proportional to N^(17/5) emitted (absorbed) by the condensate was found. It implies that short wave radiation with a huge probability of transition can be obtained if numerous atoms are trapped. A new technique developed by the authors, namely, the analytical forms of the fractional parentage coefficients, was used to calculate analytically the matrix…
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…
