We unravel the correlation effects of the second-order quantum phase transitions emerging on the ground state of a harmonically trapped spin-1 Bose gas, upon varying the involved Zeeman terms, as well as its breathing dynamics triggered by quenching the trapping frequency. It is found that the boundaries of the associated magnetic phases are altered in the presence of interparticle correlations for both ferromagnetic and anti-ferromagnetic spin-spin interactions, an effect which becomes more prominent in the few-body scenario. Most importantly, we unveil a correlation-induced shrinking of the anti-ferromagnetic and broken-axisymmetry phases implying that ground states with bosons polarized in a single spin-component are favored. Turning to the dynamical response of the spinor gas it is shown that its breathing frequency is independent of the system parameters while correlations lead to the formation of filamentary patterns in the one-body density of the participating components. The number of filaments is larger for increasing spin-independent interaction strengths or for smaller particle numbers. Each filament maintains its coherence and exhibits an anti-correlated behavior while distinct filaments show significant losses of coherence and are two-body correlated. Interestingly, we demonstrate that for an initial broken-axisymmetry phase an enhanced spin-flip dynamics takes place which can be tuned either via the linear Zeeman term or the quench amplitude.
We numerically study the breathing dynamics induced by collision between bright solitons in the one-dimensional Bose-Einstein condensates with strong dipole-dipole interaction. This breathing phenomenon is closely related to the after-collision short-lived attraction of solitons induced by the dipolar effect. The initial phase difference of solitons leads to the asymmetric dynamics after collision, which is manifested on their different breathing amplitude, breathing frequency, and atom number. We clarify that the asymmetry of breathing frequency is directly induced by the asymmetric atom numb…
We measure the position- and momentum- space breathing dynamics of trapped one-dimensional Bose gases. The profile in real space reveals sinusoidal width oscillations whose frequency varies continuously through the quasicondensate to ideal Bose gas crossover. A comparison with theoretical models taking into account the effect of finite temperature is provided. In momentum space, we report the first observation of a frequency doubling in the quasicondensate regime, corresponding to a self-reflection mechanism. The disappearance of this mechanism through the quasicondensation crossover is mapped…
We perform an extensive numerical study on the breathing dynamics of a few-body Bose polaron setup in a one-dimensional species-selective harmonic trap. The dynamics is triggered by a quench of the impurity trap. The excitation of the background majority atoms is mediated via the majority-impurity interaction. The breathing spectrum is obtained for different numbers of majority particles, several values of the majority-component interaction strengths and trap ratios. It is further compared to the breathing spectrum of a particle-balanced few-body Bose-Bose mixture. In particular, for equal pos…
We investigate a few-body mixture of two bosonic components, each consisting of two particles confined in a quasi one-dimensional harmonic trap. By means of exact diagonalization with a correlated basis approach we obtain the low-energy spectrum and eigenstates for the whole range of repulsive intra- and inter-component interaction strengths. We analyse the eigenvalues as a function of the inter-component coupling, covering hereby all the limiting regimes, and characterize the behaviour in-between these regimes by exploiting the symmetries of the Hamiltonian. Provided with this knowledge we st…
We investigate the breathing mode of harmonically trapped bosons in an optical lattice at small site occupancies. The Bose-Hubbard model with a trapping potential is used to describe the breathing-mode dynamics initiated through weak quenches of the trap strength. We connect to results for continuum bosons (Lieb-Liniger and Gross-Pitaevskii results) and also present deviations from continuum physics. We take a spectral perspective, identifying the breathing mode frequency with a particular energy gap in the spectrum of the trapped Bose-Hubbard Hamiltonian. We present the low energy eigenspectr…
In this work, we explore systematically various SO(2)-rotation-induced multiple dark-dark soliton breathing patterns obtained from stationary and spectrally stable multiple dark-bright and dark-dark waveforms in trapped one-dimensional, two-component atomic Bose-Einstein condensates (BECs). The stationary states stem from the associated linear limits (as the eigenfunctions of the quantum harmonic oscillator problem) and are parametrically continued to the nonlinear regimes by varying the respective chemical potentials, i.e., from the low-density linear limits to the high-density Thomas-Fermi r…
Motivated by a recent experiment [J. Catani et al., arXiv:1106.0828v1 preprint, 2011], we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. In the Gross-Pitaevskii regime we obtain breathing oscillations whose amplitudes are suppressed by self trapping, due to interactions with the Bose gas. Introducing phonons in the Bose gas leads to the damping of breathing oscillations and non-Markovian dynamic…
We consider impurity atoms embedded in a two-component Bose-Einstein condensate in a quasi-one dimensional regime. We study the effects of repulsive coupling between the impurities and Bose species on the equilibrium of the system for both miscible and immiscible mixtures by numerically solving the underlying coupled Gross-Pitaevskii equations. Our results reveal that the presence of impurities may lead to a miscible-immiscible phase transition due to the interaction of the impurities and the two condensates. Within the realm of the Bogoliubov-de Gennes equations we calculate the quantum fluct…
In this work, we present the study of the stationary structures and the breathing mode behavior of a two-dimensional self-bound binary Bose droplet. We employ an analytical approach using a variational ansatz with a super-Gaussian trial order parameter and compare it with the numerical solutions of the extended Gross-Pitaevskii equation. We find that the super-Gaussian is superior to the often used Gaussian ansatz in describing the stationary and dynamical properties of the system. We find that for sufficiently large non-rotating droplets the breathing mode is energetically favourable compared…
We develop a finite-temperature hydrodynamic approach for a harmonically trapped one-dimensional quasicondensate and apply it to describe the phenomenon of frequency doubling in the breathing-mode oscillations of its momentum distribution. The doubling here refers to the oscillation frequency relative to the oscillations of the real-space density distribution, invoked by a sudden confinement quench. We find that the frequency doubling is governed by the quench strength and the initial temperature, rather than by the crossover from the ideal Bose gas to the quasicondensate regime. The hydrodyna…
By analyzing breathing mode of a Bose-Einstein condensate repulsively interacting with a polarized fermionic cloud, we further the understanding of a Bose-Fermi mixture recently realized by Lous et al. [\textit{Phys. Rev. Lett.} \textbf{120}, 243403]. We show that a hydrodynamic description of a domain wall between bosonic and fermionic atoms reproduces experimental data of Huang et al. [\textit{Phys. Rev. A} \textbf{99}, 041602(R)]. Two different types of interaction renormalization are explored, based on lowest order constrained variational and perturbation techniques. In order to replicate …
Spinor Bose gases form a family of quantum fluids manifesting both magnetic order and superfluidity. This article reviews experimental and theoretical progress in understanding the static and dynamic properties of these fluids. The connection between system properties and the rotational symmetry properties of the atomic states and their interactions are investigated. Following a review of the experimental techniques used for characterizing spinor gases, their mean-field and many-body ground states, both in isolation and under the application of symmetry-breaking external fields, are discussed.…
We present an exact diagonalization study of the breathing mode collective excitations for a rotating Bose-Einstein condensate of $N=10$ spinless bosons interacting via repulsive finite-range Gaussian potential and harmonically confined in quasi-two-dimension. The yrast state and the low-lying excited states are variationally obtained in given subspaces of the quantized total angular momentum $L$ employing the beyond lowest Landau level approximation in slowly rotating regime with $0 \le L < 2N$. For a given $L$, the low-energy eigenspectra (bands) are obtained in weakly to moderately interact…
We study the breathing oscillations in bose-fermi mixtures with Yb isotopes in the largely prolate deformed trap, which are realized by Kyoto group. We choose the three combinations of the Yb isotopes, Yb170-Yb171, Yb170-Yb173 and Yb174-Yb173, whose boson-fermion interactions are weakly repulsive, strongly attractive and strongly repulsive. The collective oscillations in the deformed trap are calculated in the dynamical time-development approach, which is formulated with the time-dependent Gross-Pitaevskii and the Vlasov equations. We analyze the results in the time-development approach with t…
We calculate the breathing mode frequency $ω$ in a one-dimensional Bose gas confined to a harmonic trap of frequency $ω_z$. We predict Exciting temporal oscillations of the density distribution is a high-precision method for probing ultracold trapped atomic gases. Interaction effects in their many-body dynamics are particularly puzzling and counter-intuitive in one spatial dimension (1D) due to enhanced quantum correlations. We consider 1D quantum Bose gas in a parabolic trap at zero temperature and explain, analytically and numerically, how oscillation frequency depends on the number of parti…
In a spinor Bose-Einstein gas, the non-zero hyperfine spin of the gas becomes an accessible degree of freedom. At low temperature, such a gas shows both magnetic and superfluid order, and undergoes both density and spin dynamics. These lecture notes present a general overview of the properties of spinor Bose-Einstein gases. The notes are divided in five sections. In the first, we summarize basic properties of multi-component quantum fluids, focusing on the specific case of spinor Bose-Einstein gases and the role of rotational symmetry in defining their properties. Second, we consider the magne…
We measure the mass, gap, and magnetic moment of a magnon in the ferromagnetic $F=1$ spinor Bose-Einstein condensate of $^{87}$Rb. We find an unusually heavy magnon mass of $1.038(2)_\mathrm{stat}(8)_\mathrm{sys}$ times the atomic mass, as determined by interfering standing and running coherent magnon waves within the dense and trapped condensed gas. This measurement is shifted significantly from theoretical estimates. The magnon energy gap of $h\times 2.5(1)_\mathrm{stat}(2)_\mathrm{sys}\;\mathrm{Hz}$ and the effective magnetic moment of $-1.04(2)_\mathrm{stat}(8)\,μ_\textrm{bare}$ times the …
A dynamical theory is presented for the domain wall in the spinor Bose-Einstein condensate of "effective"one-dimension. The formulation is based on the time-dependent Landau-Ginzburg (LG) theory written in terms of the spinor order parameter. The procedure is carried out in such a way that an adiabatic change of the collective coordinates; the kink position as well as the phase function built in the spinor, is adapted to the canonical term (alias geometric phase) in the LG Lagrangian. Two problems are discussed: The first one is to explore the translational motion of the kink center in the pre…
By studying the coarsening dynamics of a one-dimensional spin-1 Bose-Hubbard model in a superfluid regime, we analytically find an unconventional universal dynamical scaling for the growth of the spin correlation length, which is characterized by the exponential integral unlike the conventional power-law or simple logarithmic behavior, and numerically confirmed with the truncated Wigner approximation.
We study the breathing oscillations in bose-fermi mixtures in the axially-symmetric deformed trap of prolate, spherical and oblate shapes, and clarify the deformation dependence of the frequencies and the characteristics of collective oscillations. The collective oscillations of the mixtures in deformed traps are calculated in the scaling method. In largely-deformed prolate and oblate limits and spherical limit, we obtain the analytical expressions of the collective frequencies. The full calculation shows that the collective oscillations become consistent with the analytically-obtained frequen…
We report direct measurements of spin transport in a trapped, partially condensed spinor Bose gas. Detailed analyses of spin flux in this out-of-equilibrium quantum gas are performed by monitoring the flow of atoms in different hyperfine spin states. The main mechanisms for motion in this system are exchange scattering and potential energy inhomogeneity, which lead to spin waves in the normal component and domain formation in the condensate. We find a large discrepancy in domain formation timescales with those predicted by potential-driven formation, indicating strong coupling of the condensat…
We introduce a Floquet spinor Bose-Einstein condensate induced by a periodically driven quadratic Zeeman coupling whose frequency is larger than any other energy scales. By examining a spin-1 system available in ultracold atomic gases, we demonstrate that such an external driving field has great effect on the condensate through emergence of a unique spin-exchange interaction. We uncover that the ferromagnetic condensate has several unconventional stationary states and thus exhibits rich continuous phase transitions. On the other hand, the antiferromagnetic condensate is found to possess a nont…
With use of a variational principle, we investigate a role of breathing width degree of freedom in the effective theory of interacting vortices in a trapped single-component Bose-Einstein condensates in 2 dimensions under the strong repulsive cubic nonlinearity. As for the trial function, we choose a product of two vortex functions assuming a pair interaction and employ the amplitude form of each vortex function in the Padé approximation which accommodates a hallmark of the vortex core. We have obtained Lagrange equation for the interacting vortex-core coordinates coupled with the time-derivat…
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…
By studying the zero-temperature and nonzero-temperature phase diagrams of the ferromagnetic spin-1 Bose-Hubbard model under an external magnetic field, we find that the competition between ferromagnetism and the quadratic Zeeman energy yields two superfluid phases, which feature discontinuous first-order phase transitions between them for a strongly spinor Bose gas such as ${}^7$Li, contrary to the corresponding continuum system.
Josephson junctions are essential ingredients in the superconducting circuits used in many existing quantum technologies. Additionally, ultracold atomic quantum gases have also become essential platforms to study superfluidity. Here, we explore the analogy between superconductivity and superfluidity to present an intriguing effect caused by a thin finite barrier in a quasi-one-dimensional toroidal spinor Bose--Einstein condensate (BEC). In this system, the atomic current density flowing through the edges of the barrier oscillates, such as the electrical current through a Josephson junction in …
Excited-state quantum phase transitions (ESQPTs) extend the notion of quantum phase transitions beyond the ground state. They are characterized by closing energy gaps amid the spectrum. Identifying order parameters for ESQPTs poses however a major challenge. We introduce spinor Bose-Einstein condensates as a versatile platform for studies of ESQPTs. Based on the mean-field dynamics, we define a topological order parameter that distinguishes between excited-state phases, and discuss how to interferometrically access the order parameter in current experiments. Our work opens the way for the expe…
We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a three-mode spinor Bose-Einstein condensate. The ground state is protected by a finite energy gap, is immune to phase noise, and the measurement of the number of particles in one mode heralds the coherent preparation of the two other modes simultaneously empty and filled. Highly entangled macroscopic superposition states are generated with large probability also taking into account quasi-adiabatic preparation of the ground state. All the key ingredients necessary to realize our proposal a…
We propose the use of stimulated Raman adiabatic passage (STIRAP) to offer a fast high fidelity method of performing SU(2) rotations on spinor Bose Einstein condensates (BEC). Past demonstrations of BEC optical control suffer from difficulties arising from collective enhancement of spontaneous emission and inefficient two-photon transitions originating from selection rules. We present here a novel scheme which allows for arbitrary coherent rotations of two-component BECs while overcoming these issues. Numerical tests of the method show that for BECs of \ce{^{87}Rb} with up to $ 10^4 $ atoms an…
We apply the number-conserving Bogoliubov theory to spinor Bose-Einstein condensates and show that the Goldstone magnon leads instability leading to fragmentation. Unlike the dynamical instability, where modes with complex eigenfrequencies grow exponentially, here the zero-energy mode exhibits algebraic growth. We also point out that a small fraction of thermally excited atoms enhances the fragmentation dynamics.
An overview on the physics of spinor and dipolar Bose-Einstein condensates (BECs) is given. Mean-field ground states, Bogoliubov spectra, and many-body ground and excited states of spinor BECs are discussed. Properties of spin-polarized dipolar BECs and those of spinor-dipolar BECs are reviewed. Some of the unique features of the vortices in spinor BECs such as fractional vortices and non-Abelian vortices are delineated. The symmetry of the order parameter is classified using group theory, and various topological excitations are investigated based on homotopy theory. Some of the more recent de…
Using effective field theories dictated by the symmetry of the system, as well as microscopic considerations, we map out the magnetic coupling-temperature phase diagrams of spin-1 Bose gases in both two- and three-dimensions. We also determine the nature of all phase boundaries, and critical properties in the case of 2nd order phase transitions at both zero and finite temperatures.
We find analytic continuous wave (cw) solutions for spinor Bose-Einstein condenates (BECs) in a magnetic field that are more general than those published to date. For particles with spin F=1 in a homogeneous one-dimensional trap, there exist cw states in which the chemical potential and wavevectors of the different spin components are different from each other. We include linear and quadratic Zeeman splitting. Linear Zeeman splitting, if the magnetic field is constant and uniform, can be mathematically eliminated by a gauge transformation, but quadratic Zeeman effects modify the cw solutions i…
We study the richer structures of quasi-one-dimensional Bogoliubov-de Genes collective excitations of F = 1 spinor Bose-Einstein condensate in a harmonic trap potential loaded in an optical lattice. Employing a perturbative method we report general analytical expressions for the confined collective polar and ferromagnetic Goldstone modes. In both cases the excited eigenfrequencies are given as function of the 1D effective coupling constants, trap frequency and optical lattice parameters. It is shown that the main contribution of the optical lattice laser intensity is to shift the confined phon…
We present an analytical model for the theoretical analysis of spin dynamics and spontaneous symmetry breaking in a spinor Bose-Einstein condensate (BEC). This allows for an excellent intuitive understanding of the processes and provides good quantitative agreement with experimental results in Phys. Rev. Lett. 105, 135302 (2010). It is shown that the dynamics of a spinor BEC initially prepared in an unstable Zeeman state mF=0 (|0>) can be understood by approximating the effective trapping potential for the state |+-1> with a cylindrical box potential. The resonances in the creation efficiency …
An inequality for spin-$F$ Bose-Einstein condensates (BECs) $ F^2(ρ^2-|Θ|^2)-\boldsymbol{M}^2\ge0 $ is reported, where $ρ$, $Θ$, and $\boldsymbol{M}$ represent the density, singlet pair amplitude, and magnetization vector, respectively. The distribution of high-symmetry spinors in the allowed region by the inequality is elucidated with using the Majorana representation. The result is illustrated by the example of spin-2 BECs.
We investigate the polarons formed by immersing a spinor impurity in a ferromagnetic state of $F=1$ spinor Bose-Einstein condensate. The ground state energies and effective masses of the polarons are calculated in both weak-coupling regime and strong-coupling regime. In the weakly interacting regime the second order perturbation theory is performed. In the strong coupling regime we use a simple variational treatment. The analytical approximations to the energy and effective mass of the polarons are constructed. Especially, a transition from the mobile state to the self-trapping state of the po…
We present experimental observations of coherent spin-population oscillations in a cold thermal, Bose gas of spin-1 sodium-23 atoms. The population oscillations in a multi-spatial-mode thermal gas have the same behavior as those observed in a single-spatial-mode antiferromagnetic spinor Bose Einstein condensate. We demonstrate this by showing that the two situations are described by the same dynamical equations, with a factor of two change in the spin-dependent interaction coefficient, which results from the change to particles with distinguishable momentum states in the thermal gas. We compar…
We theoretically and numerically study spin-wave turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates, finding direct and inverse cascades with power-law behavior. To derive these power exponents analytically, the conventional weak wave turbulence theory is applied to the spin-1 spinor Gross-Pitaevskii equation. Thus, we obtain the $-7/3$ and $-5/3$ power laws in the transverse spin correlation function for the direct and inverse cascades, respectively. To confirm these power laws, numerical calculations are performed that obtain results consistent with these power laws.
Using a variational method, we derive an exact upper bound for one-magnon excitation energy in ferromagnetic spinor gases, which limits the quantum corrections to the effective mass of a magnon to be positive. We also derive an upper bound for one-magnon excitation energy in lattice systems. The results hold for both Bose and Fermi systems in $d$ dimensions as long as the interaction is local and invariant under spin rotation.
We develop theory for fluctuations in atom number and spin within finite-sized cells of a spinor Bose-Einstein condensate. This theory provides a model of measurements that can be performed in current experiments using finite resolution in situ imaging. We develop analytic results for quantum and thermodynamic limits of the fluctuations and apply our theory to the four equilibrium phases of a spin-1 condensate. We then validate these limits and examine the behaviour over a wide parameter regime using numerical calculations specialised to the case of a spinor condensate confined to be quasi-two…
Spin-1 spin-orbit-coupled spinor Bose-Einstein condensates have been realized in experiment. We study spin-orbit-coupled spinor gap solitons in this experimentally realizable system with an optical lattice. The spin-dependent parity symmetry of the spin-orbit coupling plays an important role in properties of gap solitons. Two families of solitons with opposite spin-dependent parity are found. Using an approximating model by replacing the optical lattice with a Harmonic trap, we demonstrate the physical origination of these two families. For a large negative quadratic Zeeman shift, we also find…
We study numerically the spin turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates (BECs). Spin turbulence (ST) is characterized by a -7/3 power law in the spectrum of the spin-dependent interaction energy. The direction of the spin density vector is spatially disordered but temporally frozen in ST, showing some analogy with the spin glass state. Thus, we introduce the order parameter of spin glass into ST in spinor BECs. When ST develops through some instability, the order parameter grows with a -7/3 power law, thus succeeding in describing ST well.
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 dynamics of a spinor Bose-Einstein condensate inside an optical cavity, driven transversely by a laser with a controllable polarization angle. We focus on a two-component Dicke model with complex light-matter couplings, in the presence of photon losses. We calculate the steady-state phase diagram and find dynamical instabilities in the form of limit cycles, heralded by the presence of exceptional points and level attraction. We show that the instabilities are induced by dissipative processes which generate non-reciprocal couplings between the two collective spins. Our predic…
We study the effects of an on-site disorder potential in a gas of spinor (spin-1) ultracold atoms loaded in an optical lattice corresponding to both ferromagnetic and antiferromagnetic spin dependent interactions. Starting with a disordered spinor Bose-Hubbard model (SBHM) on a two dimensional square lattice, we observe the appearance of a Bose glass phase using the fraction of the lattice sites having finite superfluid order parameter and non integer local densities as an indicator. A precise distinction between three different types of phases namely, superfluid (SF), Mott insulator (MI) and …
We calculate the Bose-Einstein condensation (BEC) temperature of spin-1 atomic bosons in external magnetic field, taking into account the influence of the quadratic Zeeman effect. In case that the quadratic Zeeman coefficient is positive, the BEC temperature exhibits a nontrivial dependance on the magnetic field and a magnetic-field-induced reentrant phenomenon of BEC is observed. This phenomenon could be well understood by the competition between the linear and quadratic Zeeman effects. Reentrance of BEC in a trapped spinor Bose gas is also discussed.
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.
Spin-superflow turbulence (SST) in spin-1 ferromagnetic spinor Bose-Einstein condensates is theoretically and numerically studied by using the spinor Gross-Pitaevskii (GP) equations. SST is turbulence in which the disturbed spin and superfluid velocity fields are coupled. Applying the Kolmogorov-type dimensional scaling analysis to the hydrodynamic equations of spin and velocity fields, we theoretically find that the -5/3 and -7/3 power laws appear in spectra of the superflow kinetic and the spin-dependent interaction energy, respectively. Our numerical calculation of the GP equations confirms…
The response of spinor Bose-Einstein condensates to dynamical modulation of magnetic fields is discussed with linear response theory. As an experimentally measurable quantity, the energy absorption rate (EAR) is considered, and the response function is found to access quadratic spin correlations which come from the perturbation of the quadratic Zeeman term. By applying our formalism to spin-1 condensates, we demonstrate that the EAR spectrum as a function of the modulation frequency is able to characterize the different magnetically ordered phases.
We introduce a novel mechanism to develop a turbulent flow in a spinor Bose-Einstein condensate, consisting in the stirring of a single line vortex by means of an external magnetic field. We find that density and velocity fluctuations have white-noise power spectra at large frequencies and that Kolmogorov 5/3 law is obeyed in the turbulent region. As the stirring is turned off, the flow decays to an agitated non-equilibrium state that shows an energy bottleneck crossover at small length scales. We demonstrate our findings by numerically solving two-state spinor coupled 3D Gross-Pitaevskii equa…
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 propose a pump scheme for quantum circulations, including counter-circulations for superposition states, of a spinor Bose-Einstein condensate. Our scheme is efficient and can be implemented within current experimental technologies and setups. It remains valid for non-classical atomic states, such as pseudo-spin squeezed states and maximal entangled N-GHZ or NooN states. Moreover, it is capable of transforming several enhanced sensing protocols relying on reduced fluctuations from quantum correlation and entanglement of atomic internal states to enhanced measurement of spatial interference a…
We propose a method for systematically finding ground states of spinor Bose-Einstein condensates by utilizing symmetry properties of the system. By this method, we can find not only an inert state, whose symmetry is maximal in the manifold under consideration, but also a non-inert state, which has lower symmetry and depends on the parameters in the Hamiltonian. We establish the symmetry-classification method for the spin-1, 2 and 3 cases at zero magnetic field, and find a new phase in the last case. Properties of vortices in the spin-3 system are also discussed.
The spinor dynamics of Bose-Einstein condensates of 87Rb atoms with hyperfine spins 1 and 2 were investigated. A technique of simultaneous Ramsey interferometry was developed for individual control of the vectors of two spins with almost the same Zeeman splittings. The mixture of spinor condensates is generated in the transversely polarized spin-1 and the longitudinally polarized spin-2 states. The time evolution of the spin-1 condensate exhibits dephasing and rephasing of the Larmor precession due to the interaction with the spin-2 condensate. The scattering lengths between spin-1 and -2 atom…
