Ferromagnetic Spinor Bose-Einstein Condensate Research Articles

Emission of Spin-Correlated Matter-Wave Jets from Spinor Bose-Einstein Condensates.

We report the observation of matter-wave jet emission in a strongly ferromagnetic spinor Bose-Einstein condensate of ^{7}Li atoms. Directional atomic beams with |F=1,m_{F}=1⟩ and |F=1,m_{F}=-1⟩ spin states are generated from |F=1,m_{F}=0⟩ state condensates or vice versa. This results from collective spin-mixing scattering events, where spontaneously produced pairs of atoms with opposite momentum facilitates additional spin-mixing collisions as they pass through the condensates. The matter-wave jets of different spin states (|F=1,m_{F}=±1⟩) can be a macroscopic Einstein-Podolsky-Rosen state with spacelike separation. Its spin-momentum correlations are studied by using the angular correlation function for each spin state. Rotating the spin axis, the inter- and intraspin-momentum correlation peaks display a high-contrast oscillation, indicating collective coherence of the atomic ensembles. We provide numerical calculations that describe the experimental results at a quantitative level. Our Letter paves the way to generating macroscopic quantum entanglement with the spin and motional degree of freedom with massive particles. It has a wide range of applications from quantum information science to the fundamental studies of quantum entanglement.

Direct and inverse cascades of spin-wave turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates

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.

Spontaneous symmetry breaking of a ferromagnetic superfluid in a gradient field

We consider the interaction of a ferromagnetic spinor Bose-Einstein condensate with a magnetic-field gradient. The magnetic-field gradient realizes a spin-position coupling that explicitly breaks time-reversal symmetry and space parity , but preserves the combined symmetry. We observe, using numerical simulations, a phase transition spontaneously breaking this remaining symmetry. The transition to a low-gradient phase, in which gradient effects are frozen out by the ferromagnetic interaction, suggests the possibility of high-coherence magnetic sensors unaffected by gradient dephasing.

Coherent spin dynamics in spin-imbalanced ferromagnetic spinor condensates**Project supported by the National Natural Science Foundation of China (Grant No. 11104217), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2014JQ1022), and the Youth Foundation of XUPT, China (Grant No. ZL2013-36).

We study the coherent spin dynamics of a ferromagnetic spinor Bose–Einstein condensate (BEC) in its domain formation process with an arbitrary spin configuration. Through a simplified schematic view of the domain structure, a semiclassical theory that captures the essential dynamics of the system is presented, and the coherent spin mixing dynamics can be understood in terms of oscillation in the phase space diagram. Using the phase diagram analysis method, we identify new phases, including the π phase oscillation and the running phase for the spin-imbalanced ferromagnetic spinor BEC.

Spin-superflow turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates

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 SST with the coexistence of disturbed spin and superfluid velocity field with two power laws.

Spin-glass-like behavior in the spin turbulence of spinor Bose-Einstein condensates

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.

Collective magnetism in arrays of spinor Bose–Einstein condensates

We elucidate dipolar magnetic interaction effects in spinor condensates at a low-background field. In particular, we show that arrays of ferromagnetic spinor Bose–Einstein condensates show a rich phase structure that is strongly influenced by the competition of shape anisotropy and higher-order magnetostatic contributions both depending on the condensate's form.

Long-time-scale dynamics of spin textures in a degenerateF=187Rb spinor Bose gas

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 the degenerate spinor gas remains close to its initial value. These observations support the mean-field equilibrium phase diagram predicted for a ferromagnetic spinor Bose-Einstein condensate and also illustrate that equilibration is achieved under a narrow range of experimental settings, making the $F=1$ ${}^{87}$Rb gas more suitable for studies of nonequilibrium quantum dynamics.

Tunneling properties of Bogoliubov mode and spin-wave modes in supercurrent states of a spin-1 ferromagnetic spinor Bose-Einstein condensate

We investigate tunneling properties of collective excitations in the ferromagnetic phase of a spin-1 spinor Bose-Einstein condensate (BEC). In addition to the Bogoliubov mode, this superfluid phase has two spin excitations, namely, the gapless transverse spin wave and the quadrupolar mode with a finite excitation gap. In the mean-field theory at T=0, we examine how these collective modes tunnel through a barrier potential that couples to the local density of particles. In the presence of supercurrent with a finite momentum $q$, while the Bogoliubov mode shows the so-called anomalous tunneling behavior (which is characterized by perfect transmission) in the low energy limit, the transverse spin-wave transmits perfectly only when the momentum $k$ of this mode coincides with $\pm q$. At $k=\pm q$, the wave function of this spin wave has the same form as the condensate wave function in the current carrying state, so that the mechanism of this perfect transmission is found to be the same as tunneling of supercurrent. Using this fact, the perfect transmission of the spin wave is proved for a generic barrier potential. We show that such perfect transmission does not occur in the quadrupolar mode. Further, we consider the effects of potentials breaking U(1) and spin rotation symmetries on the transmission properties of excitations. Our results would be useful for understanding excitation properties of spinor BECs, as well as the anomalous tunneling phenomenon in Bose superfluids.

Spin squeezing of high-spin, spatially extended quantum fields

Investigations of spin squeezing in ensembles of quantum particles have been limited primarily to a subspace of spin fluctuations and a single spatial mode in high-spin and spatially extended ensembles. Here, we show that a wider range of spin squeezing is attainable in ensembles of high-spin atoms, characterized by sub-quantum-limited fluctuations in several independent planes of spin-fluctuation observables. Further, considering the quantum dynamics of an f=1 ferromagnetic spinor Bose–Einstein condensate, we demonstrate theoretically that a high degree of spin squeezing is attained in multiple spatial modes of a spatially extended quantum field and that such squeezing can be extracted from spatially resolved measurements of magnetization and nematicity, i.e. the vector and quadrupole magnetic moments, of the quantum gas. Taking into account several experimental limitations, we predict that the variance of the atomic magnetization and nematicity may be reduced as far as 20 dB below the standard quantum limits.

Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate

A central goal in condensed matter and modern atomic physics is the exploration of quantum phases of matter--in particular, how the universal characteristics of zero-temperature quantum phase transitions differ from those established for thermal phase transitions at non-zero temperature. Compared to conventional condensed matter systems, atomic gases provide a unique opportunity to explore quantum dynamics far from equilibrium. For example, gaseous spinor Bose-Einstein condensates (whose atoms have non-zero internal angular momentum) are quantum fluids that simultaneously realize superfluidity and magnetism, both of which are associated with symmetry breaking. Here we explore spontaneous symmetry breaking in 87Rb spinor condensates, rapidly quenched across a quantum phase transition to a ferromagnetic state. We observe the formation of spin textures, ferromagnetic domains and domain walls, and demonstrate phase-sensitive in situ detection of spin vortices. The latter are topological defects resulting from the symmetry breaking, containing non-zero spin current but no net mass current.

Continuous vortices and collective excitations in ferromagnetic spinor Bose–Einstein condensates

Bose–Einstein condensates (BEC) realized in alkali atomic gases with the hyperfine state F=1 keep “spin” states degenerate and active under an optical trap. These systems, so-called spinor BEC are analogous to the A-phase of the superfluid 3 He . Among various topological structures, the Mermin–Ho and Anderson–Toulouse vortices are proposed in superfluid 3 He-A phase. We demonstrate by solving the extended Gross–Pitaevskii equation that these topological structures are thermodynamically stable in ferromagnetic spinor BEC under rotation. Furthermore, we show the collective modes for such the vortices within Bogoliubov theory.