Spontaneous magnetic ordering in a ferromagnetic spinor dipolar Bose-Einstein condensate

Kawaguchi, Yuki; Saito, Hiroki; Kudo, Kazue; Ueda, Masahito

doi:10.1103/physreva.82.043627

Cited by 37 publications

(52 citation statements)

References 33 publications

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“…We observe two quantum phase transitions: one is between a longitudinal polar phase and a BA phase at a fixed positive q net , and the other is an AFM-BA phase transition at a given m. We also calculate the energy gap between the ground states and the first excited states in a spinor BEC, which provides an explanation for the feasibility of this new method. In addition, spin domains and spatial modes are not observed in our system, and our data can be well fit by predictions of the single spatial-mode approximation (SMA).The SMA assumes all spin states share the same spatial wavefunction, which has been a successful model to understand spinor microcondensates [8][9][10][11][12][13][20][21][22]. After taking into account that N and m are independent of time t and neglecting all constant terms in the Hamiltonian of spinor BECs, we use the SMA to express the BEC energy E and the time evolution of ρ 0 and θ as [1,20,21] E(t) = cρ 0 (t){[1 − ρ 0 (t)] + [1 − ρ 0 (t)] 2 − m 2 cos[θ(t)]} + q net (t)[1 − ρ 0 (t)] ;…”

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confidence: 64%

Mapping the phase diagram of spinor condensates via adiabatic quantum phase transitions

et al. 2014

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We experimentally study two quantum phase transitions in a sodium spinor condensate immersed in a microwave dressing field. We also demonstrate that many previously unexplored regions in the phase diagram of spinor condensates can be investigated by adiabatically tuning the microwave field across one of the two quantum phase transitions. This method overcomes two major experimental challenges associated with some widely used methods, and is applicable to other atomic species. Agreements between our data and the mean-field theory for spinor Bose gases are also discussed.PACS numbers: 67.85. Hj, 03.75.Mn, 67.85.Fg, 03.75.Kk A spinor Bose-Einstein condensate (BEC) is a multicomponent BEC with an additional spin degree of freedom, which has provided exciting opportunities to study quantum magnetism, superfluidity, strong correlations, spin-squeezing, and massive entanglement [1][2][3][4][5]. The interesting interactions in spinor BECs are interconversions among multiple spin states and magnetic field interactions (or microwave dressing field interactions) characterized by q net , the net quadratic Zeeman energy. The interplay of these interactions leads to oscillations among multiple spin populations, which has been experimentally confirmed in F =123 Na spinor BECs [6][7][8][9][10][11][12], and in both F =1 and F =287 Rb spinor condensates [13][14][15][16][17].Several groups demonstrated the mean-field (MF) ground states of spinor BECs by holding BECs in a fixed magnetic field and letting spin population oscillations damp out over a few seconds [8][9][10][11]. The required damping time, determined by energy dissipation, may in some cases exceed the BEC lifetime. The exact mechanism involved in energy dissipation requires further study, although it has been shown that energy dissipates much faster in high magnetic fields [10]. For F =1 BECs, a magnetic field introduces only a positive q net , while a microwave field has a distinct advantage since it can induce both positive and negative q net [1,7,12,18,19]. As shown in Ref. [12], the same physics model explains spin-mixing dynamics observed in both microwave fields and magnetic fields. One would assume that, if given a long enough exposure to a microwave field, a spinor BEC could also reach its MF ground states. However, experimental studies on ground states of spinor BECs in microwave fields have proven to be very difficult, since these fields are created by near-resonant microwave pulses. Two major experimental challenges associated with microwave fields are atom losses and variations in magnetization m. Microwave-induced changes in both m and the atom number N can be detrimental, especially when a spinor BEC is exposed to a large microwave field for a prolonged time [7,12]. As a result, the phase diagram of F =1 BECs has not been well explored in the q net ≤ 0 region, where applying microwave fields may be necessary.In this paper, we demonstrate a new method to overcome the aforementioned experimental challenges and report the observation of two quantum phase ...

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confidence: 64%

Mapping the phase diagram of spinor condensates via adiabatic quantum phase transitions

et al. 2014

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“…When we consider a quasi-2D BEC, n tot ,f , and v mass are defined by means of ψ m instead of Ψ m [36]. If one replaces Ψ m with ψ m , a S with ηa S , c dd with ηc dd , and b withb, the equation is the same as Eq.…”

Section: Magnetic Dipole-dipole Interactionmentioning

confidence: 99%

“…The dynamical instability (linear instability) under a strong magnetic field has been discussed previously, both for the hydrodynamic equation [7] and for the GP equation [36]. For the hydrodynamic equation, the growth rate of the unstable mode is calculated from the eigenvalues of the linearized equation of small deviations from the uniform initial condition.…”

Section: A Dynamical Instabilitymentioning

confidence: 99%

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Dissipative hydrodynamic equation of a ferromagnetic Bose-Einstein condensate: Analogy to magnetization dynamics in conducting ferromagnets

Kudo

Kawaguchi

2011

Phys. Rev. A

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The hydrodynamic equation of a spinor Bose-Einstein condensate (BEC) gives a simple description of spin dynamics in the condensate. We introduce the hydrodynamic equation of a ferromagnetic BEC with dissipation originating from the energy dissipation of the condensate. The dissipative hydrodynamic equation has the same form as an extended Landau-Lifshitz-Gilbert (LLG) equation, which describes the magnetization dynamics of conducting ferromagnets in which localized magnetization interacts with spin-polarized currents. Employing the dissipative hydrodynamic equation, we demonstrate the magnetic domain pattern dynamics of a ferromagnetic BEC in the presence and absence of a current of particles, and discuss the effects of the current on domain pattern formation. We also discuss the characteristic lengths of domain patterns that have domain walls with and without finite magnetization.

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“…However, recent experiments on spatially extended spinor gases revealed variegated magnetization textures produced upon cooling unmagnetized spinor gases into the quantum degenerate regime [8]. Theoretical works examined whether such textures could be favored at equilibrium by the substantial magnetic dipolar interactions in the 87 Rb gas; however, while some inhomogeneous textures do appear to be energetically favored, or at least metastable, they are predicted to evince spin-density modulations only on much longer lengths scales than observed experimentally [16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2011

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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.

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Spontaneous magnetic ordering in a ferromagnetic spinor dipolar Bose-Einstein condensate

Cited by 37 publications

References 33 publications

Mapping the phase diagram of spinor condensates via adiabatic quantum phase transitions

Mapping the phase diagram of spinor condensates via adiabatic quantum phase transitions

Dissipative hydrodynamic equation of a ferromagnetic Bose-Einstein condensate: Analogy to magnetization dynamics in conducting ferromagnets

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

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