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arXiv:2002.08723 · Physical Review A

Stoner-Wohlfarth switching of the condensate magnetization in a dipolar spinor gas and the metrology of excitation damping

Seong-Ho Shinn, Daniel Braun, Uwe R. Fischer

Published Jul 16, 2020• 8 citations
arXivHTMLPDF

Abstract

We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates in the homogeneous-local-spin-orientation approximation, that is, with unidirectional local magnetization. By analytically calculating the exact effective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbert equation for the dissipative condensate magnetization dynamics, and show how it leads to the Stoner-Wohlfarth model of a uniaxial ferromagnetic particle, where the latter model determines the stable magnetization patterns and hysteresis curves for switching between them. For an external magnetic field pointing along the axial, long direction, we analytically solve the Landau-Lifshitz-Gilbert equation. The solution explicitly demonstrates that the magnetic dipole-dipole interaction accelerates the dissipative dynamics of the magnetic moment distribution and the associated dephasing of the magnetic moment direction. Under suitable conditions, dephasing of the magnetization direction due to dipole-dipole interactions occurs within time scales up to two orders of magnitude smaller than the lifetime of currently experimentally realized dipolar spinor condensates, e.g., those produced with the large magnetic-dipole-moment atoms $^{166}\mathrm{Er}$. This enables experimental access to the dissipation parameter $\mathrm{\ensuremath{\Gamma}}$ in the Gross-Pitaevskii mean-field equation, for a system currently lacking a complete quantum kinetic treatment of dissipative processes and, in particular, an experimental check of the commonly used assumption that $\mathrm{\ensuremath{\Gamma}}$ is a single scalar independent of spin indices.

DOI
10.1103/physreva.102.013315

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We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates in the homogeneous-local-spin-orientation approximation, that is, with unidirectional local magnetization. By analytically calculating the exact effective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbert equation for the dissipative condensate magnetization dynamics, and show how it leads to the Stoner-Wohlfarth model of a uniaxial ferromagnetic particle, where the latter model determines the stable magnetization patterns and hysteresis curves for switching between them. For an external magnetic field pointing along the axial, long direction, we analytically solve the Landau-Lifshitz-Gilbert equation. The solution explicitly demonstrates that the magnetic dipole-dipole interaction accelerates the dissipative dynamics of the magnetic moment distribution and the associated dephasing of the magnetic moment direction. Under suitable conditions, dephasing of the magnetization direction due to dipole-dipole interactions occurs within time scales up to two orders of magnitude smaller than the lifetime of currently experimentally realized dipolar spinor condensates, e.g., those produced with the large magnetic-dipole-moment atoms 166Er^{166}\mathrm{Er}166Er. This enables experimental access to the dissipation parameter \ensuremathΓ\mathrm{\ensuremath{\Gamma}}\ensuremathΓ in the Gross-Pitaevskii mean-field equation, for a system currently lacking a complete quantum kinetic treatment of dissipative processes and, in particular, an experimental check of the commonly used assumption that \ensuremathΓ\mathrm{\ensuremath{\Gamma}}\ensuremathΓ is a single scalar independent of spin indices.
We used the Gross-Pitaevskii equations to investigate ferromagnetic resonance in spin-1 Bose-Einstein condensates with a magnetic dipole-dipole interaction. By introducing the dipole interaction, we obtained equations similar to the Kittel equations used to represent ferromagnetic resonance in condensed-matter physics. These equations indicated that the ferromagnetic resonance originated from dipolar interaction, and that the resonance frequency depended upon the shape of the condensate. Furthermore, spin currents driven by spin diffusions are characteristic of this system.
We study the spin dynamics of a spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interaction (MDDI) based on the Gross-Pitaevskii and Bogoliubov theories. We find that various magnetic structures such as checkerboards and stripes emerge in the course of the dynamics due to the combined effects of spin-exchange interaction, MDDI, quadratic Zeeman and finite-size effects, and nonstationary initial conditions. However, the short-range magnetic order observed by the Berkeley group [Phys. Rev. Lett. 100, 170403 (2008)] is not fully reproduced in our calculations; the periodicity of the order differs by a factor of 3 and the checkerboard pattern eventually dissolves in the course of time. Possible reasons for the discrepancy are discussed.
With current magnetic-field shielding and high-precision detection in dipolar spinor Bose-Einstein condensates, it is possible to experimentally detect the low- or zero-field nonsecular dipolar dynamics. Here we analytically investigate the zero-field nonsecular magnetic dipolar interaction effect, with an emphasis on magnetization dynamics in a spin-1 Bose-Einstein condensate under the single spatial mode approximation within the mean-field theory. Due to the biaxial nature of the dipolar interaction, a novel resonance occurs in the condensate magnetization oscillation, in contrast to the previous assumption of a conserved magnetization in strong magnetic fields. Furthermore, we propose a dynamical-decoupling detection method for such a resonance, which cancels the stray magnetic fields in experiment but restores the magnetization dynamics. Our results shed light on the dipolar systems and may find potential applications beyond cold atoms.
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.
Selected topics on spinor-dipolar aspects of Bose-Einstein condensation are overviewed. Spinor aspects include spin correlations, fragmentation, dynamical symmetries, and quantum mass acquisition. Dipolar aspects include magnetostriction, d-wave collapse, roton-maxon spectrum, supersolidity, and ferrofluidity. Finally, spinor-dipolar aspects concern the Einstein–de Haas effect and spontaneous mass and spin currents in the ground state. Introduction Bose-Einstein condensation is a phenomenon in which a macroscopic number of particles occupy the same single-particle state as a consequence of symmetrization of a many-body wave function and thereby quantum effects are amplified to the macroscopic level. The amplified single-particle state serves as a complex order parameter whose phase behaves as an emergent thermodynamic quantity, with its temporal and spatial variations giving the chemical potential and the superfluid velocity, respectively. If the interparticle interaction is repulsive, a Bose-Einstein condensate (BEC) acquires stability against excitations out of the condensate because they would cost the Fock exchange energy. This rigidity of the order parameter or the condensate wave function endows a BEC with several remarkable transport properties which are collectively known as superfluidity. In particular, the superfluid fraction can be 100% at zero temperature even though the condensate fraction is depleted due to interparticle interactions. Interparticle interactions also make excited particles phase-locked to the condensate, leading to Bogoliubov quasiparticles, which are the manifestation of phase-coherent particle– hole excitations. When constituent particles have spin degrees of freedom, a BEC features magnetism and spin nematicity which conspire with superfluidity to produce a rich phase diagram. In the absence of an external magnetic field, the mean-field groundstate phase diagram includes two [1, 2], five [3, 4, 5], and eleven phases [6, 7] for spin-1, 2, and 3 BECs, respectively. BECs with spin degrees of freedom are called spinor condensates. Moreover, the magnetic dipole–dipole interaction (MDDI) between atoms lends distinct twists to spinor condensates because it is long-ranged and anisotropic in sharp contrast with other interactions, which are short-ranged and isotropic. In this chapter, we will present a brief overview on the spinordipolar aspects of BEC. An early experimental work of spinor BECs is reviewed in Ref. [8]. Later developments with an emphasis on theoretical aspects are described in Ref. [9]. Many-body physics of polarized dipolar gases is reviewed in Ref. [10].
This work concerns a theoretical study of a two-component ultra-cold bosonic gas of polarised magnetic dipolar atoms. The atoms interact by short-ranged contact interactions and long-ranged dipole-dipole interactions. The two components can correspond to two different spin-states of a single atomic species or two different atomic species, as realised in recent experiments. Here, we develop a general theory for the ground states and excitations of a two-component dipolar Bose-Einstein condensate. The ground states are described by dipolar Gross-Pitaevskii equations and Bogoliubov-de Gennes equations describe the excitations. We apply these theories to systems in 3D harmonic traps and a uniform planar potential. Specialised numerical methods are developed to provide accurate solutions of these equations, and to deal with the singular dipole-dipole interaction kernel. These methods involve spectral representations based on plane waves and Bessel functions. We also discuss the methods we used for obtaining ground state solutions of the nonlinear Gross-Pitaevskii energy functional. Dipole-dipole interactions can favour spatial structure, as demonstrated in the recent observation of supersolid states of matter in a single-component dipolar gas. In the two-component system these interactions can also favour a ground state with a periodic order in the pseudo-spin density. A two-component system can be either miscible (components overlap) or immiscible (components are separated). Our focus here is in the spin-stripe state, which occurs in a flattened trap geometry and involves an immiscible stripe pattern along one of the weakly trapped or untrapped directions. We examine the dynamical stability conditions of the uniform miscible state in planar confinement, and produce an associated stability phase diagram. We identify the various instabilities and analytical criteria for estimating these. We focus on the occurrence of, and conditions that favour, density-roton or spin-roton excitations, anticipating that the softening of these excitations will lead to structured ground states. To characterize these excitations we introduce density and spin dynamical structure factors, which can be measured in experiments using Bragg spectroscopy. Building on the stability phase diagram we compute ground states where the immiscible state is unstable to spin-rotons, finding triangular and stripe immiscible states with a length scale set by the confinement and interactions. We find that the transition to the stripe state is continuous and coincides with the spin-roton softening in the uniform miscible state. We study the excitations of the spin stripe state which exhibits three gapless excitation branches arising from the spontaneous broken symmetries. We identify a balanced parameter regime, where the excitations exhibit a nonsymmorphic symmetry (a symmetry is nonsymmorphic when it is a combination of point-group operations with nonprimitive lattice translations, i.e. not an integer multiple of lattice constants), which is revealed in the density and spin dynamical structure factors. We also consider the dynamics of the system following a quench from the uniform to immiscible stripe states. In the early time dynamics, a spin-stripe state is formed in a such way that the stripe order only extends over small domains. In subsequent dynamics, these domain sizes grow as the system phase-orders towards its equilibrium state. We identify the relevant topological defects such as disclinations, dislocations and grain boundaries. Using ensembles of large scale simulations we show that dynamical scaling holds for the growth of order.