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arXiv:0802.0822

Effect of magnetic fields on the spin evolution of non-polarized 87Rb Bose-Einstein condensates

Zhifeng Chen, Bao Cheng-guang, Zhibing Li

Published Feb 6, 2008• 0 citations
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Abstract

The spin mixing dynamics of spin-1 Bose-Einstein condensates with zero magnetization and under an external magnetic field is investigated. The time-dependent solutions are obtained via a diagonalization of the Hamiltonian, which has a simple form under the single mode approximation. The features of evolution are compared in detail with those with the field removed so as to emphasize the effect of the field, which can induce strong oscillation in population of atoms in spin component 0 . A new mode of oscillation characterized by a high frequency and a low frequency, is found when the field is sufficiently strong.

DOI
10.48550/arxiv.0802.0822

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The spin mixing dynamics of spin-1 Bose-Einstein condensates with zero magnetization and under an external magnetic field is investigated. The time-dependent solutions are obtained via a diagonalization of the Hamiltonian, which has a simple form under the single mode approximation. The features of evolution are compared in detail with those with the field removed so as to emphasize the effect of the field, which can induce strong oscillation in population of atoms in spin component 0 . A new mode of oscillation characterized by a high frequency and a low frequency, is found when the field is sufficiently strong.
The spin mixing dynamics of spin-1 Bose–Einstein condensates with zero magnetization and under an external magnetic field is investigated in a systematic way. Beyond the mean field theory, the time-dependent solutions of the Hamiltonian under the single mode approximation are obtained via a procedure of diagonalization. Thereby the time-dependent populations of spin-0 component starting from various initial states are obtained and analyzed. The features of evolution are compared in detail with those with the field removed so as to emphasize the effect of the field. Since the solutions are exact for the Hamiltonian, we can study the long-term behavior of the evolution, where periodicity and inherent symmetry emerge. In particular, some special cases are found in which the evolution is highly sensitive to the field, very strong oscillation in population can be thereby induced. A new mode of oscillation of the population characterized by having two frequencies, one is high and one is low, is found when the field is sufficiently strong.
Dynamic response of the F=2F=2F=2 spinor Bose-Einstein condensate (BEC) under the influence of external magnetic fields is studied. A general formula is given for the oscillation period to describe population transfer from the initial polar state to other spin states. We show that when the frequency and the reduced amplitude of the longitudinal magnetic field are related in a specific manner, the population of the initial spin-0 state will be dynamically localized during time evolution. The effects of external noise and nonlinear spin-exchange interaction on the dynamics of the spinor BEC are studied. We show that while the external noise may eventually destroy the Rabi oscillations and dynamic spin localization, these coherent phenomena are robust against the nonlinear atomic interaction.
We experimentally studied the spin-dependent collision dynamics of 87Rb^{87}\mathrm{Rb}87Rb spin-2 Bose-Einstein condensates confined in an optical trap. The condensed atoms were initially populated in the $\ensuremath{\mid}F=2,{m}_{F}=0⟩$ state, and their time evolutions in the trap were measured in the presence of external magnetic field strengths ranging from 0.1 to 3.0G3.0\phantom{\rule{0.3em}{0ex}}\mathrm{G}3.0G. The atom loss rate due to inelastic two-body collisions was found to be $1.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{3}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Spin mixing in the F=2F=2F=2 manifold developed dramatically for the first few tens of milliseconds, and the oscillations in the population distribution between different magnetic components were observed over a limited range of magnetic field strengths. The antiferromagnetic property of this system was deduced from the magnetic field dependence on the evolution of relative populations for each mF{m}_{F}mF​ component.
In this paper, we study the dynamics properties of three-component antiferromagnetic dipolar Bose–Einstein condensates with external magnetic field. Our results are obtained by numerical simulations of the spinor Gross–Pitaevskii equation. We find that the population of the spin components is seriously influenced by magnetic field. The dynamical evolution process is accelerated in the presence of magnetic field. As a result, the periodic oscillation of spin exchange dynamics emerges and the components [Formula: see text] have the same amplitude. In addition, the density profile displays that the influences of dipolar interaction are masked by magnetic field. Moreover, we introduce an order parameter to characterize the disorder-order crossover, where it is seen that the system develops toward the disordered state with strong dipole strength when magnetic field is included.
In this thesis we investigate the static, dynamic, and thermodynamic properties\nof atomic spin-1 Bose gases in external magnetic fields. At low magnetic fields\nthe properties of single-component, or scalar condensates, are essentially\nunaffected but can become significantly altered for spinor Bose condensates as\nshown by our studies.\n\nWe first study the Bose-Einstein condensation of trapped spin-1 Bose gases by\nemploying the Hartree-Fock approximation and the two-fluid model within a mean\nfield approximation. Our detailed investigation reveals that the\nferromagnetically interacting spin-1 condensates exhibit triple condensations\nwhile the antiferromagnetically interacting ones show double condensations.\n\nThe ground state structure of homogeneous and trapped spin-1 Bose condensates\nwith ferromagnetic and antiferromagnetic interactions at zero temperature in\nmagnetic fields are then investigated systematically. We further illuminate the\nimportant effect of quadratic Zeeman shift which causes a preferred occupation\nof the $|m_F=0\nangle$ state through spin exchange collisions, $2|m_F=0\nangle\nleftrightarrow |m_F=1\nangle + |m_F=-1\nangle$.\n\nWe also present detailed studies of the off-equilibrium coherent dynamics of\nspin-1 Bose condensates in magnetic fields within the single spatial mode\napproximation. Dynamical instabilities of the off-equilibrium oscillations are\nshown to be responsible for the formation of multiple domains as recently\nobserved in several 87^{87}87Rb experiments.\n\nFinally, we discuss briefly excited condensate states, or soliton-like states,\nin cigar-shaped spin-1 Bose condensates with an effective quasi-1D description,\nusing the developed nonpolynomial Schr"odinger equation.
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.