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arXiv:1212.0482 · Physical Review A

Magnetic resonance spectroscopy and characterization of magnetic phases for spinor Bose-Einstein condensates

Akiyuki Tokuno, Shun Uchino

Published Jun 20, 2013• 5 citations
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Abstract

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.

DOI
10.1103/physreva.87.061604

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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.
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We predict a dynamical resonant effect, which is driven by externally applied linear and quadratic Zeeman fields, in a spin-orbit-coupled spin-1 Bose-Einstein condensate. The Bose-Einstein condensate is assumed to be initialized in some superposed state of Zeeman sublevels and subject to a sudden shift of the trapping potential. It is shown that the time-averaged center-of-mass oscillation and the spin polarizations of the Bose-Einstein condensate exhibit remarkable resonant peaks when the Zeeman fields are tuned to certain strengths. The underlying physics behind this resonance can be traced back to the out-of-phase interference of the dynamical phases carried by different spin-orbit states. By analyzing the single-particle spectrum, the resonant condition is summarized as a simple algebraic relation, connecting the strengths of the linear and quadratic Zeeman fields. This property is potentially applicable in quantum information and quantum precision measurement.
We develop a general theory of spin-dependent Bragg spectroscopy for spinor Bose-Einstein condensates. This spectroscopy involves using a density and spin-coupled optical probe to excite the system. We show that within the linear-response regime the momentum or energy transferred by the probe is determined by a set of density and spin-density dynamic structure factors. We derive a set of fff-sum rules that provides rigorous constraints for the first energy moments of these structure factors. As an application we compute the dynamic structure factors for cases within all four distinct phases of a spin-1 condensate using Bogoliubov theory. Our results demonstrate that spin-dependent Bragg spectroscopy can be used to selectively investigate the various phonon and magnon excitation branches and will be a useful tool for advancing our understanding of spinor condensates.
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We show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor F=1F=1F=1 Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicate the absence of metastability.
Spinor Bose Einstein condensates have widely been sought after as perfect emulators of condensed matter phenomena, providing widely tunable and highly controlled systems. Utilizing a novel spin sensitive phase contrast imaging technique, the vector magnetization is measured in-situ with high spatial and temporal resolution and applied to a number of experiments. Using optically trapped F = 1 87Rb spinor condensates, the equilibrium phase diagram of a spin-1 Bose gas is quantitatively explored by observing the evolution of unmagnetized spin textures and their thermal equilibrium properties. Spin domain coarsening and a strong dependence of the spin configuration on the quadratic Zeeman shift is observed, supporting the predicted mean-field equilibrium phase diagram for small values of the quadratic shift. Additionally, spinor Bose gases are demonstrated to be an effective tool in calibrating and characterizing experimental imaging systems. Sinusoidal test patterns of varying pitch are created and used to extract the modulation transfer function and quantify optical aberrations which are of immense importance in systems which claim to have high spatial resolution. Lastly we realize an optical kagome geometry in a two-dimensional optical superlattice with a scalar Bose gases. The optical superlattice can be tuned between various geometries, including kagome, one-dimensional stripe, and decorated triangular lattice. Using atom optics we characterize the various geometries and demonstrate the versatility of this optical superlattice. The kagome geometry presents a new experimental arena for studies of geometrically frustrated systems.