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Spin-dipole oscillation and polarizability of a binary Bose-Einstein condensate near the miscible-immiscible phase transition

Tom Bienaimé, Eleonora Fava, Giacomo Colzi, Carmelo Mordini, Simone Serafini, Chunlei Qu, Sandro Stringari, Giacomo Lamporesi, and Gabriele Ferrari
Phys. Rev. A 94, 063652 – Published 30 December 2016
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  • INTRODUCTION
  • MIXTURE PREPARATION
  • SPIN-DIPOLE POLARIZABILITY
  • SPIN-DIPOLE OSCILLATION
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We report on the measurement of the spin-dipole (SD) polarizability and of the frequency of the SD oscillation of a two-component Bose-Einstein condensate of sodium atoms occupying the |32S1/2,F=1,mF=±1〉 hyperfine states. This binary spin mixture presents the important properties of being, at the same time, fully miscible and rid of the limit set by buoyancy. It is also characterized by a huge enhancement of the SD polarizability and by the consequent softening of the frequency of the SD oscillation, due to the vicinity to the transition to the immiscible phase. The experimental data are successfully compared with the predictions of theory.

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    • Received 15 July 2016
    • Revised 30 August 2016

    DOI:https://doi.org/10.1103/PhysRevA.94.063652

    ©2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Bose-Einstein condensates
    Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

    Authors & Affiliations

    Tom Bienaimé1,*, Eleonora Fava1, Giacomo Colzi1,2, Carmelo Mordini1, Simone Serafini1, Chunlei Qu1, Sandro Stringari1,2, Giacomo Lamporesi1,2, and Gabriele Ferrari1,2

    • 1INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, Povo 38123, Italy
    • 2Trento Institute for Fundamental Physics and Applications, INFN, Povo 38123, Italy

    • *tom.bienaime@unitn.it

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    Issue

    Vol. 94, Iss. 6 — December 2016

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    Images

    • Figure 1
      Figure 1

      (a) Absorption images taken after a SG expansion for (I) the dipole loading, (II) the Landau-Zener transition, and (III) the Rabi pulse leading to the creation of the binary mixture. (b) Stabilization of the two components by shifting the |0〉 state using microwave dressing on the transition to |F=2,mF=0〉.

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    • Figure 2
      Figure 2

      (a) Relative displacement d=x↓−x↑ between the spin components as a function of x0 (orange dots). The green solid line corresponds to the situation of no intercomponent interaction d=2x0. The figure also shows a sketch of the experimental conditions (the dashed curve is the total cloud density). (b) SD oscillations for different values of x0 (positive and negative) observed using the second experimental protocol. The solid lines are fit to the data according to Eq. (2). In each figure of the paper, data error bars are the sum in quadrature of systematic and statistical errors (one standard deviation of the mean).

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    • Figure 3
      Figure 3

      SD polarizability extracted from the data of Fig. 2 (orange dots) and (b) (green triangles). The black (red) solid line is the prediction computed using the GPE (LDA). The shaded regions give the uncertainties taking into account error bars on the value of the coupling constants [37]. The green solid line corresponds to the situation of no intercomponent interaction P=1. We also provide the density profiles n↑,↓(x,0,0) from the GPE for x0/Rx=0.001,0.01,0.05. The experimental points overestimate the actual value of P due to the approximation of the TF fit and the interaction effect during the expansion (see text).

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    • Figure 4
      Figure 4

      (a) Ratio ω(x0)/ωx as a function of the amplitude A(x0) for the data of Fig. 2 (same marker styles). The black (red) marker is the prediction of the GPE ωSD/ωx=0.213(17) (LDA ωSD/ωx=0.189(15)). Extrapolating the linear fit of ω(x0)/ωx (solid blue line) for vanishing amplitude gives ωSD/ωx=0.18(1). (b) SD oscillations using the alternative method (blue dots) giving ωSD/ωx=0.218(2). We also show two density profiles n↑,↓(x,0,0) illustrating the out-of-phase SD oscillations. (Data obtained from the GPE taking the equilibrium state for x0/Rx=0.01 as the initial condition before setting x0=0 to start the oscillations.)

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