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6816 results in Condensed Matter Physics, Nanoscience and Mesoscopic Physics

Page 39 of 341

  • 4 - Topology and Symmetry

  • from Part II - Interacting Bose Gas
  • Hui Zhai, Tsinghua University, Beijing
  • Book:
    Ultracold Atomic Physics
    Published online:
    30 January 2021
    Print publication:
    25 February 2021, pp 118-152

  • Summary

    1. Introduce soliton in quasi-one-dimensional time-dependent Gross-Pitaevskii equation.

    2. Introduce the basic idea of topology and the homotopy groups.

    3. Introduce vortex in spinless condensate as a typical example of topological defect.

    4. Introduce the Berezinskii-Kosterlitz-Thouless transition as a topological defect driven phase transition, and emphasize the topological and energy requirements for such a transition.

    5. Discuss the geometric configuration that minimizes the energy of a vortex lattice.

    6. Introduce the Majorana stellar representation as a useful tool to visualise the symmetry of a high-spin wave function.

    7. Introduce two different phases of spin-1 condensate.

    8. Introduce the relation between a mean-field state and the singlet pair condensate.

    9. Introduce spin vortex and half vortex in spinor condensate, and discuss various possibilities of spin vortex core.

    10. Introduce two categories of topological excitations in a Bose condensate, and introduce monopole and skyrmion as the typical example of each category.

    11. Introduce simulating Dirac monopole in synthetic magnetic field.

    12. Discuss the symmetry of the Hamiltonian and the symmetry of various phases in a spin-orbit coupled BEC.

    13. Discuss the relation between symmetry and phase transitions, using spin-orbit coupled condensate as an example.

    14. Discuss the Galilean invariance and the superfluid critical velocity.

  • 6 - The Fermi Superfluid

  • from Part III - Degenerate Fermi Gases
  • Hui Zhai, Tsinghua University, Beijing
  • Book:
    Ultracold Atomic Physics
    Published online:
    30 January 2021
    Print publication:
    25 February 2021, pp 172-200

  • Summary

    1. Compare the difference between the two-body problem in a vacuum and on top of the Fermi sea.

    2. Introduce the BCS mean-field theory and the BCS ground state wave function and its excitation.

    3. Introduce the physical picture of BCS pairing.

    4. Introduce the concept of contact using the BCS state as an example.

    5. Discuss how the BCS state responds to the Zeeman field.

    6. Discuss different pairing symmetries.

    7. Discuss how the BCS-BEC crossover mean-field equation recovers features in both the BCS and the BEC limit.

    8. Discuss different behaviors of the excitation spectrum in the BCS and the BEC regimes and determine superfluid critical velocity from the excitation spectrum.

    9. Discuss how the superfluid transition temperature changes from the BCS regime to the BEC regime.

    10. Introduce a list of experimental observations on the BCS-BEC crossover.

    11. Discuss the challenging issues in studying the unitary Fermi gas.

    12. Introduce the concept of holographic duality and the prediction of the $\eta/s$ bound.

  • Contents

  • Hui Zhai, Tsinghua University, Beijing
  • Book:
    Ultracold Atomic Physics
    Published online:
    30 January 2021
    Print publication:
    25 February 2021, pp v-vi
    • Chapter
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Ultracold Atomic Physics
  • Hui Zhai
  • Published online:
    30 January 2021
    Print publication:
    25 February 2021
  • The field of ultracold atomic physics has developed rapidly during the last two decades, and currently encompasses a broad range of topics in physics, with a variety of important applications in topics ranging from quantum computing and simulation to quantum metrology, and can be used to probe fundamental many-body effects such as superconductivity and superfluidity. Beginning with the underlying and including the most cutting-edge experimental developments, this textbook covers essential topics such as Bose-Einstein condensation of alkali atoms, studies of BEC-BCS crossover in degenerate Fermi gas, synthetic gauge fields and Hubbard models, and many-body localization and dynamical gauge fields. Key physical concepts, such as symmetry and universality highlight the connections between different systems, and theory is developed with plain derivations supported by experimental results. This self-contained and modern text will be invaluable for researchers, graduate students and advanced undergraduates studying cold atom physics, from both a theoretical and experimental perspective.

Page 39 of 341