1 / 13

One Dimensional Bosons in a Harmonic trap

One Dimensional Bosons in a Harmonic trap. Sung-po Chao Rutgers University 2008/02/20 Journal club. Outline. Newton’s cradle (Nature 440,p900,2006) Integrable theory: Lieb-Liniger model (PR 130,p.1605,1963) Introduction of the experimental model (PRL 81,p938; cond-mat 0606771)

sharon-kelly
Télécharger la présentation

One Dimensional Bosons in a Harmonic trap

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. One Dimensional Bosons in a Harmonic trap Sung-po Chao Rutgers University 2008/02/20 Journal club

  2. Outline • Newton’s cradle (Nature 440,p900,2006) • Integrable theory: Lieb-Liniger model (PR 130,p.1605,1963) • Introduction of the experimental model (PRL 81,p938; cond-mat 0606771) • Experimental setup and result (Nature 440,p900,2006; Nature 429,p277,2004) • Conclusion/Questions.

  3. Newton’s cradle: A toy made in 1967 showing • energy and momentum conservation for two • particle collision. • An example of integrable classical system (If no energy loss in collision). • Q: What about the quantum version?? (Am. J. Phys. 49, 761 (1981))

  4. One dimensional bosons interact with delta function potential Equations satisfy: The exact solution is obtained by separating regions and find solution within each region. Spectrum is obtained by imposing periodic boundary condition: Bethe Ansatz (PR 130,p1605,1963)

  5. Solution of 1D Bosons in ground state Written in dimensionless parameters for ground state energy: Zero Temp Quasi-particle distribution given by: Q: Is it possible to find it experimentally? (PR 130,p1605)

  6. 1/2 M. Olshanni proposed a cigar shaped potential may demonstrate 1D behavior with For S-wave scattering and ω⊥＞Ez, we can do perturbation for z directional scattered wave and the effective interaction is given by: 1/2 With g ～1/n ; a ⊥ ～ω⊥ (PRL 81,p938,1998)

  7. What to expect in the cigar shape potential? Tow limiting cases can be computed for distribution function: (γ defined as dimensionless interaction strength controllable by n and ω) (a) Tonks-Giradeau regime γ→∞ (Spreading in k) (c) Thomas-Fermi regime γ→0 (BEC) (PRL 86,p5413,2001)

  8. Experimental Setup of Optical Trap (PRA 71, p 011602) (Science 305,p 1125) To confine the bosons a 3rd harmonic trap is added in z-axis.

  9. Interacting bosons in a cigar shape potential x z z Nature 429,277-281 (2004)

  10. Quantum Newton’s Cradle (Nature 440,900-903,2006)

  11. Raw data taken at different time (Nature 440,900-903,2006)

  12. Data after correcting heating (Nature 440,900-903)

  13. Conclusion and Outlook

More Related