1 / 138

Entanglement and Coherence in Spin-1 Bose Gas: Exact Solution for Quantum Dynamics

This research explores phase coherence and entanglement in spin-1 Bose gas, illustrating progress and application in condensed matter systems. The study examines the Penrose-Onsager characterization of Bose condensation and the existence of a single macroscopic eigenvalue. It also investigates the possibilities of fragmented condensates and strongly correlated ground states. The paper presents a controlled way to change phase coherence using a pseudo-spin 1/2 system as an example and discusses the potential to convert coherent states into Schrödinger Cat states. The research includes findings on the dynamic evolution of spin-1 Bose gas and the effect of spin degeneracy in a deep harmonic trap.

olenej
Download Presentation

Entanglement and Coherence in Spin-1 Bose Gas: Exact Solution for Quantum Dynamics

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. Entanglement and Coherence in Spin-1 Bose Gas -- an exact solution for quantum dynamics of a many-body system Jason Ho The Ohio State University International Conference in Recent Progress in Quantum Mechanics and Its Applications Chinese University of Hong Kong December 14, 2005

  2. Recent Progress in Quantum Mechanics and Its Applications (1) Phase coherence, entanglement, (2) Novel condensed matter systems/phenomena Use BEC to illustrate these progress and application

  3. Hallmark of BEC : phase coherence Off-diagonal long range order -- coherence at different location

  4. Penrose-Onsager characterization of Bose condensation Existence of a single macroscopic eigenvalue in : Eigenvalues : Eigenfunctions

  5. Off-Diagonal Oder Phase Coherence CN Yang, RMP, ORLRO paper + …

  6. Other possibilities ? Nozieres, 1992 Fragmented condensate Strongly correlated

  7. Possible type of ground states: coherent Fragmented Strongly correlated

  8. Single condensate state of spin-F Bosons Single particle density matrix contains a single eigenvalue of order N Spin-1/2 Spin-1 scalar

  9. How to change phase coherence in a controlled way?

  10. Simple Example : Pseudo-spin 1/2 system 1 2 t Hilbert space:

  11. BEC --> Fragmentation Coherence --> squeezing --> entanglement 1 2 t

  12. BEC --> Fragmentation Coherence --> squeezing --> entanglement 1 2 t

  13. BEC --> Fragmentation Coherence --> squeezing --> entanglement 1 2 t ,

  14. BEC --> Fragmentation Coherence --> squeezing --> entanglement 1 2 t ,

  15. BEC --> Fragmentation Coherence --> squeezing --> entanglement 1 2 t ,

  16. Schrodinger Cat State: huge number fluctuation => very delicate Coherent State : very robust If there is a robust mechanism that can Convert the coherent state into a Schrodinger Cat state from time to time, then can realize these cat state at these specific time. Answer : Use Bosonic enhancement

  17. Spin-1 Bose gas Consider a term like this :

  18. Spin-1 Bose gas Consider a term like this :

  19. Spin-1 Bose gas Consider a term like this :

  20. Spin-1 Bose gas Consider a term like this :

  21. Spin-1 Bose gas Consider a term like this :

  22. Dynamical Evolution of Spin-1 Bose Gas

  23. N spin-1 Boson in a single level Effect of spin degeneracy on BEC Spin-1 Bose Gas A deep harmonic trap

  24. Spin dynamics of spin-1 Bose gas Spin-1 Bose Gas A deep harmonic trap Hilbert space

  25. Effect of spin degeneracy on BEC Effect of spin degeneracy on BEC Spin-1 Bose Gas A deep harmonic trap Under spin rotation, rotates like a 3D Cartesean vector . : 3D rotation

  26. C>0 = Exact ground state :

  27. Spin dynamics of spin-1 Bose gas 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Spin-1 Bose Gas 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A deep harmonic trap Chapman et.al. PRL 04, PRL 05 Watch change with time

  28. Data in Chapman et.al. PRL 04 Oscillatory behavior in Large fluctuations Small fluctuation

  29. 0.1% magnetization Large fluctuation Oscillatory

  30. Hilbert space :

  31. is a sum of two theta functions !

  32. Elliptic Functions are mathematicians' fairy land. Those who once glazed upon them are forever captured.

  33. Relate to those at

  34. Relate to those at

  35. time

  36. N=1000

  37. Generality of the quantum Carpet

  38. Periodic generation of Cat state and coherent state. • Self similar in “space-time”. • Quantum dynamics (periodic revival) can be • revealed at short times. • **Fluctuation in Chapman’s experiment is physical. • **Specific predictions to reveal quantum dynamics Printing and deprinting phases on the quantum carpet

  39. New Era in ultra-cold atoms Strongly correlated cold atoms Engineering of quantum states

  40. N=100 N=1000

  41. Effect of spin degeneracy on BEC Effect of spin degeneracy on BEC Spin-1 Bose Gas A deep harmonic trap : spin-1 matrix

  42. Effect of spin degeneracy on BEC Spin-1 Bose Gas A deep harmonic trap : Antiferromagnetic : Ferromagnetic , What is the ground state for c>0 ?

More Related