1 / 20

Images of Excited Condensates: Diagonal Dynamical Bogoliubov Vacuum

Images of Excited Condensates: Diagonal Dynamical Bogoliubov Vacuum. Jacek Dziarmaga & Krzysztof Sacha. Kraków, Poland. PRA 67, 033608 (2003) cond-mat/0503328. Interference of BE condesates. Bogoliubov theory. Diagonal dynamical Bogoliubov vacuum. Density measurements

garron
Download Presentation

Images of Excited Condensates: Diagonal Dynamical Bogoliubov Vacuum

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. Images of Excited Condensates:Diagonal Dynamical Bogoliubov Vacuum Jacek Dziarmaga & Krzysztof Sacha Kraków, Poland PRA 67, 033608 (2003) cond-mat/0503328

  2. Interference of BE condesates Bogoliubov theory Diagonal dynamical Bogoliubov vacuum Density measurements on Bogoliubov vacuum Example: dark soliton

  3. Condensate interference Javanainen & Yoo, PRL 76, 161 (1996) Fock state Single density measurement

  4. Condensate interference In real experiment In computer experiment annihilation of atoms

  5. Condensate interference Phase ``collapse’’ by density measurement

  6. Quantum Bogoliubov theory Hamiltonian Small fluctuations Expansion Fig.Jav

  7. Bogoliubov transformation particles <-> quasiparticles Bogoliubov Hamiltonian Bogoliubov vacuum

  8. Time-dependent Bogoliubov theory Condensate in the ground state Condensate in an excited state

  9. Time-dependent Bogoliubov theory Excited state = t-dependent vacuum Ansatz Solution

  10. N-conserving theory Girardeau & Arnowitt, PR 113, 755 (1959) Castin & Dum, PRA 57, 3008 (1998) N-conserving operator Vacuum is N-particle state

  11. Diagonal dynamical vacuum Exact solution is

  12. Recipe:

  13. Quantum superposition Real coordinates q

  14. Born rule (?)

  15. Density measurement

  16. Dark soliton Burger et al., PRL 83, 5198 (1999) Fig:imprinting

  17. Phase imprinting in Bogoliubov theory Condesate Density after 2ms Total density after 2ms In focus Mode 1

  18. Density measurement

  19. CONCLUSION Exact diagonal vacuum Distribution of images

  20. Condensate in thermal state Condensate in excited state

More Related