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Images of Bose-Einstein condensates

Images of Bose-Einstein condensates. Jacek Dziarmaga & Krzysztof Sacha. PRA 67, 033608 (2003) cond-mat/0503328. Kraków, Poland. Condensate interference. Bogoliubov theory. Diagonal t-dependent vacuum. Measurements on the vacuum. Condensate interference.

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Images of Bose-Einstein condensates

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  1. Images of Bose-Einstein condensates Jacek Dziarmaga & Krzysztof Sacha PRA 67, 033608 (2003) cond-mat/0503328 Kraków, Poland

  2. Condensate interference Bogoliubov theory Diagonal t-dependent vacuum Measurements on the vacuum

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

  4. Condensate interference In 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. Diagonal dynamical vacuum We claim D & Sacha, PRA 67, 033608 (2003) cond-mat/0503328

  11. Proof (constructive)

  12. q - representation Real coordinates q

  13. q - representation Probability for q

  14. Density measurement

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

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

  17. Density measurement Truncated vacuum

  18. Conclusion

  19. Condensate in thermal state Condensate in ``excited thermal state’’

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