Images of BoseEinstein condensates Jacek Dziarmaga Krzysztof Sacha

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

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

Condensate interference In experiment In computer experiment annihilation of atoms

Condensate interference Phase ``collapse’’ by density measurement

Quantum Bogoliubov theory Hamiltonian Small fluctuations Expansion Fig. Jav

Bogoliubov transformation particles <-> quasiparticles Bogoliubov Hamiltonian Bogoliubov vacuum

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

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

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

Proof (constructive)

q - representation Real coordinates q

q - representation Probability for q

Density measurement

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

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

Density measurement Truncated vacuum

Conclusion

Condensate in thermal state Condensate in ``excited thermal state’’