Images of Bose-Einstein condensates

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Presentation transcript:

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 Javanainen & Yoo, PRL 76, 161 (1996) 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

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

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 2ms Total density after 2ms In focus Mode 1

Density measurement Truncated vacuum

Conclusion

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