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Images of a Bose–Einstein condensate: diagonal dynamical Bogoliubov vacuum

Jacek Dziarmaga and Krzysztof Sacha

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Evolution of a Bose–Einstein condensate subject to a time-dependent external perturbation can be described by a time-dependent number-conserving Bogoliubov theory: a condensate initially in its ground state Bogoliubov vacuum evolves into a time-dependent excited state which can be formally written as a time-dependent Bogoliubov vacuum annihilated by time-dependent quasiparticle annihilation operators. We prove that any Bogoliubov vacuum can be brought to a diagonal form in a time-dependent orthonormal basis. This diagonal form is tailored for simulations of quantum measurements on an excited condensate. As an example we work out phase imprinting of a dark soliton followed by a density measurement.


PACS

37.10.De Atom cooling methods

Subjects

Atomic and molecular physics

Dates

Issue 1 (14 January 2006)

Received 9 August 2005, in final form 9 September 2005

Published 5 December 2005



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