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Abstract
The behaviour of the momentum transferred to a trappedBose-Einstein condensate by a two-photon Bragg pulse reflectsthe structure of the underlying Bogoliubov spectrum. Inelongated condensates, axial phonons with different numbers ofradial nodes give rise to a multibranch spectrum which can beresolved in Bragg spectroscopy, as shown by Steinhauer et al (2003 Phys. Rev. Lett. 90 060404). Here wepresent a detailed theoretical analysis of this process. We calculate the momentum transferred by numerically solving the time-dependent Gross-Pitaevskii (GP) equation. In the case of acylindrical condensate, we compare the results with thoseobtained by linearizing the GP equation andusing a quasiparticle projection method. This analysis showshow the axial-phonon branches affect the momentum transfer, inagreement with our previous interpretation of the observeddata. We also discuss the applicability of this type ofspectroscopy to typical available condensates, as well as the role of nonlinear effects.
Highlights
In a recent paper [1] we showed that interesting features emerge in the momentum transferred to an elongated BoseEinstein condensate by a two-photon Bragg pulse when the duration of the pulse is long enough
We present a more detailed theoretical analysis that supports our previous interpretation and gives further information about the role played by Bogoliubov excitations in Bragg spectroscopy
We show that the response of such a cylindrical condensate retains all the relevant properties needed to interpret the observed behavior of a finite elongated condensate
Summary
In a recent paper [1] we showed that interesting features emerge in the momentum transferred to an elongated BoseEinstein condensate by a two-photon Bragg pulse when the duration of the pulse is long enough. On the basis of numerical simulations with the Gross-Pitaevskii (GP) equation, we interpreted those features as due to the structure of the underlying Bogoliubov spectrum: the Bragg pulse can excite axial phonons with different number of radial nodes, each one having its dispersion law. Since the energy difference between these branches is of the order of the radial trapping frequency, they can be resolved only by Bragg pulses with duration comparable with the radial trapping period, as observed in [1]. We show that the response of such a cylindrical condensate retains all the relevant properties needed to interpret the observed behavior of a finite elongated condensate. The cylindrical geometry allows us to simplify the calculations and, more important, to make the connection between the momentum transferred and the dy-
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