Excitation spectra of fragmented condensates by linear response: General theory and application to a condensate in a double-well potential

TL;DR

This paper develops a linear response theory for fragmented Bose-Einstein condensates, extending the Bogoliubov approach, and applies it to analyze excitation spectra in double-well potentials, revealing significant differences from condensed states.

Contribution

It introduces LR-BMF, a linear response framework for fragmented condensates based on number-conserving mean field theory, and applies it to double-well systems to explore excitation spectra.

Findings

Excitation spectra differ significantly between condensed and fragmented states at barrier energies.

Fragmented systems exhibit unique 'swapped' excitations involving atom transfer between wells.

Response in asymmetric wells is localized with distinct frequencies for each fragment.

Abstract

Linear response of simple (i.e., condensed) Bose-Einstein condensates is known to lead to the Bogoliubov- de Gennes equations. Here, we derive linear response for fragmented Bose-Einstein condensates, i.e., for the case where the many-body wave function is not a product of one, but of several single-particle states (orbitals). Our approach is based on the number-conserving variational time-dependent mean field theory [O. E. Alon, A. I. Streltsov, and L. S. Cederbaum, Phys. Lett. A 362, 453 (2007)], which describes the time evolution of best-mean field states. Correspondingly, we call our linear response theory for fragmented states LR-BMF. In the derivation it follows naturally that excitations are orthogonal to the ground-state orbitals. As applications excitation spectra of Bose-Einstein condensates in double-well potentials are calculated. Both symmetric and asymmetric double-wells are studied for several interaction strengths and barrier heights. The cases of condensed and two-fold fragmented ground states are compared. Interestingly, even in such situations where the response frequencies of the two cases are computed to be close to each other, which is the situation for the excitations well below the barrier, striking differences in the density response in momentum space are found. For excitations with an energy of the order of the barrier height, both the energies and the density response of condensed and fragmented systems are very different. In fragmented systems there is a class of "swapped" excitations where an atom is transfered to the neighboring well. The mechanism of its origin is discussed. In asymmetric wells, the response of a fragmented system is purely local (i.e., finite in either one or the other well) with different frequencies for the left and right fragments.