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

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.

revised version, 13 figures (1 figure added), 53 pages

References in corpus (23)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Matter-wave interferometry in a double well on an atom chip
• Squeezing and entanglement in a Bose-Einstein condensate
• The multi-configurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
• Fragmentation of Bose-Einstein Condensates
• Role of excited states in the splitting dynamics of interacting Bose-Einstein condensates when ramping-up a barrier
• Linear response theory for a pair of coupled one-dimensional condensates of interacting atoms
• Reduced density matrices and coherence of trapped interacting bosons
• General variational many-body theory with complete self-consistency for trapped bosonic systems
• Optimizing number squeezing when splitting a mesoscopic condensate
• Precision Measurements on a Tunable Mott Insulator of Ultracold Atoms
• Fragmented many-body ground states for scalar bosons in a single trap
• Spectral weight redistribution in strongly correlated bosons in optical lattices
• Best mean-field for condensates
• Death of soliton trains in attractive Bose-Einstein condensates
• Phase separations of bosonic mixtures in optical lattices from macroscopic to microscopic scales
• Time-dependent multi-orbital mean-field for fragmented Bose-Einstein condensates
• Interferences in the density of two Bose-Einstein condensates consisting of identical or different atoms
• Shapiro effect in atomchip-based bosonic Josephson junctions
• Formation and dynamics of many-boson fragmented states in attractive one-dimensional ultra-cold gases
• Fragmented Many-Body states of definite angular momentum and stability of attractive 3D Condensates
• Localization and Anomalous Transport in a 1-D Soft Boson Optical Lattice
• Collective modes of a strongly interacting Bose gas: probing the Mott transition

Cited by in corpus (11)

• A unified ab-initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures
• Many-Body Echo
• Excitation spectra of many-body systems by linear response: General theory and applications to trapped condensates
• Quantum dynamical response of ultracold few boson ensembles in finite optical lattices to multiple interaction quenches
• Many-body excitations and de-excitations in trapped ultracold bosonic clouds
• Bosonic quantum dynamics following a linear interaction quench in finite optical lattices of unit filling
• Effective two-mode description of a few ultra-cold bosons in a double-well potential
• Unified view on linear response of interacting identical and distinguishable particles from multiconfigurational time-dependent Hartree methods
• Robustness of fragmented condensate many-body states for continuous distribution amplitudes in Fock space
• Many-body excitation spectra of trapped bosons with general interaction by linear response
• Many-body effects in a composite bosonic Josephson junction