Excitation spectra of manybody systems by linear response: General theory and applications to trapped condensates
Abstract
We derive a general linearresponse manybody theory capable of computing excitation spectra of trapped interacting bosonic systems, e.g., depleted and fragmented BoseEinstein condensates (BECs). To obtain the linearresponse equations we linearize the multiconfigurational timedependent Hartree for bosons (MCTDHB) method, which provides a selfconsistent description of manyboson systems in terms of orbitals and a state vector (configurations), and is in principle numerically exact. The derived linearresponse manybody theory, which we term LRMCTDHB, is applicable to systems with interaction potentials of general form. For the special case of a δ interaction potential we show explicitly that the response matrix has a very appealing bilinear form, composed of separate blocks of submatrices originating from contributions of the orbitals, the state vector (configurations), and offdiagonal mixing terms. We further give expressions for the response weights and density response. We introduce the notion of the type of excitations, useful in the study of the physical properties of the equations. From the numerical implementation of the LRMCTDHB equations and solution of the underlying eigenvalue problem, we obtain excitations beyond available theories of excitation spectra, such as the Bogoliubovde Gennes (BdG) equations. The derived theory is first applied to study BECs in a onedimensional harmonic potential. The LRMCTDHB method contains the BdG excitations and, also, predicts a plethora of additional manybody excitations which are out of the realm of standard linear response. In particular, our theory describes the exact energy of the higher harmonic of the first (dipole) excitation not contained in the BdG theory. We next study a BEC in a very shallow onedimensional doublewell potential. We find with LRMCTDHB lowlying excitations which are not accounted for by BdG, even though the BEC has only little fragmentation and, hence, the BdG theory is expected to be valid. The convergence of the LRMCTDHB theory is assessed by systematically comparing the excitation spectra computed at several different levels of theory.
 Publication:

Physical Review A
 Pub Date:
 August 2013
 DOI:
 10.1103/PhysRevA.88.023606
 arXiv:
 arXiv:1307.1667
 Bibcode:
 2013PhRvA..88b3606G
 Keywords:

 03.75.Kk;
 05.30.Jp;
 03.65.w;
 Dynamic properties of condensates;
 collective and hydrodynamic excitations superfluid flow;
 Boson systems;
 Quantum mechanics;
 Condensed Matter  Quantum Gases;
 Quantum Physics
 EPrint:
 44 pages, 7 figures, 1 table