Time-dependent quantum many-body theory of identical bosons in a double well: Early-time ballistic interferences of fragmented and number entangled states
Abstract
A time-dependent multiconfigurational self-consistent field theory is presented to describe the many-body dynamics of a gas of identical bosonic atoms confined to an external trapping potential at zero temperature from first principles. A set of generalized evolution equations are developed, through the time-dependent variational principle, which account for the complete and self-consistent coupling between the expansion coefficients of each configuration and the underlying one-body wave functions within a restricted two state Fock space basis that includes the full effects of the condensate’s mean field as well as atomic correlation. The resulting dynamical equations are a classical Hamiltonian system and, by construction, form a well-defined initial value problem. They are implemented in an efficient numerical algorithm. An example is presented, highlighting the generality of the theory, in which the ballistic expansion of a fragmented condensate ground state is compared to that of a macroscopic quantum superposition state, taken here to be a highly entangled number state, upon releasing the external trapping potential. Strikingly different many-body matter-wave dynamics emerge in each case, accentuating the role of both atomic correlation and mean-field effects in the two condensate states.
- Publication:
-
Physical Review A
- Pub Date:
- October 2007
- DOI:
- 10.1103/PhysRevA.76.043612
- arXiv:
- arXiv:cond-mat/0702067
- Bibcode:
- 2007PhRvA..76d3612M
- Keywords:
-
- 03.75.Kk;
- 05.30.Jp;
- 03.75.Gg;
- Dynamic properties of condensates;
- collective and hydrodynamic excitations superfluid flow;
- Boson systems;
- Entanglement and decoherence in Bose-Einstein condensates;
- Condensed Matter - Other
- E-Print:
- 16 pages, 5 figures