The Quantum Dynamics of Two-component Bose-Einstein Condensate: an Symmetry Approach
arXiv:2109.03136 · doi:10.1088/1361-648X/ac8f0c
Abstract
The compact groups such as and groups have been heavily studied and applied in the study of quantum many body systems. However, the non-compact groups such as the real symplectic groups are less touched. In this paper, we will reveal that the quantum dynamics of two-component Bose-Einstein condensate can be described by a \emph{non-compact} real symplectic group . With this group, we can give a explicit form for the wavefunction in any time of the evolution, meanwhile, map this whole time evolution to a trajectory in a six-dimensional manifold. By introducing a polar coordinate, we can visualize this six-dimensional manifold in 2d unit disk and reveal the relation between the behavior of the trajectory in this manifold and the eigen-energies of the Hamiltonian. Furthermore, the time evolution of expectation value of a physical observable such as number operator is proven closely related to the behavior of the trajectory in this manifold.
arXiv comment9 pages
References in corpus (23)
- Feshbach Resonances in Ultracold Gases
- Gaussian Quantum Information
- Spinor Bose Condensates in Optical Traps
- Bose-Einstein condensation with internal degrees of freedom in alkali atom gases
- The dynamics of component separation in a binary mixture of Bose-Einstein condensates
- Spinor Bose-Einstein condensates
- Dynamics of collapsing and exploding Bose-Einstein condensates
- Spin-Orbit Coupled Spinor Bose-Einstein Condensates
- Measurements of Relative Phase in Binary Mixtures of Bose-Einstein Condensates
- Double species condensate with tunable interspecies interactions
- A two atomic species superfluid
- Quantum Simulation of Coherent Hawking-Unruh Radiation
- Collective emission of matter-wave jets from driven Bose-Einstein condensates
- Density waves and jet emission asymmetry in Bose Fireworks
- Quantum dynamics of bosons in a two-ring ladder: dynamical algebra, vortex-like excitations and currents
- Two-species boson mixture on a ring: A group theoretic approach to the quantum dynamics of low-energy excitations
- Many-Body Echo
- Four-mode squeezed states: two-field quantum systems and the symplectic group
- Complex correlations in high harmonic generation of matter-wave jets revealed by pattern recognition
- Many-body Dynamics with Time-dependent Interaction
- Geometrizing quantum dynamics of a Bose-Einstein condensate
- Control of anomalous diffusion of a Bose polaron
- Squeezing for Bloch Four-Hyperboloid via The Non-Compact Hopf Map