Effects of a rotating periodic lattice on coherent quantum states in a ring topology: The case of positive nonlinearity
arXiv:2311.15567 · doi:10.1103/PhysRevA.104.053320
Abstract
We study the landscape of solutions of the coherent quantum states in a ring shaped lattice potential in the context of ultracold atoms with an effective positive nonlinearity induced by interatomic interactions. The exact analytical solutions in the absence of lattice are used as a starting point and the transformation of those solutions is mapped as the lattice is introduced and strengthened. This approach allows a simple classification of all the solutions into states with periods commensurate/incommensruate with the lattice period and those with/without nodes. Their origins are traced to the primary dispersion curve and the swallowtail branches of the lattice-free spectrum. The commensurate states tend to remain delocalized with increasing lattice depth, whereas the incommensurate ones may be localized. The symmetry and stability properties of the solutions are examined and correlated with branch energies. The crucial importance of rotation is highlighted by its utility in continuously transforming solutions and accessing in a finite ring with a few sites the full spectrum of nonlinear Bloch waves on an infinite lattice.
14 pages, 12 figures
References in corpus (12)
- Many-Body Physics with Ultracold Gases
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Optical ferris wheel for ultracold atoms
- Coherent superposition of current flows in an Atomtronic Quantum Interference Device
- Topological Winding and Unwinding in Metastable Bose-Einstein Condensates
- Exact results for persistent currents of two bosons in a ring lattice
- Bose-Hubbard model in a ring-shaped optical lattice with high filling factors
- Realizing the Harper model with Ultracold Atoms in a Ring Lattice
- Superfluidity in Bose-Hubbard circuits
- Resonant persistent currents for ultracold bosons on a lattice ring
- Blocked populations in ring-shaped optical lattices
- Rotation Sensitive Quench and Revival of Coherent Oscillations in a Ring Lattice