Detecting level crossings without looking at the spectrum

Abstract

In many physical systems it is important to be aware of the crossings and avoided crossings which occur when eigenvalues of a physical observable are varied using an external parameter. We have discovered a powerful algebraic method of finding such crossings via a mapping to the problem of locating the roots of a polynomial in that parameter. We demonstrate our method on atoms and molecules in a magnetic field, where it has implications in the search for Feshbach resonances. In the atomic case our method allows us to point out a new class of invariants of the Breit-Rabi Hamiltonian of magnetic resonance. In the case of molecules, it enables us to find curve crossings with practically no knowledge of the corresponding Born-Oppenheimer potentials.

4 pages, new title, no figures, accepted by Phys. Rev. Lett

References in corpus (6)

• Observation of resonance condensation of fermionic atom pairs
• Observation of Bose-Einstein Condensation of Molecules
• Stable 85Rb Bose-Einstein Condensates with Widely Tunable Interactions
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Atom--Molecule Coherence in a Bose-Einstein Condensate
• Quantum phases of dipolar spinor condensates

Cited by in corpus (7)

• The complex life of hydrodynamic modes
• The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models
• Entanglement, Berry Phases, and Level Crossings for the Atomic Breit-Rabi Hamiltonian
• Generation and protection of Maximally Entangled State between many modes in an optical network with dissipation
• Exact numerical methods for a many-body Wannier Stark system
• From Spectra to Localized Networks: A Reverse Engineering Approach
• Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix