Many body generalization of the Landau Zener problem

Abstract

We formulate and approximately solve a specific many-body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving rates. The structure of the theory suggests that this finding reflects a more general phenomenon in the physics of adiabatically driven many particle systems. Our solution can be used to understand, for example, the behavior of two-level systems coupled to an electromagnetic field, as realized in cavity QED experiments.

4 pages

References in corpus (7)

• Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
• Observation of resonance condensation of fermionic atom pairs
• Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance
• Many-body effects on adiabatic passage through Feshbach resonances
• Quantum effects on curve crossing in a Bose-Einstein condensate
• Cooling many particles at once
• Production efficiency of Feshbach molecules in fermion systems

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