Counterintuitive transitions between crossing energy levels

Abstract

We calculate analytically the probabilities for intuitive and counterintuitive transitions in a three-state system, in which two parallel energies are crossed by a third, tilted energy. The state with the tilted energy is coupled to the other two states in a chainwise linkage pattern with constant couplings of finite duration. The probability for a counterintuitive transition is found to increase with the square of the coupling and decrease with the squares of the interaction duration, the energy splitting between the parallel energies, and the tilt (chirp) rate. Physical examples of this model can be found in coherent atomic excitation and optical shielding in cold atomic collisions.

References in corpus (8)

• Transition times in the Landau-Zener model
• Landau-Zener transition in a multilevel system. An exact result
• Time-dependent control of ultracold atoms and Bose-Einstein condensates in magnetic traps
• Counterintuitive transitions in the multistate Landau-Zener problem with linear level crossings
• Entanglement generation by adiabatic navigation in the space of symmetric multi-particle states
• Counterintuitive transitions in multistate curve crossing involving linear potentials
• Curve crossing in linear potential grids: the quasidegeneracy approximation
• Optical shielding of cold collisions in blue-detuned near-resonant optical lattices

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• The Quest for Solvable Multistate Landau-Zener Models
• Solvable 4-state Landau-Zener model of two interacting qubits with path interference
• Exact results for models of multichannel quantum nonadiabatic transitions
• Exact transition probabilities in a six-state Landau-Zener system with path interference
• Landau-Zener transition in a two-level system coupled to a single highly-excited oscillator
• Steering quantum transitions between three crossing energy levels
• Nonadiabatic transitions in exactly solvable quantum mechanical multichannel model: role of level curvature and counterintuitive behavior
• Coherent reaction between molecular and atomic Bose-Einstein condensates: integrable model
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• Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance
• Coherent manipulation of single electron spins with Landau-Zener sweeps
• The model of a level crossing with a Coulomb band: exact probabilities of nonadiabatic transitions
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• Competing Bosonic Reactions: Insight from Exactly Solvable Time-Dependent Models