Abstract
The coherent dynamics of a cold two-level atom in a three-dimensional optical lattice is treated in the semiclassical approximation, taking into account the coupling between the atom internal and external degrees of freedom. The nine-dimensional dynamical system with Hamilton–Bloch equations and two integrals of motion is derived in order to describe all possible modes of atomic motion inside the lattice. Atom is shown to move regularly or chaotically in the lattice labyrinth in dependence on the values of its initial momentum and on the values of the control parameters, the detuning between the atomic transition and laser frequencies and the atomic recoil frequency. Hamiltonian chaos arises under appropriate conditions and manifests itself as chaotic Rabi oscillations of the internal atomic variables and as a chaotic wandering in the real space. The chaotic behavior is quantified by positive values of the maximum Lyapunov exponent and is found to occur only near the optical resonance. The deterministic Hamiltionian chaos arises as a result of the random-like “jumps” in the magnitude of the synchronized component of the atomic electric dipole moment, when the atom approaches the nodes of the three-dimensional standing wave. Due to the coupling between internal and external degrees of freedom, these “jumps” cause pseudo-random behavior of the atomic momentum and, as a consequence, a chaotic wandering in the absolutely rigid optical lattice without any external modulation.
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Prants, S.V. Motion of Cold Atoms in a Labyrinth Created by a Three-Dimensional Optical Lattice. J Russ Laser Res 43, 18–27 (2022). https://doi.org/10.1007/s10946-022-10019-4
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DOI: https://doi.org/10.1007/s10946-022-10019-4