Chaos and flights in the atom-photon interaction in cavity QED

Abstract

We study dynamics of the atom-photon interaction in cavity quantum electrodynamics (QED), considering a cold two-level atom in a single-mode high-finesse standing-wave cavity as a nonlinearHamiltonian system with three coupled degrees of freedom: translational, internal atomic, and the field. The system proves to have different types of motion including Lévy flights and chaotic walkings of an atom in a cavity. It is shown that the translational motion, related to the atom recoils, is governed by an equation of a parametric nonlinear pendulum with a frequency modulated by the Rabi oscillations. This type of dynamics is chaotic with some width of the stochastic layer that is estimated analytically. The width is fairly small for realistic values of the control parameters, the normalized detuning δ and atomic recoil frequency α. It is demonstrated how the atom-photon dynamics with a given value of α depends on the values of δ and initial conditions. Two types of Lévy flights, one corresponding to the ballistic motion of the atom and another one corresponding to small oscillations in a potential well, are found. These flights influence statistical properties of the atom-photon interaction such as distribution of Poincaré recurrences and moments of the atom position x. The simulation shows different regimes of motion, from slightly abnormal diffusion with < x 2 >∼ τ 1.13 at δ = 1.2 to a superdiffusion with < x 2 >∼ τ 2.2 at δ = 1.92 that corresponds to a superballistic motion of the atom with an acceleration. The obtained results can be used to find new ways to manipulate atoms, to cool and trap them by adjusting the detuning δ.

Theory of chaotic atomic transport in an optical lattice

“…In the limit of the large argument 2/(ω r p node ), both the functions have a harmonic asymptotics [27], and the expression (18) reduces to the form…”

Finite-temperature nonlinear dynamics in cavity QED: A thermofield dynamics approach

“…Recently cavity QED is considered in dealing with nonlinear dynamics [7,9]. Mapping quantum equations of motion onto classical ones, for the Jaynes-Cummings Hamiltonian, which includes recoil motion of the atom, Prants et al, explored phase-space dynamics of the atom interacting with a single cavity mode by analyzing Poincare surface sections and calculating Lyapunov exponents.…”

“…Mapping quantum equations of motion onto classical ones, for the Jaynes-Cummings Hamiltonian, which includes recoil motion of the atom, Prants et al, explored phase-space dynamics of the atom interacting with a single cavity mode by analyzing Poincare surface sections and calculating Lyapunov exponents. In such a case classical and not quantum chaos described by classical equations of motion corresponding to Jaynes-Cummings Hamiltonian are studied that are classical counterpart of the atom + photon + cavity system that are described by Prants et al [7][8][9][10].…”

Dynamics of Bec Mixtures Loaded into the Optical Lattice in the Presence of Linear Inter-Component Coupling

“…spatial) and internal (corresponding to level transitions) degrees of freedom can essentially complexify atom dynamics even in the absence of interactions between atoms. Earlier studies in the semiclassical regime for the spatial atomic dynamics revealed many intriguing phenomena like chaotic Rabi oscillations [11], chaotic atomic transport and dynamical fractals [12][13][14][15], occurrence of Lévy flights and anomalous diffusion [16][17][18], synchronization between spatial and internal dynamics [19]. A detailed theory of chaotic atomic transport of atoms in a laser standing wave has been developed in Refs.…”