Abstract
Studying a single atomic ion confined in a time-dependent periodic anharmonic potential, we find large amplitude trajectories stable for millions of oscillation periods in the presence of stochastic laser cooling. The competition between energy gain from the time-dependent drive and damping leads to the stabilization of such stochastic limit cycles. Instead of converging to the global minimum of the averaged potential, the steady-state phase-space distribution develops multiple peaks in the regions of phase space where the frequency of the motion is close to a multiple of the periodic drive. Such distinct nonequilibrium behaviour can be observed in realistic radio-frequency traps with laser-cooled ions, suggesting that Paul traps offer a well-controlled test-bed for studying transport and dynamics of microscopically driven systems.
Highlights
Studying a single atomic ion confined in a time-dependent periodic anharmonic potential, we find large amplitude trajectories stable for millions of oscillation periods in the presence of stochastic laser cooling
Even if the ion is cooled by the laser, the nonequilibrium nature of the dynamics implies in general that the peaks of its spatial probability distribution may not coincide with the minima of the potential
In this Rapid Communication, we show that the anharmonicity in a periodically driven Paul trap can capture an ion at a large amplitude motion, corresponding to a stable limit cycle with sizable basins of attraction in phase space, even in the presence of damping by laser cooling and the associated randomness
Summary
The distribution may develop new maxima, and complex stochastic limit cycles and hysteretic behavior may emerge [18,19,20] In this Rapid Communication, we show that the anharmonicity in a periodically driven Paul trap can capture an ion at a large amplitude motion, corresponding to a stable limit cycle with sizable basins of attraction in phase space, even in the presence of damping by laser cooling and the associated randomness. We consider dynamics in an effectively onedimensional time-periodic potential in the presence of weak damping and first examine the stability of the limit cycles based on an analytic expansion We use this expansion to account for the stochastic process of photon scattering from a cooling laser, and further numerically demonstrate that this mechanism remains robust for a realistic trap potential, when the remaining degrees of freedom corresponding to 3D confinement are taken into account.
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