Creating and Transporting Trojan Wave Packets

Abstract

Nondispersive localized Trojan wave packets with n i $ 305 moving in near-circular Bohr-like orbits are created and transported to localized near-circular Trojan states of higher n, n f $ 600, by driving with a linearly polarized sinusoidal electric field whose period is slowly increased. The protocol is remarkably efficient with over 80% of the initial atoms being transferred to the higher n states, a result confirmed by classical trajectory Monte Carlo simulations.

Trojan quasiparticles

“…In a seminal paper, Bialynicki-Birula, Kaliński and Eberly have pointed out that this classical, stable, periodic asteroid motion has a quantum analog in microwave-driven Rydberg atoms which emerges when the classical Kepler frequency of the orbiting electron equals the microwave frequency [3]; the nonspreading wave functions describing the entailing stable, though nonstationary states were aptly termed Trojan wave packets [4,5]. In a pioneering experiment, such nondispersive Trojan wave packets could be observed with Li Rydberg atoms for more than 15 000 cycles [6]; meanwhile even Trojans with principal quantum numbers close to n = 600 have been generated in a controlled manner [7]. Theoretically, Trojan wave packets have been identified as Floquet states with ground state-like properties which arise upon quantization of a resonance zone in classical phase space [8][9][10].…”

Bohr's model: Extreme atoms

“…Last year, they added radio waves that enabled that motion to be maintained indefinitely 8 . "It only took a century, but we recreated Bohr's atom," says Dunning proudly.…”

Quasiparticle tunneling in a periodically driven bosonic Josephson junction

“…This stable celestial motion has a quantum-mechanical counterpart, discovered in 1994 by Bialynicki-Birula, Kalihski, and Eberly: If one exposes Rydberg electrons to strong microwave radiation, such that the classical Kepler frequency of the orbiting electron equals the frequency of the external driving electric microwave field, one finds stable, though nonstationary, quantum states which are described by nonspreading wave packets centered around a classical periodic orbit [2,3]. Such Trojan states were first realized with lithium Rydberg atoms in a linearly polarized microwave field [4] and still are the subject of ongoing research in atomic physics [5], More generally, "Trojan" single-particle wave packets belong to Floquet states which are semiclassically attached to a nonlinear resonance island of the corresponding classical phase space, thus explaining their nondispersive nature [6,7], It has been pointed out recently that Trojan states can also occur in periodically driven many-body systems, where they correspond to stable collective excitations, or quasiparticles, moving in phase with the driving force [8]. Here we show that there exists a genuinely quantum-mechanical beating effect between similar many-body Trojan states which perform subharmonic motion with respect to the drive; this beating can be understood as quasiparticle tunneling.…”