Abstract
We argue that a time-periodically driven bosonic Josephson junction supports stable, quasiparticle-like collective response modes which are N-particle analogs of the nonspreading Trojan wave packets known from microwave-driven Rydberg atoms. Similar to their single-particle counterparts, these collective modes, dubbed ‘flotons’, are well described by a Floquet–Mathieu approximation, and possess a well-defined discrete set of excitations. In contrast to other, ‘chaotic’ modes of response, the nonheating Trojan modes conform to a mean-field description, and thus may be of particular interest for the more general question under which conditions the reduction of quantum N-particle dynamics to a strongly simplified mean-field evolution is feasible. Our reasoning is supported by phase-space portraits which reveal the degree of correspondence beween the N-particle dynamics und the mean-field picture in an intuitive manner.
Highlights
The Trojan asteroids move around the sun close to the stable Lagrangian points L4 and L5 of Jupiter, sharing its orbit [1]
Bialynicki-Birula, Kalinski, 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]; even Trojans with principal quantum numbers close to n = 600 have been generated in a controlled manner [7]
Summary
The Trojan asteroids move around the sun close to the stable Lagrangian points L4 and L5 of Jupiter, sharing its orbit [1]. Bialynicki-Birula, Kalinski, 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]. When the driving frequency is resonant, such that it matches the slowly varying level spacing at a particular unperturbed state, we predict stable, nonheating, collective modes of response exhibiting properties typical of Trojan single-particle wave packets. The following phase-space analysis [14], put forward in Sec. IV, shows that the ground state of this hierarchy is tied to a periodic mean-field orbit in precisely the same manner as a Trojan single-particle wave packet is tied to a periodic solution of the corresponding classical equations of motion.
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