Trojan quasiparticles

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.

Modeling spontaneous breaking of time-translation symmetry

“…The results pave the way for understanding and realization of the time crystal idea. We consider N atoms that form a Bose-Einstein condensate and bounce on an oscillating, horizontally oriented, atomic mirror in the presence of the gravitational field [23][24][25]. We assume that the atomic cloud is strongly confined in the transverse directions by means of a harmonic potential so that description of the system can be reduced to the one-dimensional Hamiltonian.…”

Adiabatic preparation of Floquet condensates

“…This is due to the fact that our driving frequency ω = Ω, times , is somewhat lower than the energy level spacing of the system (28) in the vicinity of its ground state; for other choices of ω the condensatecarrying Floquet ground state may not be connected to the unperturbed ground state n = 0 [17,18].…”

“…On the other hand, the overall phase of |Ψ(τ, t) is uniquely fixed by the requirement that this function be a solution to the initial-value problem posed by Eqs. (17) and (20). Therefore, following Berry [26], we have introduced a phase γ n (τ ) to ensure the equality of the total phase on both sides of Eq.…”

Quasiparticle tunneling in a periodically driven bosonic Josephson junction

“…The key point now is that the driving frequency be chosen such that cor = co/v, meaning that one oscillation cycle of the unperturbed system governed by Ho is as long as v cycles of the external drive, so that we have a v:l resonance. The case v = 1 applies to the usual Trojans [3,7,8]; here we demand instead that v ^ 2 be a small integer larger than unity. It is then natural to search for solutions to the time-dependent Schrodinger equation of the form where the sum again extends over states close to the resonant state n -r. Because of the resonance condition, the expo nential exhibits the first-order expansions of the energies E" around n = r. This implies that the remaining time dependence of the coefficients cn(t), given by the exact system / ha>\ ihcn(t) = \ En -Er -( n -r)-\cn(t)…”

“…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.…”