Can quantum fractal fluctuations be observed in an atom-optics kicked rotor experiment?

Abstract

Abstract. We investigate the parametric fluctuations in the quantum survival probability of an open version of the δ-kicked rotor model in the deep quantum regime. Spectral arguments [Guarneri I and Terraneo M 2001 Phys. Rev. E 65 015203(R)] predict the existence of parametric fractal fluctuations owing to the strong dynamical localisation of the eigenstates of the kicked rotor. We discuss the possibility of observing such dynamically-induced fractality in the quantum survival probability as a function of the kicking period for the atom-optics realisation of the kicked rotor. The influence of the atoms' initial momentum distribution is studied as well as the dependence of the expected fractal dimension on finite-size effects of the experiment, such as finite detection windows and short measurement times. Our results show that clear signatures of fractality could be observed in experiments with cold atoms subjected to periodically flashed optical lattices, which offer an excellent control on interaction times and the initial atomic ensemble.

Transient localization in the kicked Rydberg atom

“…9). A similar build-up of fluctuations in the survival probability with time is observed for the kicked rotor [35]. In the very-long time-limit beyond τ D , where the dynamics of the kicked system is governed by the decay of the ground state, no further fluctuations are produced but δ ν 0 (K) saturates.…”

“…Strong fluctuations in the survival probability have also been found e.g. in the harmonically driven Rydberg atom [11] and in the kicked rotor when subjected to a varying Aharonov-Bohm flux [34] or a variation of the kicking frequency [35].…”

“…It is now tempting to inquire whether the complexity of the fluctuations in the P qm sur can be described by an approximate fractal dimension. For example, the fluctuations in the kicked rotor in the chaotic regime have been shown to have a fractal structure [34,35]. Fractal conductance fluctuations have been predicted [36] and experimentally found, e.g.…”

Multifractal fluctuations in the survival probability of an open quantum system

“…As a consequence, the restriction of β to the unit interval does make no difference to the, in principle, unboundedness of τ (in fact, to avoid different dynamical properties of the system, τ was chosen in a restricted window too, c.f. [8]).…”

“…In this paper, we directly study the fluctuations properties of a global conductance like quantity in a regime of strong localization (Anderson or dynamical localization in our context of quantum dynamical systems). The studied quantity is the survival probability of an open, classically chaotic system, which in the deep quantum realm was found to obey a monofractal scaling if certain conditions on the quantum eigenvalue spectrum are fulfilled [7,8]. In particular, the distribution of decay rates of the weakly opened system needs to obey a power-law with an exponent γ ∼ −1, which translates into an ana Electronic address: a.facchini@unisi.it alytic prediction for the corresponding box counting dimension (of the survival probability as a function of a proper scan parameter): D BC ≃ 2 − |γ|/2.…”