Atom optics quantum pendulum

Abstract

We explain the dynamics of cold atoms, initially trapped and cooled in a magneto-optic trap, in a monochromatic stationary standing electromagnetic wave field. In the large detuning limit the system is modeled as a nonlinear quantum pendulum. We show that wave packet evolution of the quantum particle probes parametric regimes in the quantum pendulum which support classical period, quantum mechanical revival and super revival phenomena. Interestingly, complete reconstruction in particular parametric regime at quantum revival times is independent of potential height.

Расщепление Энергий При Динамическом Туннелировании

“…Квантовый маятник является одной из классических моделей квантовой механи-ки [24], [41], [42], а стационарное уравнение Шредингера (1) эквивалентно уравне-нию Матье. В настоящем разделе показано, как из общей формулы для расщепле-ния (см.…”

Delicate and robust dynamical recurrences of matter waves in driven optical crystals

“…As recurrence time scales of a driven optical crystal are expressed in terms of an undriven system, we present classical period, quantum-revival, and super-revival time scales of a matter wave in an undriven optical crystal [38,39].…”

“…In the shallow lattice potential limit, i.e., q o 1, the classical frequency is ω = 2n{1 − (n 2 −1) 3 . The classical period of the condensate is inversely proportional to the average classical frequency ω and is calculated [38] as…”

Approximate solutions to Mathieu's equation

“…has appeared in theoretical physics in many different contexts. Mathieu originally formulated the equation to describe the vibration modes of an elliptical membrane [1], but the equation has since been applied to the theory of quadrupole ion traps [2][3][4], ultracold atoms [5] and quantum rotor models [6,7]. This equation has also found attention as a simplified model of a particle moving in a periodic potential [8].…”