Fractional-Period Excitations in Continuum Periodic Systems

TL;DR

This paper explores how non-adiabatic switching of an optical lattice in a Bose-Einstein condensate leads to transient fractional-period states, analyzed through a resonant oscillator model, with implications for observing such states.

Contribution

It introduces a novel analytical framework for understanding fractional-period states as resonant phenomena in continuum periodic systems.

Findings

Fractional-period states occur during non-adiabatic lattice turn-on.

These states can be modeled as resonant states of a parametrically forced Duffing oscillator.

Transient fractional states are potentially observable in experiments.

Abstract

We investigate the generation of fractional-period states in continuum periodic systems. As an example, we consider a Bose-Einstein condensate confined in an optical-lattice potential. We show that when the potential is turned on non-adiabatically, the system explores a number of transient states whose periodicity is a fraction of that of the lattice. We illustrate the origin of fractional-period states analytically by treating them as resonant states of a parametrically forced Duffing oscillator and discuss their transient nature and potential observability.