One-Dimensional Matter Waves as a Multi-State Bit

Jacopo Giacomelli

doi:10.3390/appliedmath2010008

Abstract

We design a simple technique to control the position of a localized matter wave. Our system is composed of two counter-phased periodic potentials and a third optical lattice, which can be either periodic or disordered. The only control needed on the system is a three-state switch that allows the sudden selection of the desired potential. The method is proposed as a possible new alternative to achieving the realization of a multi-state bit. We show that this framework is robust, and that the multi-state bit behavior can be observed under weak assumptions. Given the current degree of development of matter wave control in optical lattices, we believe that the proposed device would be easily reproducible in a laboratory, allowing for testing and industrial applications.

Highlights

Nowadays, Bose–Einstein condensates (BEC) [1–4] are routinely used in combination with optical potentials to have direct access to the fundamental quantum behaviors on a macroscopic scale
We show that this framework is robust, and that the multi-state bit behavior can be observed under weak assumptions
We have developed a technique to change and preserve the position of a localized matter wave

Summary

Introduction

Bose–Einstein condensates (BEC) [1–4] are routinely used in combination with optical potentials to have direct access to the fundamental quantum behaviors on a macroscopic scale. The dimensionality of the system can be reduced by flattening the BEC (effective 2D system [14]) or elongating it (effective 1D system [11–13]). In the 1D case, interesting boundary conditions can be realized: the elongated BEC can be trapped in a box [15], in a torus [24], or in a harmonic trap [9,10], among other possibilities [7,8]. Without any presumption of being exhaustive, we recall the possibility of generating both periodic [11–14] and disordered [16–23,25–27] lattices. The latter family of potentials has been employed to observe Anderson localization phenomena [16,17,21,22,27]. One-dimensional speckle potentials, in particular, have been the object of an intensive study in recent years, both from the theoretical and experimental sides. In addition to the wide selection of feasible optical potentials, we recall the recent possibility of painting an arbitrary shape time-averaged optical dipole potential [7]

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