Dynamics of Macroscopic Wave Packet Passing through Double Slits: Role of Gravity and Nonlinearity

TL;DR

This paper investigates how gravity and nonlinearity influence the behavior of a macroscopic wave packet passing through double slits in Bose-Einstein condensates, revealing their effects on interference patterns and proposing experimental setups.

Contribution

It introduces a detailed analysis of the interplay between gravity and nonlinearity in wave packet dynamics using the nonlinear Schrödinger equation, highlighting their impact on interference fringes.

Findings

Peak-to-peak distance scales as g^(-1/2)

Number of interference peaks scales as u_0^(1/2)g^(1/4)

Proposes experimental design under controlled conditions

Abstract

Using the nonlinear Schroedinger equation (Gross-Pitaevskii equation), the dynamics of a macroscopic wave packet for Bose-Einstein condensates falling through double slits is analyzed. This problem is identified with a search for the fate of a soliton showing a head-on collision with a hard-walled obstacle of finite size. We explore the splitting of the wave packet and its reorganization to form an interference pattern. Particular attention is paid to the role of gravity (g) and repulsive nonlinearity (u_0) in the fringe pattern. The peak-to-peak distance in the fringe pattern and the number of interference peaks are found to be proportional to g^(-1/2) and u_0^(1/2)g^(1/4), respectively. We suggest a way of designing an experiment under controlled gravity and nonlinearity.