Time-of-Flight Signatures of Bosons in a Double Well

TL;DR

This paper analyzes the momentum distribution of two bosons in a double-well potential, demonstrating how time-of-flight measurements can reveal system states, with improved computational methods for low-energy excitations.

Contribution

It provides analytical and numerical methods for evaluating time-of-flight distributions in a two-boson system, including efficient finite element techniques for low-energy states.

Findings

Time-of-flight distributions effectively profile bosonic states.

Finite element method improves efficiency over finite difference methods.

Results applicable to both Tonks and noninteracting regimes.

Abstract

We present analytical and numerical treatments for evaluating the time-of-flight momentum distribution for the stationary states of a two-boson system trapped in a quartic double-well potential, paying particular attention to the Tonks and noninteracting regimes. We find that the time-of-flight distributions can serve as a valuable tool in profiling the states of this system, and provide the tof plots for low-energy excitations using a nonadaptive finite element method that is more efficient than traditional finite difference methods.