Response to comment on "Quantum time crystals and interacting gauge theories in atomic Bose-Einstein condensates" by Syrwid, Kosior, and Sacha

TL;DR

This paper responds to critiques about the calculation of energy in a proposed quantum time crystal system, clarifying that despite earlier errors, the system can still exhibit time crystal behavior with a localized, rotating ground state.

Contribution

The authors correct their previous energy calculation and demonstrate that their atomic Bose-Einstein condensate system can support quantum time crystal behavior despite prior criticisms.

Findings

Corrected the calculation of ${ m E}_{LAB}$

Showed the system can have a localized, rotating ground state

Confirmed the possibility of quantum time crystal behavior

Abstract

In a recent comment [1] on our paper [2] Syrwid, Kosior, and Sacha (SKS) asserted that we did not correctly calculate the chiral soliton energy ${\cal E}_{LAB}$ in the lab frame, and further that the system we proposed is not capable of supporting a genuine quantum time crystal. We concede that we did not correctly calculate ${\cal E}_{LAB}$ but we illustrate below that our system can nonetheless display time crystal behavior with a ground state that is spatially localized and rotating.