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arXiv:2003.05655

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

Patrik Öhberg, Ewan M. Wright

Published Mar 12, 2020• 1 citation
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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.

DOI
10.48550/arxiv.2003.05655

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Physical Review A•Jul 15, 2024•2 citations
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 ELAB{\cal E}_{LAB}ELAB​ 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 ELAB{\cal E}_{LAB}ELAB​ but we illustrate below that our system can nonetheless display time crystal behavior with a ground state that is spatially localized and rotating.
In a recent Letter [Phys. Rev. Lett. 123, 250402PRLTAO0031-900710.1103/PhysRevLett.123.250402], Öhberg and Wright describe a Bose-Einstein condensate trapped on a ring in the presence of the density-dependent gauge potential. It is claimed that the ground state of the system corresponds to a rotating chiral bright soliton and consequently it forms a genuine time crystal which minimizes its energy by performing periodic motion. We show that the energy of the chiral soliton in the laboratory frame is not correctly calculated in the Letter. The correct energy becomes minimal if the soliton does not move.
We present numerical simulations for a chiral soliton model with N=2,3 bosons in a ring, this being a few-particle version of our previous mean-field model for a quantum time crystal. Following Syrwid, Kosior, and Sacha (SKS), the notion is that a precise position measurement of one particle can lead to spontaneous formation of a bright soliton that in a time crystal should rotate intact for at least a few revolutions around the ring. In their work SKS find spontaneous formation of a soliton due to the position measurement, but quantum fluctuations cause the soliton to subsequently decay before it has a chance to perform even one revolution of the ring. Based on this they conclude that time crystal dynamics are impossible. In contrast, for our few boson chiral soliton model, and allowing for imprecise (weak) measurements of the particle position, we show that time crystal behavior is possible allowing for several revolutions of the spontaneously formed soliton around the ring. We therefore argue that our chiral soliton model can realize a quantum time crystal when weak position measurements are allowed for.
We present numerical simulations for a chiral soliton model with N = 2 , 3 bosons in a ring, which is a few-particle version of our previous mean-field model for a quantum time crystal. Following Syrwid, Kosior, and Sacha (SKS), the notion is that a precise position measurement of one particle can lead to spontaneous formation of a bright soliton that in a time crystal should rotate intact for at least a few revolutions around the ring. In their work SKS found spontaneous formation of a soliton due to the position measurement, but quantum fluctuations cause the soliton to subsequently decay before it has a chance to perform even one revolution of the ring. Based on this, they concluded that time-crystal dynamics are impossible for Wilczek's model of a bright soliton in a ring. In contrast, for our few-boson chiral soliton model, allowing for imprecise (weak) measurements of the particle position, we show that time-crystal-like behavior is possible, allowing for several revolutions of the spontaneously formed soliton around the ring. Published by the American Physical Society 2024