Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Simulation of time-crystal-like behavior for a few-boson chiral soliton model in a ring

Patrik Öhberg, Ewan M. Wright

Published Jul 15, 2024• 2 citations
Publisher

Abstract

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

DOI
10.1103/physreva.110.013315

Related papers

Simulation of time crystal behavior for a few boson chiral soliton model in a ring

Patrik Öhberg, Ewan M. Wright

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.

arXiv:2401.04843•Jan 9, 2024•0 citations

Can a bright soliton model reveal a genuine time crystal for a finite number of bosons?

Andrzej Syrwid, Arkadiusz Kosior, Krzysztof Sacha

Abstract We analyze time crystal effects in a finite system of bosons which form a bright soliton clump on the Aharonov-Bohm ring. In the large particle number limit, N → ∞ , this setup corresponds to the Wilczek model, where it is known that the time crystal behavior cannot be observed in the ground state of the system because a spontaneously formed soliton does not move. Here, we show that while the spontaneous formation of a moving soliton in the ground state can occur for , the soliton decays before it makes a single revolution along the ring and the time crystal dynamics is impossible.

arXiv:2108.11905•Europhysics Letters (EPL)•Jun 1, 2021•5 citations

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

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.

arXiv:2003.05655•Mar 12, 2020•1 citation

Comment on "Lack of a genuine time crystal in a chiral soliton model" by Syrwid, Kosior, and Sacha

Patrik Öhberg, Ewan M. Wright

We present a comment on A. Syrwid, A. Kosior, and K. Sacha, "Lack of a genuine time crystal in a chiral soliton model," arXiv:2005.12313.

arXiv:2008.10940•Aug 25, 2020•2 citations

Comment on “Quantum Time Crystals and Interacting Gauge Theories in Atomic Bose-Einstein Condensates”

Andrzej Syrwid, Arkadiusz Kosior, Krzysztof Sacha

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.

arXiv:2002.11186•Physical Review Letters•Apr 29, 2020•22 citations

Quantum Time Crystals and Interacting Gauge Theories in Atomic Bose-Einstein Condensates

Patrik Öhberg, Ewan M. Wright

We study the dynamics of a Bose-Einstein condensate trapped circumferentially on a ring, and which is governed by an interacting gauge theory. We show that the associated density-dependent gauge potential and concomitant current nonlinearity permits a ground state in the form of a rotating chiral bright soliton. This chiral soliton is constrained to move in one direction by virtue of the current nonlinearity, and represents a time crystal in the same vein as Wilczek's original proposal.

arXiv:1812.04672•Physical Review Letters•Dec 20, 2019•41 citations
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
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.
Abstract We analyze time crystal effects in a finite system of bosons which form a bright soliton clump on the Aharonov-Bohm ring. In the large particle number limit, N → ∞ , this setup corresponds to the Wilczek model, where it is known that the time crystal behavior cannot be observed in the ground state of the system because a spontaneously formed soliton does not move. Here, we show that while the spontaneous formation of a moving soliton in the ground state can occur for , the soliton decays before it makes a single revolution along the ring and the time crystal dynamics is impossible.
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.