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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.01528 |
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| _version_ | 1866914515754418176 |
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| author | Zhan, Yi-Ling Liu, Chun-Fu Bu, J. -T. Cui, K. -F Su, S. -L. Yan, L. -L. Chen, Gang |
| author_facet | Zhan, Yi-Ling Liu, Chun-Fu Bu, J. -T. Cui, K. -F Su, S. -L. Yan, L. -L. Chen, Gang |
| contents | Time crystals constitute a novel phase of matter defined by the spontaneous breaking of timetranslation symmetry. Here we present a scheme to realize a continuous-time crystal of the vibrational phonon in the normal mode of two coupled ultra-cold ions. By utilizing two addressable standing-wave lasers and adiabatic elimination method, we generate a controllable nonlinear phonon mode with the well-designed efficient linear gain and nonlinear damping. By controlling these parameters to satisfy the phase transition conditions of Hopf bifurcation and limit cycle phase, it behaves as a stable dissipative dynamics over timescales significantly longer than the oscillation period, indicating the emergence of discrete time-translation symmetry breaking in the phonon mode, i.e., a phonon time crystal. We further numerically simulate this phonon time crystal by using accessible experimental parameters and also demonstrate a robustness to the initial thermal state and thermalization of phonon mode, spin dephasing, and the control errors of Rabi frequencies. These results provide a practical scheme for observing a time crystal in a nonlinear phonon mode and will advance the research of time crystals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time Crystal in the Nonlinear Phonon Mode of the Trapped Ions Zhan, Yi-Ling Liu, Chun-Fu Bu, J. -T. Cui, K. -F Su, S. -L. Yan, L. -L. Chen, Gang Quantum Physics Time crystals constitute a novel phase of matter defined by the spontaneous breaking of timetranslation symmetry. Here we present a scheme to realize a continuous-time crystal of the vibrational phonon in the normal mode of two coupled ultra-cold ions. By utilizing two addressable standing-wave lasers and adiabatic elimination method, we generate a controllable nonlinear phonon mode with the well-designed efficient linear gain and nonlinear damping. By controlling these parameters to satisfy the phase transition conditions of Hopf bifurcation and limit cycle phase, it behaves as a stable dissipative dynamics over timescales significantly longer than the oscillation period, indicating the emergence of discrete time-translation symmetry breaking in the phonon mode, i.e., a phonon time crystal. We further numerically simulate this phonon time crystal by using accessible experimental parameters and also demonstrate a robustness to the initial thermal state and thermalization of phonon mode, spin dephasing, and the control errors of Rabi frequencies. These results provide a practical scheme for observing a time crystal in a nonlinear phonon mode and will advance the research of time crystals. |
| title | Time Crystal in the Nonlinear Phonon Mode of the Trapped Ions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.01528 |