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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2302.03918 |
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| _version_ | 1866909031841398784 |
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| author | Gu, Jie Zhang, X. -G. |
| author_facet | Gu, Jie Zhang, X. -G. |
| contents | Quantum adiabaticity is the evolution of a quantum system that remains close to an instantaneous eigenstate of a time-dependent Hamiltonian. Using Floquet formalism, we derive a rigorous sufficient condition for adiabaticity in closed, finite-dimensional periodically driven systems that is valid for arbitrarily many driving periods. The condition is stroboscopic and geometric, depending only on single-cycle information: the Fubini--Study length of the instantaneous eigenray and a quasienergy-separation measure extracted from the Floquet operator. We also formulate a state-targeted refinement that reduces conservativeness when only one adiabatic branch is relevant. Rather than synthesizing control pulses, the result provides a certification criterion for a given periodic protocol. We illustrate the criterion and contrast it with conventional instantaneous-gap conditions in three representative examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03918 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometric Floquet Condition for Quantum Adiabaticity Gu, Jie Zhang, X. -G. Quantum Physics Quantum adiabaticity is the evolution of a quantum system that remains close to an instantaneous eigenstate of a time-dependent Hamiltonian. Using Floquet formalism, we derive a rigorous sufficient condition for adiabaticity in closed, finite-dimensional periodically driven systems that is valid for arbitrarily many driving periods. The condition is stroboscopic and geometric, depending only on single-cycle information: the Fubini--Study length of the instantaneous eigenray and a quasienergy-separation measure extracted from the Floquet operator. We also formulate a state-targeted refinement that reduces conservativeness when only one adiabatic branch is relevant. Rather than synthesizing control pulses, the result provides a certification criterion for a given periodic protocol. We illustrate the criterion and contrast it with conventional instantaneous-gap conditions in three representative examples. |
| title | Geometric Floquet Condition for Quantum Adiabaticity |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2302.03918 |