Counterdiabatic driving for random-gap Landau-Zener transitions
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| Format: | Preprint |
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2026
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| _version_ | 1866908769005338624 |
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| author | Theologou, Georgios Andersen, Mikkel F. Wimberger, Sandro |
| author_facet | Theologou, Georgios Andersen, Mikkel F. Wimberger, Sandro |
| contents | The Landau--Zener (LZ) model describes a two-level quantum system that undergoes an avoided crossing. In the adiabatic limit, the transition probability vanishes. An auxiliary control field $H_\text{CD}$ can be reverse-engineered so that the full Hamiltonian $H_0 + H_\text{CD}$ reproduces adiabaticity for all parameter values. Our aim is to construct a single control field $H_1$ that drives an ensemble of LZ-type Hamiltonians with a distribution of energy gaps. $H_1$ works best statistically, minimizing the average transition probability. We restrict our attention to a special class of $H_1$ controls, motivated by $H_\text{CD}$. We found a systematic trade-off between instantaneous adiabaticity and the final transition probability. Certain limiting cases with a linear sweep can be treated analytically; one of them being the LZ system with Dirac $δ(t)$ function. Comprehensive and systematic numerical simulations support and extend the analytic results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_10659 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counterdiabatic driving for random-gap Landau-Zener transitions Theologou, Georgios Andersen, Mikkel F. Wimberger, Sandro Quantum Physics Atomic Physics The Landau--Zener (LZ) model describes a two-level quantum system that undergoes an avoided crossing. In the adiabatic limit, the transition probability vanishes. An auxiliary control field $H_\text{CD}$ can be reverse-engineered so that the full Hamiltonian $H_0 + H_\text{CD}$ reproduces adiabaticity for all parameter values. Our aim is to construct a single control field $H_1$ that drives an ensemble of LZ-type Hamiltonians with a distribution of energy gaps. $H_1$ works best statistically, minimizing the average transition probability. We restrict our attention to a special class of $H_1$ controls, motivated by $H_\text{CD}$. We found a systematic trade-off between instantaneous adiabaticity and the final transition probability. Certain limiting cases with a linear sweep can be treated analytically; one of them being the LZ system with Dirac $δ(t)$ function. Comprehensive and systematic numerical simulations support and extend the analytic results. |
| title | Counterdiabatic driving for random-gap Landau-Zener transitions |
| topic | Quantum Physics Atomic Physics |
| url | https://arxiv.org/abs/2601.10659 |