Suppressing excitations in the nonlinear Landau-Zener model
arXiv:2506.11759 · doi:10.1209/0295-5075/adfd7a
Abstract
Many complex quantum systems can be described by effectively nonlinear dynamics. While such dynamics have many appealing characteristics, they also make the analysis significantly more involved. This is due to the fact that only a few analytical treatments exist, and that the language of quantum mechanics is built for linear operators. For instance, the very formulation of the quantum adiabatic theorem requires the underlying dynamics to be linear. In this work we show that in a generalized Landau-Zener model, nonlinear dynamics can be leveraged to suppress excitations and coherences of the corresponding linear scenario. To this end, we introduce a generalized "energy spectrum", which is defined by the expectation values of the energy under the stationary states. As a main result, we show that the nonlinear term in the evolution equation acts like an effective shortcut to adiabaticity for the linear Landau-Zener problem.
6 pages, 7 figures
References in corpus (15)
- Max- relative entropy of coherence: an operational coherence measure
- Macroscopic quantum information processing using spin coherent states
- Fast quantum state discrimination with nonlinear PTP channels
- Nonlinear feedforward enabling quantum computation
- Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity
- Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations
- Reservoir-engineering shortcuts to adiabaticity
- Enhancing precision thermometry with nonlinear qubits
- Deterministic entangling gates with nonlinear quantum photonic interferometers
- Nonlinear and non-CP gates for Bloch vector amplification
- Speeding up Quantum Annealing with Engineered Dephasing
- Proposal for a Lorenz qubit
- Wigner-Yanase skew information-based uncertainty relations for quantum channels
- Protocol for nonlinear state discrimination in rotating condensate
- Constant-Time Quantum Search with a Many-Body Quantum System