Powered by Indico
v3.2.3
By the adiabatic theorem, a system prepared in an instantaneous eigenstate of a time-dependent Hamiltonian H(t) will stay in the corresponding eigenstate, provided that H varies slowly compared to the time-scale set by the energy gap to the neighboring states. In practical situations, however, such as when doing quantum operations on a qubit, this slowness is in conflict with the need to do as many operations as possible within the finite coherence time of the system. One way out is to modify the dynamics by adding an extra field which suppresses non-adiabatic transitions, the adiabatic gauge potential (AGP). In this talk, we quantify this suppression. We show that the AGP modifies the famous Landau-Zener formula for the probability of non-adiabatic transitions by a universal, non-perturbative prefactor. We show that, just as in the Landau-Zener case, the non-adiabatic transitions are dominated by paths which go around a branch point of the eigenvalues in the complex time plane, but that the AGP suppresses their contribution by introducing interference, in a mechanism similar to the Aharonov-Bohm phase. Finally, we prove that the AGP is compatible with time-dependent quantum integrability, which extends our conclusions to a wider class of models, including for example Gaudin magnets and multi-level Landau-Zener problems.
Gabriel received his undergraduate degree from the Federal University of Parana (Brazil) in 2017 and his PhD from Stony Brook University (USA) in 2022. Since 2023, he is a TDLI/Nordita joint postdoctoral fellow, working on geometrical and non-perturbative properties of topological phases as well as their practical applications in quantum computation.