Experimental Tomography of Quantum Many-Body Hamiltonians in Solids via Thermalization
Phys. Rev. Lett. 137, 170402 – Published 21 October, 2026
DOI: https://doi.org/10.1103/3qlc-bqv9
Abstract
Characterizing the unknown Hamiltonian of a quantum many-body system is essential for exploring fundamental physical phenomena and advancing frontier quantum technologies. However, the complexity of many-body interactions and limited control capabilities in realistic experimental systems render this task formidable. Here, we experimentally demonstrate efficient Hamiltonian tomography in a solid-state nuclear spin system by exploiting high-temperature thermalization. In an interacting spin network subject to periodic driving, we extract the dominant interaction structures of the engineered effective Hamiltonian using a sequence in which a tunable global rotation is sandwiched between two identical thermalization processes governed by the target Hamiltonian. By performing an SO(3) Fourier transform and principal component analysis on the response signals sampled across rotation angles, we successfully reconstruct the relative coefficients of all two-body terms, as well as selected three- and four-body interactions. Our protocol scales polynomially with the number of Hamiltonian parameters, providing an efficient and practical tool for investigating complex quantum many-body systems.
