Abstract
We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect. Notime-dependent quantities need to be measured; it fully suffices to observe spectral shifts induced by fields applied to local "markers." We demonstrate the idea with a simple tight-binding Hamiltonian and numerically show stability with respect to Gaussian noise on the spectral measurements. Then we generalize the result to show applicability to a wide range of systems, including quantum spin chains, networks of qubits, and coupled harmonic oscillators, and suggest potential experimental implementations.
Highlights
We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect
No time-dependent quantities need to be measured; it fully suffices to observe spectral shifts induced by fields applied to local “markers.” We demonstrate the idea with a simple tight-binding Hamiltonian and numerically show stability with respect to Gaussian noise on the spectral measurements
Hamiltonians are of paramount importance in our understanding of matter and its properties, but they can do some work for us: in quantum technology, they can trigger quantum simulations or even form the basis of quantum computing
Summary
Fourier transform provides the spectrum fekg and the coefficients jh1jekij, and it was shown that for one-dimensional systems these limited data can suffice to estimate the full system This initial work has been extended in several directions. We show in this Letter that two spectra do the job: one being the original spectrum of H, and one being the spectrum of a modified Hamiltonian H0 which arises from applying a local field to a probe that we call the “Zeeman marker.” This probe does not have to be measured locally and no time-dependent data are required. We first demonstrate this idea with a simple (but common) tightbinding Hamiltonian, analyze its stability, and generalize to spin Hamiltonians, free fermions and bosons, 0031-9007=17=119(3)=030402(5)
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