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Frontiers in Optics

Determination of System Hamiltonian with Multi-dimensional Spectroscopy

Steven T. Cundiff, Hebin Li, Alan D. Bristow, Mark E. Siemens, Galan Moody

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We present the use of three-dimensional coherent spectroscopy to isolate quantum pathways. Isolation of individual quantum pathways allows the parameters of the Hamiltonian to be determined. We demonstrate this possibility using an atomic vapor.
DOI
10.1364/ls.2013.lm3h.5

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Abstract Three-dimensional coherent spectroscopy techniques and experiments are presented in this chapter. The chapter begins with a discussion of different implementations of three-dimensional spectroscopy. The technique can be used to unravel contributions from different quantum pathways, providing a clear picture of the nonlinear response of complex systems. Application of the technique is discussed for three specific systems, including atomic vapors, semiconductor quantum wells, and light-harvesting complexes.
Predicting and controlling quantum mechanical phenomena require knowledge of the system Hamiltonian. A detailed understanding of the quantum pathways used to construct the Hamiltonian is essential for deterministic control and improved performance of coherent control schemes. In complex systems, parameters characterizing the pathways, especially those associated with inter-particle interactions and coupling to the environment, can only be identified experimentally. Quantitative insight can be obtained provided the quantum pathways are isolated and independently analysed. Here we demonstrate this possibility in an atomic vapour using optical three-dimensional Fourier-transform spectroscopy. By unfolding the system's nonlinear response onto three frequency dimensions, three-dimensional spectra unambiguously reveal transition energies, relaxation rates and dipole moments of each pathway. The results demonstrate the unique capacity of this technique as a powerful tool for resolving the complex nature of quantum systems. This experiment is a critical step in the pursuit of complete experimental characterization of a system's Hamiltonian.