# Parameter estimation of a 3-level quantum system with a single population measurement

**Authors**: Zaki Leghtas, Mazyar Mirrahimi, Pierre Rouchon, 48th IEEE Conference on Decision and Control, pp: 3816-3820, 2009 DOI: 10.1109/CDC.2009.5400060

An observer-based Hamiltonian identification al- gorithm for quantum systems has been proposed in [2]. The later paper provided a method to estimate the dipole moment matrix of a quantum system requiring the measurement of the populations on all states, which could be experimentally difficult to achieve. We propose here an extension to a 3-level quantum system, having access to the population of the ground state only. By a more adapted choice of the control field, we will show that a continuous measurement of this observable, alone, is enough to identify the field coupling parameters (dipole moment).

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**BibTeX**:

@Proceedings{,

author = {Zaki Leghtas, Mazyar Mirrahimi, Pierre Rouchon},

editor = {},

title = {Parameter estimation of a 3-level quantum system with a single population measurement},

booktitle = {48th IEEE Conference on Decision and Control, pp: 3816-3820, 2009},

volume = {},

publisher = {},

address = {Shanghai},

pages = {3816-3820},

year = {2009},

abstract = {An observer-based Hamiltonian identification al- gorithm for quantum systems has been proposed in [2]. The later paper provided a method to estimate the dipole moment matrix of a quantum system requiring the measurement of the populations on all states, which could be experimentally difficult to achieve. We propose here an extension to a 3-level quantum system, having access to the population of the ground state only. By a more adapted choice of the control field, we will show that a continuous measurement of this observable, alone, is enough to identify the field coupling parameters (dipole moment).},

keywords = {Nonlinear systems, quantum systems, parameter estimation, nonlinear observers, averaging.}}