# [Dr. Jae-Gyun Baak and Prof. Uwe R. Fischer] Parameter Estimation for Interacting Many-Body Systems Redefined (published in PRL)

**Parameter Estimation for Interacting Many-Body Systems Redefined**

It is shown by Prof. Uwe R. Fischer and his recent PhD graduate Jae-Gyun Baak, whose culminating achievement during his graduate studies at Seoul National University is this publication in Physical Review Letters, that for a correct interpretation of measurement data, in an experiment which tries to gain knowledge about a given physical parameter in a many-body system, the knowledge of the fully self-consistent evolution of the interacting particles' quantum mechanical wave function is necessary.

Distinct from conventional approaches, focusing on the occupation number distribution of the single-particle orbitals only, it is demonstrated that the change of the orbitals' shape during dynamical evolution, in which occupation distribution and shape of orbitals are coupled, can crucially affect the parameter estimation accuracy.

Hence the very notion of a genuine many-body metrology is defined, namely one which is fully adapted to the intricacies of the many-body wave functions containing the (generally very complex) parameter dependent evolution of the interacting system.

As an illustrative example, we treat the well known double well potential to contain the particles, and show that self-consistent evolution enables the estimation of a linear tilt applied to an initially completely symmetric well (the tilt could for example represent gravity), while the non-self-consistent evolution yields a null result, i.e., renders it impossible to estimate the tilt from the measurement data.

Figure caption:

Figure caption:

"An atomic gas used to estimate the inclination imposed on a double well system confining the particles when they do not interact (upper row) or do interact (lower row) with each other.

https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.132.240803Without interaction, the dynamics of the system is rather simple and the degree of inclination (a metrological parameter) can be readily estimated from a given set of measurement outcomes. interaction, however, makes it necessary to introduce more complex mathematics (i.e., a self-consistent many-body dynamics formulation) for an accurate description of the interacting system. Such a self-consistent description does in fact lead to different measurement outcomes for the same degree of inclination (the parameter). Hence in order to appropriately interpret the set of measurement results and estimate the parameter accurately, the self-consistency of many-body evolution needs to be incorporated into the metrological process."