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In one-channel, finite-size Luttinger one-dimensional quantum dots, bothFriedel oscillations and Wigner correlations induce oscillations in theelectron density with the same wavelength, pinned at the same position.Therefore, observing such a property does not provide any hint about theformation of a Wigner molecule when electrons interact strongly and other toolsmust be employed to assess the formation of such correlated states. We comparehere the behavior of three different correlation functions and demonstrate thatthe integrated two point correlation function, which represents the probabilitydensity of finding two particles at a given distance, is the only faithfulestimator for the formation of a correlated Wigner molecule.

Correlation functions for the detection of Wigner molecules in a one-channel Luttinger liquid quantum dot