Fermionization of two Distinguishable Fermions

Eloisa Cuestas, A. P. Majtey

G. Zürn, Friedhelm Serwane, Thomas Lompe +4 more

We study a system of two distinguishable fermions in a 1D harmonic potential. This system has the exceptional property that there is an analytic solution for arbitrary values of the interparticle interaction. We tune the interaction strength and compare the measured properties of the system to the theoretical prediction. For diverging interaction strength, the energy and square modulus of the wave function for two distinguishable particles are the same as for a system of two noninteracting identical fermions. This is referred to as fermionization. We have observed this phenomenon by directly comparing two distinguishable fermions with diverging interaction strength with two identical fermions in the same potential. We observe good agreement between experiment and theory. By adding more particles our system can be used as a quantum simulator for more complex systems where no theoretical solution is available.

Sangita Bera, Rhombik Roy, Barnali Chakrabarti

Fermionization is what happens when repulsive interacting bosons in one spatial dimension feel infinite interaction. Due to their strong repulsion the bosons try to minimize their spatial overlap like the fermions. Fermionized bosons and noninteracting fermions resemble each other and we trace these similarities of strongly correlated one-dimensional bosonic systems and fermionic system by exploring their ground state properties using the one- and two-body density matrix in coordinate space. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. Using the one- and two-body density in momentum space, fermionized bosons can be distinguished from noninteracting fermions.

Yuan Le, Joshua M. Wilson, Neel Malvania +3 more

Fedor Herbut

Usually fermions and bosons behave very differently. Regarding distinguishability, they behave in one and the same way. Two-identical-particle quantum theory is discussed on the example of the deuteron and that of distant correlations, as well as on the example of the real interference and quantum erasure experiments in the Hong–Ou–Mandel two-photon interferometer (with and without polarizers and analyzers). Distinguishability and indistinguishability of two identical photons in the experiments are illustrated. It is demonstrated, using a simple formalism valid simultaneously for fermions and for bosons, that there exists an isomorphism giving theoretical foundation to distinguishing two identical particles. But the distinguishing has a limited range of exact applicability. In most cases of interest, only the indistinguishability approach has a first-principle (and universal) validity.