Statistical signatures of states orthogonal to the Fock-state ladder of composite bosons

TL;DR

This paper investigates the unique quantum signatures of states orthogonal to the Fock-state ladder in composite bosons, revealing how finite entanglement causes deviations from ideal bosonic behavior and proposing experimental methods to detect these effects.

Contribution

It introduces a theoretical framework to identify and analyze states orthogonal to the Fock ladder in composite bosons using a Gedanken-experiment involving beam-splitters and interference.

Findings

Orthogonal states cause deviations from ideal bosonic behavior.

Consecutive beam-splitter dynamics amplify these deviations.

Experimental signatures can reveal microscopic properties of fermionic constituents.

Abstract

The theory of composite bosons (cobosons) made of two fermions [Phys. Rev. A 71, 034306 (2005), Phys. Rev. Lett. 109, 260403 (2012)] converges to ordinary structureless bosons in the limit of infinitely strong entanglement between the fermionic constituents. For finite entanglement, the annihilation operator $\hat c$ of a composite boson couples the $N$-coboson Fock-state not only to the $(N-1)$-coboson state -- as for ordinary bosons --, but also to a component which is orthogonal to the Fock-state ladder of cobosons. Coupling with states orthogonal to the Fock ladder arises also in dynamical processes of cobosons. Here, with a Gedanken-experiment involving both mode-splitting and collective Hong-Ou-Mandel-like interference, we derive the characteristic physical signature of the states orthogonal to the Fock ladder generated in the splitting process. This allows to extract microscopic properties of many-fermion-wave functions from the collective coboson behavior. We show that consecutive beam-splitter dynamics increases the deviation from the ideal bosonic behavior pattern, which opens up a rigorous approach to the falsification of coboson theory.