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arXiv:2512.23867 · Physics Letters A

Squeezed states for Frenkel-like two-fermion composite bosons

Francisco Figueiredo, Itzhak Roditi

quant-phSubmitted Dec 29, 2025• Announced Dec 31, 2025• 1 citation• Revised Jan 15, 2026 (v2)
v1 · Dec 29, 2025v2 · Jan 15, 2026
arXivHTMLPDF

Abstract

We investigate squeezed states of composite bosons (cobosons) formed by pairs of spin-$1/2$ fermions, with emphasis on Frenkel-like cobosons. While squeezing for standard bosonic modes is well established, its extension to cobosons requires accounting for Pauli blocking and the resulting non-canonical commutation algebra. Building on earlier constructions of coboson coherent states, we define squeezed cobosons as eigenstates of a Bogoliubov transformed coboson operator and derive explicit expressions for the associated quadrature variances. We show that the underlying fermionic structure leads to state-dependent modifications of the Heisenberg--Robertson uncertainty bound, which may fall below the canonical bosonic limit without implying any violation of uncertainty principles. Numerical results based on finite-dimensional matrix representations illustrate how these effects constrain the attainable squeezing. Our framework is relevant to composite boson systems such as tightly bound electron-hole pairs and provides a physically transparent setting to probe compositeness through observable quadrature fluctuations.

Journal reference
Physics Letters A Volume 582, 28 June 2026, 131579
DOI
10.1016/j.physleta.2026.131579
Comments
8 pages, 3 figures Small changes to the text and new references included

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Ultracold atomic systems provide a versatile platform for exploring quantum phenomena, offering tunable interactions and diverse trapping geometries. In this study, we investigate a one-dimensional system of trapped fermionic atoms using the composite boson formalism, which describes pairs of opposite-spin fermions as cobosons (short for composite bosons). We solve the Schr\"odinger equation for a $2\ensuremath{\uparrow}+2\ensuremath{\downarrow}$ fermionic system across a broad range of attractive and repulsive interactions by constructing the system's wave function as a superposition of two-coboson states. We determine key observables such as particle density profiles and two-body correlations. The density profiles calculated agree with both the Tonks-Girardeau and Lieb-Liniger limits and provide a portrait of the transition between those regimes. In the strong repulsive regime, the ansatz captures the Fridel-Wigner transition characterized by a doubling of the peaks in the density profiles. Additionally, we compute the low-lying energy spectrum and estimate the pairing gap. Our results highlight the usefulness of the coboson superposition ansatz for exploring quantum phenomena in strongly correlated few-body systems.
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The theory of composite bosons (cobosons) made of two fermions [C. K. Law, Phys. Rev. A 71, 034306 (2005); M. C. Tichy et al., 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 $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{c}$ of a composite boson couples the NNN-coboson Fock state not only to the $(N\ensuremath{-}1)$-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 us to extract the 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.