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arXiv:2608.09224

Jaynes--Cummings dynamics of fermionic heteronuclear dimers in the Mott regime

R. J. Lewis-Swan, K. V. Kheruntsyan

cond-mat.quant-gasquant-phSubmitted Aug 10, 2026• Announced Aug 11, 2026• 0 citations
v1 · Aug 10, 2026v2 · Sep 13, 2026
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Abstract

We formulate and exactly solve a model for coherent association and dissociation of fermionic heteronuclear dimers in the deep-lattice Mott regime. Starting from the onsite three-component atom--molecule Hamiltonian, we show how the single-site model maps to the paradigmatic Jaynes--Cummings Hamiltonian from quantum optics. In this mapping, the fermionic molecular/free-atom sector forms an effective two-level system, while the bosonic atomic mode plays the role of the oscillator degree of freedom. We fix the conserved number of fermionic constituent atoms to one but allow an arbitrary conserved number $N$ of bosonic constituent atoms. The accessible doublet is then $|e,N-1\rangle\leftrightarrow|g,N\rangle$, and the coherent conversion coupling is bosonically enhanced to $χ\sqrt{N}$. Exact analytic expressions are derived for molecular dissociation, atom-pair association, mode populations, and boson--fermion correlation dynamics. The model provides a transparent matter-wave realization of Jaynes--Cummings physics in a heteronuclear Bose--Fermi system and an exactly solvable setting for understanding coherent atom--molecule conversion and bosonic enhancement in lattice systems.

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We formulate and exactly solve a model for coherent association and dissociation of fermionic heteronuclear dimers in the deep-lattice Mott regime. Starting from the onsite three-component atom--molecule Hamiltonian, we show how the single-site model maps to the paradigmatic Jaynes--Cummings Hamiltonian from quantum optics. In this mapping, the fermionic molecular/free-atom sector forms an effective two-level system, while the bosonic atomic mode plays the role of the oscillator degree of freedom. We fix the conserved number of fermionic constituent atoms to one but allow an arbitrary conserved number NNN of bosonic constituent atoms. The accessible doublet is then ∣e,N−1⟩↔∣g,N⟩|e,N-1\rangle\leftrightarrow|g,N\rangle∣e,N−1⟩↔∣g,N⟩, and the coherent conversion coupling is bosonically enhanced to χNχ\sqrt{N}χN​. Exact analytic expressions are derived for molecular dissociation, atom-pair association, mode populations, and boson--fermion correlation dynamics. The model provides a transparent matter-wave realization of Jaynes--Cummings physics in a heteronuclear Bose--Fermi system and an exactly solvable setting for understanding coherent atom--molecule conversion and bosonic enhancement in lattice systems.
We consider the photodissociation of ground-state bosonic molecules trapped in an optical lattice potential into a two-component gas of fermionic atoms. The system is assumed to be described by a single-band resonantly coupled Bose-Fermi Hubbard model. We show that in the strong fermion-fermion interaction limit the dissociation dynamics is governed by a spin-boson lattice Hamiltonian. In the framework of a mean-field analysis based on a generalized Gutzwiller ansatz, we then examine the crossover of the dissociation from a regime of independent single-site dynamics to a regime of cooperative dynamics as the molecular tunneling increases. We also show that in the limits of weak and strong intersite tunneling the mean-field solutions agree well with the results from the quantum optical Jaynes-Cummings and Tavis-Cummings models, respectively. Finally, we identify two types of self-trapping transitions, a coherent and an incoherent one, depending on the ratio of the repulsive molecule-molecule interaction strength to molecular tunneling.
We propose to subject two Bose-Einstein condensates to a periodic potential, so that one condensate undergoes the Mott-insulator transition to a state with precisely one atom per lattice site. We show that photoassociation of heteronuclear molecules within each lattice site is described by the quantum optical Jaynes-Cummings Hamiltonian. In analogy with studies of this Hamiltonian with cavity fields and trapped ions, we are thus able to engineer quantum optical states of atomic matter wave fields and we are able to reconstruct these states by quantum state tomography.
It is today possible to test many quantum mechanical predictions, even the most puzzling ones, setting up sophisticated experiments on exemplary "textbook" physical systems like a single atom or molecule or a single material quantum harmonic oscillator. It is therefore conceptually highly exciting to conceive simple but not trivial physical situations representable by exactly solvable hamiltonian models, in the grasp of the experimentalists. In this paper we study a physical system consisting of two coupled identical dimers. Each molecule possesses both fermionic and bosonic degrees of freedom and its internal non adiabatic dynamics is governed by a bilinear term conserving the total excitation number. The two molecules are assumed to interact by a dipole like term. Our main result is that the hamiltonian model representing such a composite system may be unitarily put in a form describing two fictitious uncoupled JC dimers provided the initial excitation number is less than two. The advantage of these canonical transformations is that it makes the restricted dynamical problem exactly tractable. In this way we may successfully study the time evolution of quantum correlation effects get established in the dimer-dimer system due to dipolar like coupling.
Abstract The measurement and characterisation of correlation functions has recently become one of the central themes in the studies of ultracold quantum gases. By probing complex many-body states of these interacting systems, correlation functions facilitate the most in-depth understanding of the underlying physics, not accessible through simple density profile measurements. In this thesis, we study the dynamics of second-order correlation functions for atoms created in pair-production processes such as molecular dissociation and atomic four-wave mixing. More specifically, in Chapter 3 we analyse the dynamics of correlated atom pairs created via controlled dissociation of a Bose-Einstein condensate of diatomic molecules. The atomic constituents can be either a pair of bosonic or fermionic atoms. 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Using the undepleted molecular-field approximation, we obtain explicit analytic results for the short-time asymptotic behaviour of the second-order correlation functions and for relative number squeezing between the dissociated atoms in one, two, and three spatial dimensions. Comparisons with the numerical results, which incorporate the molecular depletion and s-wave scattering interactions, show that the analytic approaches employed here capture the main underlying physics and provide useful insights into the dynamics of dissociation for conversion efficiencies up to 10%. The results show explicitly how the strength of atom-atom correlations and relative number squeezing degrade with the reduction of the size of the molecular condensate. In Chapter 4, we study highly anisotropic molecular condensates in order to quantify the effects of bosonic stimulation and fermionic Pauli blocking on the dissociation dynamics. We show that the difference in quantum statistics of the atomic constituent is manifest as complementary geometric structures in the density profiles of the dissociated atoms. Atomic bosons are preferentially emitted along the long axis of the molecular condensate due to bosonic stimulation, while atomic fermions are preferentially emitted along the short axis due to Pauli blocking. This anisotropy potentially simplifies the measurement of correlations between the atoms through relative number squeezing. In Chapter 5 we apply our analytic approaches to a related problem of atomic four-wave mixing and analyze atom-atom correlations in the s-wave scattering halo of two colliding condensates. The results in the short-time limit are in agreement with the first-principles simulations using the positive-P representation and provide analytic insights into the experimental observations of Perrin et al. [Phys. Rev. Lett. 99, 150405 2007]. 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We study a fermionic atom optics counterpart of parametric down-conversion with photons. This can be realized through dissociation of a Bose-Einstein condensate of molecular dimers consisting of fermionic atoms. We present a theoretical model describing the quantum dynamics of dissociation and find analytic solutions for mode occupancies and atomic pair correlations, valid in the short time limit. The solutions are used to identify upper bounds for the correlation functions, which are applicable to any fermionic system and correspond to ideal particle number-difference squeezing.