Dynamics of nonclassicality in a generalized Tavis Cummings model with XY spin $(1/2,1)$ atomic interactions

AI summary

Overview

Research area: Quantum optics and cavity quantum electrodynamics (cavity QED), specifically the dynamical generation, transfer, and redistribution of nonclassicality in hybrid light–matter systems.

Technical level: Intermediate. The paper uses standard cavity-QED Hamiltonians and a specific information-theoretic quantifier (Wigner–Yanase skew information), so familiarity with spin operators, the Jaynes–Cummings/Tavis–Cummings models, and density-matrix language is helpful, but the physical narrative is accessible.

Scope (one sentence): The paper tracks how a Wigner–Yanase-skew-information measure of nonclassicality evolves in the cavity field and in the atomic spins for a spin-1 Jaynes–Cummings model, then for a hybrid spin-(1/2, 1) Tavis–Cummings model with and without a direct XY spin–spin interaction and a longitudinal magnetic field.

What This Paper Is About

The standard Jaynes–Cummings and Tavis–Cummings models describe a two-level atom (or a set of identical two-level atoms) exchanging excitations with a single cavity mode. This paper asks what changes when the atoms are genuinely multi-level: a spin-1 atom alone, and then a hybrid pair consisting of one spin-1/2 and one spin-1 atom coupled to the same cavity mode, optionally with a direct anisotropic XY exchange interaction and an external longitudinal magnetic field between them.

The goal is to determine which mechanisms — the nature of the initial field state, the initial spin preparation, resonance versus detuning, collective atomic degrees of freedom, and direct spin–spin coupling — actually control where nonclassicality is generated and where it ends up residing during the evolution.

Key Contributions

1. A unified quantifier-based comparison of two models. The authors apply the same Wigner–Yanase skew-information framework to both the generalized Jaynes–Cummings model (one spin-1 atom) and the generalized Tavis–Cummings model (spin-1/2 plus spin-1), so that changes attributable purely to the added collective atomic degree of freedom can be separated from effects already present in the single-atom case.

2. Nonclassicality thresholds worked out for the hybrid spin system. For the combined spin-1/2 plus spin-1 subsystem, the angular-momentum decomposition into total spin sectors j ∈ {1/2, 3/2} is used to fix an absolute upper bound N_max = j_max(j_max+1) = (3/2)(3/2+1) = 15/4 = 3.75, an initial spin-coherent baseline of N(ρ_spin(0)) = j₁ + j₂ = 3/2, and therefore a sufficient (not necessary) witness N(ρ_spin) > 3/2 for collective atomic nonclassicality beyond the spin-coherent regime.

3. A systematic scan of initial-state dependence. Three field families (Fock, thermal, coherent) at two different mean excitations each are combined with three spin preparations (ground, excited, superposition), for both the field and the atomic measures, giving a map of when nonclassicality is amplified, damped, or frozen.

4. Identification of detuning, rather than direct exchange, as the dominant role of the longitudinal field. The paper argues that an increasing longitudinal magnetic field acts primarily as an effective detuning parameter: it weakens the atom–field coupling, localizes excitations in the atomic subsystem, suppresses coherent energy transfer to the cavity, and thereby reduces field nonclassicality while the atomic subsystem retains most of the quantum correlations.

Main Findings

• Resonance produces regular, coherent oscillations. Under resonance conditions the generalized Jaynes–Cummings dynamics shows oscillatory nonclassicality in both the cavity field and the spin, reflecting reversible excitation exchange and continuous redistribution of quantum coherence between the two subsystems.

• Initial spin preparation controls field nonclassicality. For a coherent field with |α|² = 2 and |α|² = 20, an initially excited spin produces pronounced field nonclassicality peaks reaching N(ρ,K) ≈ 3.20, well above the single-mode bosonic threshold N(ρ,K) > 1/2, whereas an initially ground-state spin gives a weaker maximum of about N(ρ,K) ≈ 2.40; the superposition state lies in between, with quantum interference playing an important role.

• Larger coherent amplitude can mean stronger dynamical nonclassicality. Comparing |α|² = 2 with |α|² = 20, the field becomes more classical in relative-fluctuation terms but supplies more exchangeable excitations; for ground and excited spin preparations the nonclassicality grows to values close to the limit associated with the mean photon number. This growth occurs on a shorter time scale than that reported by Fu et al. [54] for a single-mode bosonic field coupled to a two-level atom, suggesting the extra spin-1 degrees of freedom enhance and accelerate the field's nonclassical response. For the superposition state, nonclassicality rises to a finite value and then stabilizes, indicating a quasi-stationary regime.

• Thermal fields damp quickly; Fock fields stay robust. For thermal fields at n_th = 2 and n_th = 20, nonclassicality remains generally weak with rapid temporal damping, exceeding the 1/2 threshold only transiently and staying below the maxima reported by Fu et al. [54]. For Fock states from n = 2 to n = 20, nonclassicality is significantly stronger, remains highly sensitive to spin preparation, and becomes more complex with increasing photon number; constructive interference enhances oscillations for the superposition state, and significant persistent nonclassicality survives even with a ground-state spin.

• Spin nonclassicality is bounded by the spin's own Hilbert space. In the generalized Jaynes–Cummings model, N(ρ_spin(t)) stays at or below its initial value N(ρ_spin(0)) = 1 for all configurations considered, consistent with the analytical results of Ref. [50] where atomic coherent states |1, ±1⟩ give N = 1 and superposition states follow N = 2 − 8ζ/(2+ζ)², which with ζ = 2 also gives N = 1. In this model the spin measure remains below N(ρ_spin) < 2. The decrease is attributed to an effective quantum dephasing induced by the spin–field interaction even without explicit dissipation.

• Field and spin play complementary roles. The field, with its many-dimensional Hilbert space, acts as a quantum reservoir able to generate and redistribute substantial nonclassicality, while the spin gives a more constrained response tied to its internal structure; nonclassicality is therefore a dynamical resource whose distribution is continuously modified, not a static property localized in one component.

• Adding a spin-1/2 greatly amplifies field nonclassicality in the Tavis–Cummings model. For intense coherent states (|α|² = 20), simultaneous coupling to both spins produces strong oscillations reaching peaks between 25 and 40, exceeding the 1/2 threshold by nearly two orders of magnitude. Fock states at n = 20 show dense, high-amplitude oscillations reaching values above 22, while thermal states at n_th = 20 remain restricted to N ≲ 2.2 because statistical mixing suppresses buildup of quantum coherence.

• Collective atomic nonclassicality is transiently generated. In the Tavis–Cummings model, N(ρ_spin(t)) rises from the 3/2 baseline and shows recurrent excursions reaching values close to the theoretical ceiling, up to N ≈ 3.4 (below the 3.75 bound), confirming transient generation of highly nonclassical collective states. Subsequent decreases reflect reversible transfer of correlations back to the cavity rather than irreversible decoherence, since the evolution is unitary. A thermal field instead collapses N(ρ_spin) near zero (below 0.15), as thermal noise destroys collective atomic coherence.

• The XY interaction and longitudinal field introduce a competition between two excitation-transfer mechanisms. The paper frames the combined cavity-mediated coupling and direct XY spin–spin coupling as competing channels that modify the energy-level structure, alter coherent redistribution of excitations, and produce interference from multiple transition pathways. At the abstract level, the reported outcome is that increasing longitudinal field acts mainly as effective detuning rather than as a direct exchange interaction: atom–field coupling weakens, excitations localize in the atomic subsystem, field nonclassicality is strongly reduced while the atomic subsystem keeps most of the quantum correlations, and atomic superposition states display highly irregular spin dynamics interpreted as detuning-induced redistribution of quantum correlations. (The truncated content provided here does not include the detailed numerical figures for the XY case beyond the Hamiltonian in Eq. (15).)

• Governing principle. The dynamics of spin and field nonclassicality are governed primarily by interaction-mediated excitation flow and resonance conditions rather than by the initial energy distribution alone, with detuning and collective couplings serving as control mechanisms for stabilizing quantum resources.

Methodology in Plain English

The authors write down Hamiltonians for the two setups. In the single-atom case, a quantized cavity mode with frequency ω_c interacts, at coupling strength g and under the rotating-wave approximation, with a three-level spin-1 atom whose levels are labeled |1,−1⟩, |1,0⟩, |1,+1⟩, with atomic transition frequency ω₀. In the two-atom case, a spin-1/2 and a spin-1 atom are both coupled to the same mode with the same strength g, and an optional XY term is added with anisotropic exchange strength λ_XY, anisotropy parameter γ, and a uniform longitudinal magnetic field h along z.

They then evolve an initial product state of field and atoms under the Hamiltonian (the evolution is unitary, |ψ(t)⟩ = exp(−iHt)|ψ(0)⟩) and compute two numbers at each time: a field nonclassicality measure defined as the maximum over phase angle θ of the skew information with respect to the homodyne quadrature K_θ, and an atomic nonclassicality measure defined as the sum of skew informations with respect to the three SU(2) generators J_x, J_y, J_z.

These measures are calibrated against reference values rather than arbitrary scales. For the field, every coherent state gives exactly 1/2, so any value above 1/2 certifies nonclassicality. For a pure spin-j state the measure is at least j, with equality only for atomic coherent states, and at most j(j+1). The authors sweep three field types (Fock, thermal, coherent) at two mean excitations each against three spin preparations, and plot the measures as functions of the scaled time gt. Analytical results for both models are given in the Appendix.

Why This Matters

Impact on research. The paper extends nonclassicality dynamics beyond the two-level paradigm that dominates the Jaynes–Cummings and Tavis–Cummings literature, and it does so with a single quantifier applied consistently to both the bosonic and the spin side. That makes it possible to say precisely which features are intrinsic to multi-level atoms and which come from collective coupling, and it gives a concrete, threshold-based reading of numerical amplitudes (1/2 for the field, 3/2 for the two-spin baseline, 3.75 as the ceiling).

Real-world applications (as motivated by the paper's framing):

• Cavity-QED platforms where multi-level atoms or hybrid spin species are coupled to a common mode.
• Hybrid quantum architectures that combine different spins in one device and need to know where quantum resources accumulate.
• Quantum metrology, since Wigner–Yanase skew information is a form of quantum Fisher information and thus directly tied to rotation sensitivity and precision limits.
• Quantum information processing tasks — computing, communication, and sensing — that depend on generating and preserving nonclassical states.

Industry relevance. The results give device designers a control knob: resonance maximizes excitation flow and field nonclassicality, while a longitudinal field detunes the system and parks correlations in the atoms. For hardware where the cavity is the fragile or lossy element, deliberately detuning to localize quantum resources in the atomic subsystem is an attractive protection strategy.

Future Directions

• Open-system versions. The present evolution is unitary with no explicit dissipation, yet the paper attributes the spin's decay in nonclassicality to effective dephasing. Adding cavity loss, spontaneous emission, or thermal noise would test whether the reported localization and stabilization survive realistic conditions.

• Full mapping of the XY parameter space. The truncated content only presents the XY Hamiltonian and its abstract-level conclusions. A systematic scan over λ_XY, γ, and h — including the competition regime where cavity-mediated and direct spin–spin transfer are comparable — is a natural next step.

• Larger and more heterogeneous spin chains. The paper motivates the extension from a spin-(1/2, 1) pair to larger hybrid registers; whether the collective thresholds and ceiling values generalize to longer XY chains coupled to one mode is open.

• Operational and experimental translation. Since the measure is tied to quantum Fisher information, connecting the predicted nonclassicality peaks (for example the 25–40 range for |α|² = 20 in the Tavis–Cummings case) to an actual measurement protocol or metrological advantage would make the results directly testable.

Target Audience

Researchers and graduate students in quantum optics, cavity QED, and quantum information who work on nonclassicality, spin squeezing, or hybrid light–matter architectures, and who want a quantitative, threshold-calibrated account of how multi-level atomic structure and direct spin–spin coupling redistribute quantum resources between a cavity field and its atoms. It is also useful for readers already familiar with the standard Jaynes–Cummings and Tavis–Cummings models who want to see what a spin-1 atom and a spin-(1/2, 1) pair change.

Authors’ abstract

We investigate the dynamics of nonclassicality, quantified by the Wigner Yanase skew information, in generalized Jaynes Cummings (JC) and Tavis Cummings (TC) models describing light matter interactions in cavity quantum electrodynamics. We first analyze a generalized JC model consisting of a single bosonic cavity mode coupled to a spin 1 atom, focusing on the temporal evolution of nonclassicality in both the cavity field and the atomic subsystem. We then extend this framework to a generalized TC model by introducing an additional spin $1/2$ atom, enabling us to examine the influence of collective atomic degrees of freedom. The global dynamics are investigated both with and without an $XY$ spin interaction. Our results show that, under resonance conditions, the system exhibits efficient excitation exchange between the cavity field and the atomic subsystem, resulting in regular, coherent nonclassicality dynamics and enhanced field nonclassicality generation. Conversely, an increasing longitudinal magnetic field acts primarily as an effective detuning parameter rather than a direct exchange interaction. In this off resonant regime, the atom field coupling is substantially weakened, localizing excitations within the atomic subsystem. This localization suppresses coherent energy transfer to the cavity field, leading to a pronounced reduction in field nonclassicality, while the atomic subsystem retains the majority of the quantum correlations. Notably, atomic superposition states exhibit highly irregular spin dynamics, reflecting a detuning-induced redistribution of quantum correlations. These findings demonstrate that the dynamics of spin and field nonclassicality are governed primarily by interaction mediated excitation flow and resonance conditions rather than the initial energy distribution alone, ..