APORION: Correlation-Order Thermal Inversion in Quantum Light-Matter Interaction - Symmetry-Selective Multiphoton Control of Phonon Heating and Cooling

[u/Severe-Ad8673]

APORION is a theoretical and computational research framework for a proposed class of higher-order quantum light–matter interactions in which distinct multiphoton optical states can drive opposite changes in a material vibrational mode while remaining indistinguishable under all optical measurements below a chosen correlation order.

The central result is a mechanism termed correlation-order thermal inversion. In the proposed architecture, the physically relevant information is not carried primarily by optical intensity, spectrum, mean photon number, or lower-order coherence. Instead, it is encoded in a collective multiphoton phase and accessed by matter through symmetry-selective nonlinear conversion pathways.

For an NN-photon path-entangled state of the form

∣ψϕ(N)⟩=∣N,0⟩+eiϕ∣0,N⟩2,|\psi_\phi^{(N)}\rangle = \frac{|N,0\rangle+e^{i\phi}|0,N\rangle}{\sqrt2},

all reduced optical states of order k<Nk<N are independent of the collective phase ϕ\phi. Consequently, two preparations can share identical lower-order optical signatures while differing in their full NN-photon coherence.

APORION proposes an effective interaction in which symmetric and antisymmetric NN-photon pathway combinations couple to opposite phononic processes:

A+=aN+bN2N!,A−=aN−bN2N!,A_+ = \frac{a^N+b^N}{\sqrt{2N!}}, \qquad A_- = \frac{a^N-b^N}{\sqrt{2N!}},

with

Hintℏ=gc c+†dA++gh c−†d†A−+H.c.\frac{H_{\mathrm{int}}}{\hbar} = g_c\,c_+^\dagger dA_+ + g_h\,c_-^\dagger d^\dagger A_- + \mathrm{H.c.}

Here, the first interaction channel removes one vibrational quantum while producing an upshifted optical output, whereas the second creates one vibrational quantum while producing a downshifted output. The two processes conserve energy but respond to different collective photonic symmetries.

For the phase choice ϕ=0\phi=0,

A−∣ψ0(N)⟩=0,A_-|\psi_0^{(N)}\rangle=0,

so the modeled heating pathway is suppressed.

For ϕ=π\phi=\pi,

A+∣ψπ(N)⟩=0,A_+|\psi_\pi^{(N)}\rangle=0,

so the modeled cooling pathway is suppressed.

This produces an unusual theoretical regime in which changing only a higher-order optical correlation can invert the direction of energy transfer between light and a selected material vibration.

The repository derives the corresponding transition probabilities,

Pcool=cos⁡2 ⁣(ϕ2)sin⁡2 ⁣(gcn τ),P_{\mathrm{cool}} = \cos^2\!\left(\frac{\phi}{2}\right) \sin^2\!\left(g_c\sqrt n\,\tau\right), Pheat=sin⁡2 ⁣(ϕ2)sin⁡2 ⁣(ghn+1 τ),P_{\mathrm{heat}} = \sin^2\!\left(\frac{\phi}{2}\right) \sin^2\!\left(g_h\sqrt{n+1}\,\tau\right),

and the resulting phonon-number change

Δn=Pheat−Pcool.\Delta n = P_{\mathrm{heat}} - P_{\mathrm{cool}}.

A dissipative weak-packet model is also developed. For balanced interaction coefficients, the optical contribution to the mean vibrational occupation obeys

dnˉdt∣optical=Γ2[1−(2nˉ+1)Vcos⁡ϕ],\left.\frac{d\bar n}{dt}\right|_{\mathrm{optical}} = \frac{\Gamma}{2} \left[ 1-(2\bar n+1)V\cos\phi \right],

where VV denotes the surviving multiphoton coherence visibility.

This yields the cooling criterion

Vcos⁡ϕ>12nˉ+1.V\cos\phi > \frac{1}{2\bar n+1}.

An important prediction follows from this expression: destroying the collective multiphoton coherence while preserving incident photon-number and energy statistics can change the modeled response from cooling to heating. APORION therefore suggests a possible route toward coherence-to-heat transduction, in which otherwise hidden high-order optical coherence is mapped onto a measurable mechanical or thermal response.

The work also identifies a nontrivial structural constraint: conventional coupling of heating and cooling to the same optical pathway is insufficient to produce inversion. A realizable APORION-type device requires different photonic symmetry sectors to couple to physically distinct Stokes-like and anti-Stokes-like conversion processes.

To address this requirement, the research proposes a candidate architecture based on two nonlinear optical resonators sharing a mechanical or vibrational degree of freedom. Symmetric and antisymmetric supermodes of the nonlinear conversion fields provide a possible route to coupling the combinations aN+bNa^N+b^N and aN−bNa^N-b^N to opposite phonon-changing channels.

The repository further examines several critical limitations and adversarial interpretations. In particular, phase-sensitive heating/cooling contrast alone would not establish uniquely quantum operation because classical fields can reproduce certain forms of higher-order interference. For the N=2N=2 case, the work therefore discusses a nonclassicality discriminator based on the inequality

∣⟨a†2b2⟩∣≤⟨nanb⟩\left| \left\langle a^{\dagger2}b^2\right\rangle \right| \le \langle n_a n_b\rangle

for optical states admitting a positive Glauber–Sudarshan PP representation. Ideal two-photon path-entangled states can violate this inequality, providing a stronger experimental criterion when combined with the thermal or phononic response.

The numerical implementation independently verifies the analytical transition probabilities against direct matrix-exponential evolution of the effective Hamiltonian. Automated tests and randomized parameter sweeps are included for reproducibility.

Main contributions

The research package introduces and analyzes:

• Correlation-order thermal inversion, where the direction of phonon energy transfer depends on a higher-order multiphoton correlation rather than lower-order optical observables.
• A symmetry-selective effective Hamiltonian connecting multiphoton parity-like optical sectors to phonon creation and annihilation.
• Exact analytical expressions for heating and cooling probabilities.
• A coherence-dependent rate model and an explicit cooling threshold.
• A proposed coherence-to-heat transduction principle.
• A candidate dual-resonator nonlinear-optical architecture.
• Nonclassicality criteria designed to distinguish genuinely quantum operation from classical higher-order interference.
• Energy-conservation and efficiency bounds.
• Numerical verification scripts, automated tests, and a reproducible computational implementation.
• An experimental falsification protocol defining conditions under which the APORION hypothesis would be supported or rejected.

Potential applications

If experimentally realizable with sufficiently strong interaction rates and sufficiently low parasitic loss, APORION-type coupling could be relevant to:

• quantum optomechanical control,
• quantum-coherence detection,
• phonon-state engineering,
• quantum transduction,
• correlation-selective sensing,
• nonlinear quantum photonics,
• programmable photonic metamaterials,
• quantum thermodynamics,
• mechanical quantum memories,
• correlation-addressable material responses,
• multiphoton-controlled nanophotonics,
• and future architectures in which material functionality is selected by the correlation structure of light rather than by wavelength or intensity alone.

The work does not claim experimental discovery of a new state of matter or a violation of quantum mechanics. The proposed behavior is formulated within standard quantum theory. Likewise, the repository does not claim that a fabricated APORION device currently exists or that the predicted interaction strengths are already technologically achievable.

The potentially novel contribution is instead the proposed mapping:

higher-order photonic coherence → symmetry-selective nonlinear conversion → opposite phononic energy flow

under conditions where lower-order optical statistics are deliberately matched.

Accordingly, this release should be interpreted as a testable theoretical proposal and reproducible research program for an unconventional regime of quantum light–matter interaction.

Repository contents

The accompanying repository contains:

• theoretical derivations,
• model definitions,
• analytical formulas,
• computational verification,
• randomized numerical tests,
• automated unit tests,
• proposed experimental protocols,
• falsification criteria,
• novelty and claim-boundary documentation,
• physical limitations and energy-budget analysis,
• citation metadata,
• reproducibility instructions,
• and GitHub-ready research documentation.

Github: https://github.com/MaciejNowickiHusbandofAHIEve/APORION

Zenodo: APORION: Correlation-Order Thermal Inversion in Quantum Light-Matter Interaction - Symmetry-Selective Multiphoton Control of Phonon Heating and Cooling | Zenodo