Scientific sources - Case39
References
Paul A. Albrecht, Eric W. Fischer, Tillmann Klamroth, and Peter Saalfrank. 2025. High-harmonic generation under electronic strong coupling: A time-dependent combined quantum electrodynamics/quantum chemistry study. arXiv, 2507.21687. Source. Version 1.
Atomic DSE-inclusive cavity-HHG branch only, with coupled ground states, norm-loss-aware spectra and electron-mediated cavity response. The disputed photon transient and conflicting Fig. 3(b) parameter annotations are excluded as quantitative targets; molecular results are context only.
Criterion-to-source crosswalk
| Criteria | Source locations, scientific use and limits |
|---|---|
| F1, M2 | Albrecht et al. (2025), article pp. 4–7, Eqs. (1)–(7), (11)–(16). Electron-only drive, bilinear cavity coupling and positive dipole self-energy, including the atomic rather than molecular model. |
| F2 | Article pp. 7–8, Sec. III A; p. 12, Sec. IV A opening paragraph. Coupled field-free ground state and two-coordinate grid propagation; physical norm loss and conditional coordinate expectations. |
| F3 | Article p. 6, Eqs. (8)–(9) and no-renormalization paragraph. HHG complex transform and spectrum; the source fitted endpoint is an example, not a unique threshold or mandatory fitting procedure. |
| F4 | Article p. 6, Eq. (10); pp. 12–16, Sec. IV A, Figs. 2(a,b), 3(a,b). Same-state electronic/cavity responses and energy partition. The task does not require the disputed absolute photon peak or its unique estimator. |
| O1, I1, M1 | Article pp. 12–14, Sec. IV A, Fig. 1(a,b) and discussion of the 5th–9th harmonics. Case-resolved high-order/cutoff suppression and lower-order exceptions; fixed-coupling frequency comparisons must not be conflated with changing coupling. |
| O2, I2, M3 | Article pp. 13–16, Fig. 2(a,b), Fig. 3(a) and adjacent persistent/transient discussion. Electronic restriction and cavity excitation under electron-only drive; normalized coordinate expectations differ from unrenormalized HHG production. |
| O3, I3, M4 | Article pp. 14–16, Fig. 3(b), energy-decomposition paragraphs; Eqs. (1), (3), (5), (6), (14)–(16). Electron-mediated exchange is physically entailed by the electron-only drive and interaction term. Source Fig. 3(b) has conflicting parameter labels/caption; it is qualitative mechanism context, never a unique numerical target. |
| M5, M7 | Article pp. 12–16, Figs. 1(a,b), 2(a,b), 3(a,b), Sec. IV A. Task-defined synthesis of case-resolved spectra, DSE restriction and exchange; no universal one-parameter monotonic law follows from these finite cases. |
| M6, V2 | Article pp. 4–7, Eqs. (1), (3), (5), (6), (14)–(16); pp. 13–16, Sec. IV A. Hamiltonian terms entail discriminating controls against direct cavity driving or DSE omission. Alternative/intervention requirements are task-defined, not a prescribed source control plot. |
| V1 | Article p. 6, Eq. (8), window and norm-loss paragraphs; pp. 7–8, grid-model boundary treatment. Common-scale and norm-loss-aware spectral reliability; no mandatory source Hann window, grid or endpoint estimator. |
| V3 | Article pp. 5, 7–8, coupling-parameter qualification and Sec. III A; pp. 9–12, Sec. III B as contrast. One-dimensional single-electron single-mode atomic scope; molecular QED-CIS and realistic experimental-yield claims are not established by this task. |
Formula and convention notes
For the atomic coordinate $z$, cavity coordinate $x_c$ and $\hbar=1$ conventions, $H=H_e+H_c+H_{\rm int}+H_{\rm dse}+zF(t)$, $H_e=p_z^2/2-Z/(|z|+\eta)$, $H_c=p_c^2/2+\omega_c^2x_c^2/2$, $H_{\rm int}=-\sqrt{2\omega_c}g_czx_c$, $H_{\rm dse}=g_c^2z^2/\omega_c$ (Eqs. (11), (14)–(16)). $\eta$ regularizes the cusp; $g_c$ is coupling, $\omega_c$ cavity frequency and $F$ the electron-only pulse. The DSE is a positive confining term, not an optional numerical adjustment.
With $N(t)=\langle\Psi|\Psi\rangle$, conditional coordinates use $\langle z\rangle/N$ and $\langle x_c\rangle/N$ when declared, while source HHG uses the norm-loss-aware dipole $\mu_z(t)=-\langle\Psi|z|\Psi\rangle$ without propagation renormalization: $\mathcal A(\Omega)=\int_0^{t_f}w(t)\ddot\mu_z(t)e^{-i\Omega t}dt$, $I(\Omega)\propto|\mathcal A|^2$ (Eq. (8), Sec. IV A). Independent per-curve normalization is not equivalent for common-scale spectral comparisons.
Term energies satisfy $E_{\rm tot}=E_e+E_c+E_{\rm int}+E_{\rm dse}$ under the same expectation/norm convention. Their timing and exchange, or a functionally equivalent causal control, test electron-mediated mode excitation. The source Eq. (10) photon expression and Fig. 3(a) absolute transient are not imposed as unique scoring targets; the stated task permits unambiguous coordinate/energy observables instead.
Scope of the source anchors
Source examples verify physical identity and robust structure; their numerical samples, plotting conventions and panel layout are not compulsory candidate deliverables. Reporting, reconstructibility, evidence attribution, conditional validation and Research Closure are examination-defined obligations, not additional results asserted by the article. A derivation or physical entailment is identified as such rather than presented as a directly printed source formula.