Multiphoton Laguerre polynomial state as minimum uncertainty states of intensity-dependent squeezing
Bibliographic record
Abstract
For a general multiphoton annihilation operator, F = f(N)ap, where N = a†a, we find the explicit form of an operator, G†, which satisfies [F, G†] = 1. Based on the nonlinear realization of the SU(1,1) Lie algebra whose generators are [Formula: see text], [Formula: see text], and R0 = [N/p] + 1/2. We introduce the concept of intensity-dependent multiphoton squeezing and find that the state Lm(–yR†)|j⟩, 0 ≤ j ≤ p, where Lm(x) is a Laguerre polynomial, is a minimum uncertainty state for intensity-dependent multiphoton squeezing. We also construct the phase states for multiphoton operator, which turn out to be SU(1,1) generalized coherent states. Additionally, we show that the photon-added coherent state |α, m⟩ (m is a non-negative integer), which can be interpreted as a nonlinear coherent state, can be expressed as [Formula: see text] in the whole Fock space.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".