Dispersive regime of multiphoton qubit-oscillator interactions
Bibliographic record
Abstract
The dispersive regime of $n$-photon qubit-oscillator interactions is analyzed using Schrieffer-Wolff perturbation theory. Effective Hamiltonians are derived up to the second order in the perturbation parameters. These effective descriptions reveal higher-order qubit-oscillator cross-Kerr and oscillator self-Kerr terms. The cross-Kerr term combines a qubit Pauli operator with an $n$-degree polynomial in the oscillator photon number operator, while the self-Kerr term is an $(n\ensuremath{-}1)$-degree polynomial in the oscillator photon number operator. In addition to the higher-order Kerr terms, a qubit-conditional $2n$-photon squeezing term appears in the effective non-rotating-wave-approximation Hamiltonian. Furthermore, perturbation theory is applied to the case of multiple qubits coupled to a shared oscillator. A photon-number-dependent qubit-qubit interaction emerges in this case, which can be leveraged to tune the effective multiqubit system parameters using the oscillator state. Results for the converse setup of multiple oscillators and a single qubit are also derived. In this case, a qubit-conditional oscillator-oscillator nonlinear interaction is found. The spectral instabilities plaguing multiphoton qubit-oscillator models are carefully treated by introducing stabilizing higher-order terms in the Hamiltonian. The stabilizing terms preserve low-photon subspaces, avoid negative infinite energies, and facilitate reliable numerical calculations used to validate analytical predictions. The effective descriptions developed here offer a simple and intuitive physical picture of dispersive multiphoton qubit-oscillator interactions that can aid in the design of implementations harnessing various nonlinear effects.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".