Beyond transcoherent states: Field states for effecting optimal coherent rotations on single or multiple qubits
Bibliographic record
Abstract
Semiclassically, laser pulses can be used to implement arbitrary transformations on atomic systems; quantum mechanically, residual atom-field entanglement spoils this promise. Transcoherent states are field states that fix this problem in the fully quantized regime by generating perfect coherence in an atom initially in its ground or excited state. We extend this fully quantized paradigm in four directions: First, we introduce field states that transform an atom from its ground or excited state to any point on the Bloch sphere without residual atom-field entanglement. The best strong pulses for carrying out rotations by angle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B8;</mml:mi></mml:math> are are squeezed in photon-number variance by a factor of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mi>&#x03B8;</mml:mi></mml:math>. Next, we investigate implementing rotation gates, showing that the optimal Gaussian field state for enacting a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B8;</mml:mi></mml:math> pulse on an atom in an arbitrary, unknown initial state is number squeezed by less: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mstyle displaystyle="false" scriptlevel="0"><mml:mfrac><mml:mi>&#x03B8;</mml:mi><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:math>. Third, we extend these investigations to fields interacting with multiple atoms simultaneously, discovering once again that number squeezing by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mstyle displaystyle="false" scriptlevel="0"><mml:mfrac><mml:mi>&#x03C0;</mml:mi><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:math> is optimal for enacting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mstyle displaystyle="false" scriptlevel="0"><mml:mfrac><mml:mi>&#x03C0;</mml:mi><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:math> pulses on all of the atoms simultaneously, with small corrections on the order of the ratio of the number of atoms to the average number of photons. Finally, we find field states that best perform arbitrary rotations by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B8;</mml:mi></mml:math> through nonlinear interactions involving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>m</mml:mi></mml:math>-photon absorption, where the same optimal squeezing factor is found to be <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mi>&#x03B8;</mml:mi></mml:math>. Backaction in a wide variety of atom-field interactions can thus be mitigated by squeezing the control fields by optimal amounts.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".