PROTOCOL_Phase1_Tabletop.md

Experimental Protocol: Phase 1 — Tabletop Validation

John Bollinger | December 2025
Framework #6 — Coherence Telephone

---

Objective: Detect topology-specific, non-classical correlation between E·B modulation and coherence-sensitive observables, under conditions that rule out conventional electromagnetic coupling.

---

Core Hypothesis

Two topologically-matched systems (Chern number 𝒞=3) will exhibit a measurable correlation in response to E·B modulation that is absent when their topologies are mismatched.

The kill shot: Same signal for matched AND mismatched = classical leakage (theory fails).

---

1. Experimental Schematic

┌──────────────────────────────────────────────────────────────────┐
│                    SINGLE DILUTION REFRIGERATOR                   │
│                         (Base T < 20 mK)                          │
├──────────────────────────────────────────────────────────────────┤
│                                                                   │
│   ┌─────────────────┐              ┌─────────────────┐           │
│   │   SOURCE NODE   │              │  DETECTOR NODE  │           │
│   │      (A)        │   SHIELDED   │       (B)       │           │
│   │                 │   BARRIER    │                 │           │
│   │  ┌───────────┐  │      ║       │  ┌───────────┐  │           │
│   │  │  𝒞 = 3    │  │      ║       │  │  𝒞 = 3    │  │           │
│   │  │  Array    │  │      ║       │  │  Array    │  │           │
│   │  └─────┬─────┘  │      ║       │  └─────┬─────┘  │           │
│   │        │        │      ║       │        │        │           │
│   │  ┌─────▼─────┐  │      ║       │  ┌─────▼─────┐  │           │
│   │  │ Microwave │  │      ║       │  │  Readout  │  │           │
│   │  │  Cavity   │  │      ║       │  │   Qubit   │  │           │
│   │  └─────┬─────┘  │      ║       │  └─────┬─────┘  │           │
│   │        │        │      ║       │        │        │           │
│   │  ┌─────▼─────┐  │      ║       │  ┌─────▼─────┐  │           │
│   │  │E·B Drive  │  │      ║       │  │ Resonator │  │           │
│   │  │ (ω_d, θ₁) │  │      ║       │  │ (Readout) │  │           │
│   │  └───────────┘  │      ║       │  └───────────┘  │           │
│   │                 │      ║       │                 │           │
│   └────────┬────────┘      ║       └────────┬────────┘           │
│            │               ║                │                    │
│            └───────────────╫────────────────┘                    │
│                            ║                                     │
│                    ┌───────▼───────┐                             │
│                    │  CONTROL &    │                             │
│                    │    DATA       │                             │
│                    │ ACQUISITION   │                             │
│                    └───────────────┘                             │
│                                                                   │
└──────────────────────────────────────────────────────────────────┘

Key Design Principle: Both nodes in separately shielded compartments within the same cryostat. Millikelvin temperatures with precise isolation control.

---

2. Component Specifications

2.1 Topological Qubit Arrays (Source A & Detector B)

Parameter	Specification	Notes
Platform	Superconducting qubit array	Google Sycamore / Quantinuum H2 techniques
Topology	Tunable Chern insulator	In-situ tunable to 𝒞 = 2, 3, 4
Verification	Quantized Hall conductance	Confirms topological phase
Coherence	T₂* > 50 μs	State-of-the-art transmon

Critical requirement: Arrays must be tunable in-situ between Chern numbers for control experiments.

2.2 Source Node A: Modulation Cavity & Drive

Component	Specification	Purpose
Cavity	High-Q 3D microwave, ω_c/2π ~ 6-8 GHz	Resonant enhancement
E·B Modulator	Orthogonal antenna/coil pair	Crossed E and B fields
Drive signal	Coherent tone at ω_d	δθ(t) = θ₁ cos(ω_d t)
Control knob	θ₁ amplitude	Primary experimental variable

2.3 Detector Node B: Readout System

Component	Specification	Purpose
Readout qubit	High-coherence transmon (T₂* > 50 μs)	Frequency shift sensor
Coupling	Dispersive to 𝒞=3 array	Coherence field → qubit shift
Resonator	Standard readout circuit	QND measurement
Measurement	Ramsey interferometry	Precise frequency determination

2.4 Shared Infrastructure

System	Specification	Purpose
Cryostat	Dilution refrigerator, T < 20 mK	Quantum coherence
Magnetic shield	Cryoperm + superconducting Al	Field isolation
RF shield	Separate enclosures per node	EM isolation
Control	Phase-locked μW generators	Timing precision
DAQ	Ultra-low-noise digitizers	Signal acquisition

---

3. Experimental Sequence

Step 1: Calibration & Characterization

┌─────────────────────────────────────────────────────────────┐
│  1.1  Cool system to base temperature (< 20 mK)             │
│  1.2  Tune BOTH arrays to 𝒞 = 3                             │
│  1.3  Verify topology via transport or spectroscopy         │
│  1.4  Calibrate E·B drive amplitude θ₁ (radians)            │
│  1.5  Calibrate dispersive shift χ₀ (qubit + array ground)  │
│  1.6  Measure noise floor (no drive)                        │
└─────────────────────────────────────────────────────────────┘

Step 2: Primary Experiment (Matched Topology)

Configuration: Source 𝒞 = 3, Detector 𝒞 = 3 (MATCHED)

For shot i = 1 to N_shot:
    
    2.1  INITIALIZE
         └─ Prepare both arrays in ground state
         └─ Reset readout qubit
    
    2.2  MODULATE
         └─ Apply E·B drive δθ(t) = θ₁ cos(ω_d t) at Node A
         └─ Duration: T_pulse = 1-10 μs
    
    2.3  MEASURE
         └─ Ramsey sequence on readout qubit (Node B)
         └─ Extract frequency shift χᵢ
    
    2.4  RECORD
         └─ Store (timestamp, θ(t), χᵢ)

Accumulate N_shot = 10⁴ to 10⁶ measurements

Step 3: Control Experiment (Mismatched Topology)

Configuration: Source 𝒞 = 2, Detector 𝒞 = 3 (MISMATCHED)

    3.1  Re-tune Source Node A to 𝒞 = 2
         └─ Detector Node B remains at 𝒞 = 3
    
    3.2  Repeat EXACTLY the same sequence as Step 2
    
    3.3  Expected result (if hypothesis correct):
         └─ Correlated shift χ(t) → ZERO (noise floor only)

Step 4: Supplementary Controls

Control	Procedure	Purpose
4.1 RF Shunting	Disconnect all μW lines to Node B during modulation	Rule out EM crosstalk
4.2 Frequency Detuning	Set ω_d far off any resonance	Rule out cavity coupling
4.3 Thermal Test	Replace coherent drive with heating pulse	Rule out thermal effects
4.4 Time Reversal	Swap source/detector roles	Verify symmetry

---

4. Data Analysis

4.1 Raw Data Structure

Data matrix D[i, t]:
    i = shot index (1 to N_shot)
    t = time bin
    
    D[i, t] = {
        θ(t)  : Drive envelope at time t
        χᵢ(t) : Measured frequency shift
        config: Topology configuration (3-3 or 2-3)
    }

4.2 Primary Metric: Cross-Correlation

Compute cross-correlation between drive and response:

$$C(\tau) = \frac{\langle \theta(t) \cdot \chi(t+\tau) \rangle}{\sigma_\theta \sigma_\chi}$$

Predicted outcomes:

Configuration	C(0) Prediction	Physical Meaning
𝒞=3 ↔ 𝒞=3 (matched)	Strong peak	Topology-mediated coupling
𝒞=2 ↔ 𝒞=3 (mismatched)	Zero (noise)	No coupling (different channel)

4.3 Secondary Metrics

Metric	Formula	Purpose
Selectivity ratio	S = C(0)_matched / σ_mismatched	Topology discrimination
SNR	χ_peak / σ_noise	Detection significance
p-value	From null hypothesis test	Statistical confidence

---

5. Success Criteria

5.1 Binary Success Conditions

The experiment is a SUCCESS if ALL of the following are true:

Criterion	Threshold	Meaning
Matched signal	p-value < 10⁻⁵ (≥ 4.4σ)	Real correlation detected
Control null	p-value > 0.05	No signal in mismatched case
Selectivity	S > 5	Clear topology discrimination
Reproducibility	3+ independent runs	Not a statistical fluke

5.2 Failure Modes

The experiment FAILS (falsifies hypothesis) if:

Failure Mode	Observation	Interpretation
Classical leakage	Equal signal in matched AND mismatched	EM crosstalk, not topology
Null result	No signal in either condition	Coupling too weak or mechanism wrong
Inconsistent	Non-reproducible results	Systematic error

---

6. Outcome Interpretation Matrix

Matched (3-3)	Mismatched (2-3)	Interpretation	Next Step
✅ Strong	❌ Zero	HYPOTHESIS SUPPORTED	Proceed to Phase 2
✅ Strong	✅ Strong	CLASSICAL LEAKAGE	Improve shielding or abandon
❌ Zero	❌ Zero	NULL RESULT	Increase sensitivity or abandon
❌ Zero	✅ Strong	ANOMALOUS	Investigate systematic error

---

7. Timeline & Resources

7.1 Personnel

Role	Responsibility	FTE
PI (Theorist)	Framework, analysis, interpretation	0.5
Experimentalist	Cryogenics, qubit fabrication, measurement	1.0
Technician	Fabrication, cooldown support	0.5
Postdoc/Student	Data acquisition, analysis	1.0

7.2 Timeline

Month 1-3:   DESIGN & PROCUREMENT
             └─ Finalize component specs
             └─ Procure/fabricate arrays and cavities
             └─ Prepare control software

Month 4-6:   INTEGRATION & CALIBRATION
             └─ Cooldown and system characterization
             └─ Tune arrays to target Chern numbers
             └─ Calibrate all drives and readout

Month 7-9:   DATA COLLECTION
             └─ Primary matched-topology experiment
             └─ Control experiments (mismatched, shunted, etc.)
             └─ Statistical accumulation

Month 10-12: ANALYSIS & PUBLICATION
             └─ Data analysis and interpretation
             └─ Manuscript preparation
             └─ Peer review submission

7.3 Facility Requirements

Requirement	Specification	Potential Sites
Dilution refrigerator	< 20 mK base, advanced μW control	University labs, NHMFL
Qubit fabrication	Transmon + tunable arrays	IBM, Google, academic fabs
Shielding	Multi-layer magnetic + RF	Standard cryogenic practice

---

8. Risk Assessment

Risk	Probability	Impact	Mitigation
Insufficient isolation	Medium	High	Multiple shielding layers, separate enclosures
Topology not tunable	Low	Critical	Pre-characterize arrays before cooldown
Signal below noise	Medium	High	Optimize photon number n, integration time
Qubit decoherence	Low	Medium	Use state-of-the-art fabrication
Systematic errors	Medium	Medium	Extensive control experiments

---

9. Deliverables

9.1 Primary Deliverable

Dataset: Cross-correlation C(0) for matched vs. mismatched topology configurations, with full statistical analysis.

9.2 Publication

Title: "Search for Topology-Mediated Coherence Field Coupling in a Tunable Chern Insulator Array"

Structure:

1. Introduction: Coherence field hypothesis and predictions
2. Theory: Signal formula χ = (α/2π)(g₀²/Δ)(gθ₁/m)n
3. Methods: This protocol
4. Results: Cross-correlation analysis
5. Discussion: Interpretation and implications
6. Conclusion: Support/refutation of hypothesis

9.3 If Successful → Phase 2

Phase 2 objective: Increase spatial separation to separate cryostats (meters apart) while maintaining millikelvin temperatures.

Phase 3 objective: Earth-Moon test for faster-than-light correlation (the ultimate kill shot).

---

10. Connection to Theoretical Framework

This protocol tests the predictions from PREDICTIONS_SIGNAL_STRENGTH.md:

Prediction	Protocol Test	Success Criterion
P1: Topology addressing	Step 2 vs Step 3	Signal only in matched case
P2: Linear scaling	Vary θ₁	χ ∝ θ₁
P3: Resonance	Sweep ω_d	Peak at ω_d = m
P5: C² scaling	Vary Chern number	Signal ∝ 𝒞²

---

11. Summary

The Experiment in One Sentence

Modulate E·B at a 𝒞=3 source, measure qubit frequency shift at a 𝒞=3 detector, and verify the signal vanishes when source is changed to 𝒞=2.

The Success Criterion in One Sentence

Strong correlation for matched topology (>4.4σ), zero correlation for mismatched topology (>5× selectivity).

The Kill Condition in One Sentence

Equal signal in both configurations = classical leakage = theory falsified.

---

Appendix A: Parameter Quick Reference

Parameter	Symbol	Typical Value	Units
Fine structure constant	α	1/137	—
Vacuum Rabi coupling	g₀/2π	50-200	MHz
Qubit-cavity detuning	Δ/2π	1-5	GHz
Drive amplitude	θ₁	0.1-0.5	rad
Photon number	n	10³-10⁶	—
Qubit dephasing time	T₂*	>50	μs
Base temperature	T	<20	mK
Chern number (matched)	𝒞	3	—
Chern number (control)	𝒞	2	—

---

Appendix B: Expected Signal Estimates

From PREDICTIONS_SIGNAL_STRENGTH.md:

g/m (rad⁻¹)	χ (Hz)	Integration	Feasibility
10⁻³	290	~120 ms	✅ Easy
10⁻⁴	29	~12 s	✅ Feasible
10⁻⁵	2.9	~20 min	✅ Doable
10⁻⁶	0.29	~1.4 days	⚠️ Hard
10⁻⁹	—	—	❌ Falsified

---

"This protocol turns equations into measurements. If it works, we've found something real. If it fails cleanly, we've learned something true."

— John Bollinger, December 2025