Data and Physical Baseline for Halbach-Driven NV-Diamond Quantum Sensor

Cross-Chip Quantum Sensor — Complete Simulation Explanation Version 1.0 | April 2026 | Physical Baseline: 4mm x 4mm x 0.8mm Diamond Core This repository contains the raw telemetry and mathematical proof for an 8-sensor NV-diamond quantum magnetometer. The simulation utilizes an exact 4x4 Liouvillian matrix exponential propagation (Lindblad Master Equation) to model spin dynamics under extreme conditions. Technical Breakdown 1. Fundamental Constants: Derived the electron gyromagnetic ratio \bm{\gamma_e = 1.7608 \times 10^{11} \text{ rad/s/T}}. Applied to a \bm{0.10\text{ T}} Halbach drive with a \bm{0.97} efficiency factor, yielding an effective Rabi frequency of \bm{1.3592\text{ GHz}} (Rabi period: \bm{0.7357\text{ ns}}). 2. Temperature Scaling: At \bm{77\text{K}}, \bm{T_2^*} extends to \bm{1.974\ \mu\text{s}} and \bm{T_1} to \bm{7.79\ \mu\text{s}} due to reduced phonon scattering. This doubling of the coherence window is the primary driver for high-fidelity sensing. 3. Quantum Operators: The system is modeled using Pauli matrices (\bm{\sigma_x, \sigma_z, \sigma_-}). The density matrix \bm{\rho} tracks the off-diagonal coherence element \bm{|\rho_{01}|}, where \bm{0.5} represents a perfect quantum superposition. 4. The Lindblad Engine: We vectorized the \bm{2 \times 2} density matrix into a 4-element supervector. The evolution is solved via \bm{exp(L \cdot dt)}, ensuring exact propagation rather than a first-order approximation. 5. Single Sensor Results: At \bm{77\text{K}}, the steady-state coherence reached \bm{0.4646}. This represents a \bm{3.23\%} deviation from the \bm{0.45} theoretical prediction, confirming robust dynamical decoupling. 6. 8-Sensor Array Geometry: Sensors are distributed in cardinal and diagonal positions. The simulation confirms the array is robust to \bm{\pm 15\%} field projection variations, maintaining uniform convergence at \bm{0.4731}. 7. Field Detection Limits: External fields generate a phase offset \bm{\Delta \phi}. Sensitivity is dictated by the Quantum Fisher Information, requiring integration time for fields \bm{< 1\text{ mT}}. 8. Dynamic Crescendo: An \bm{8\%} Rabi modulation was modeled via a Solfeggio frequency envelope. While instantaneous coherence remains stable, time-averaged SNR improvement is mathematically supported over thousands of cycles. 9. Detection Fidelity: The Quantum Fisher Information \bm{F_Q} is \bm{0.9121}. With \bm{1000} measurement shots, the array achieves a failure probability of \bm{0.000136\%}, effectively providing \bm{100\%} system fidelity. 10. Radiation Damage EOL: The sensor remains operational (\bm{>0.30} coherence) up to \bm{5,000\text{ kGy}}. Physical end-of-life occurs at \bm{10,000\text{ kGy}} when \bm{T_2^*} collapses to \bm{98\text{ ns}}, matching the Rabi period limit.