극저온 초전도-나노기계 공진기(Quantum NEMS) 광역학 양자 압축상태(Ponderomotive Squeezing) 제어 및 영점 요동 피드백 냉각 C# SIMD 엔진

3. Zero-Allocation C# SIMD 양자 압축 서보 엔진

고속 평형 호모다인 I/Q 샘플을 입력받아 피에조 전압 위상 천이 및 능동 댐핑 구동력을 20,000 Hz로 실시간 연산하는 C# .NET 9.0 엔진입니다.

using System;
using System.Runtime.CompilerServices;
using System.Runtime.Intrinsics;
using System.Runtime.Intrinsics.X86;

namespace ZeliDesk.Quantum.Optomechanics
{
    public readonly ref struct HomodyneRawTelemetry
    {
        public readonly float QuadratureI;          // In-phase signal
        public readonly float QuadratureQ;          // Quadrature signal
        public readonly float MechanicalFreqMhz;    // e.g. 10.45 MHz
        public readonly float CavityLinewidthMhz;   // kappa / 2pi ~ 2.5 MHz
        public readonly float CryostatTempMillikelvin; // 12 mK

        public HomodyneRawTelemetry(float i, float q, float mechMhz, float kappaMhz, float tempMilliK)
        {
            QuadratureI = i;
            QuadratureQ = q;
            MechanicalFreqMhz = mechMhz;
            CavityLinewidthMhz = kappaMhz;
            CryostatTempMillikelvin = tempMilliK;
        }
    }

    public ref struct SqueezingServoCommands
    {
        public float HomodyneLoPhaseShiftRad;
        public float ColdDampingFeedbackGain;
        public float SqueezingLevelDb;
        public float MechanicalThermalOccupancyNth;
        public bool BelowStandardQuantumLimit;
    }

    public static class QuantumNemsSqueezingServoEngine
    {
        private const float MechResonanceBaseHz = 10.45e6f;
        private const float IntrinsicMechLinewidthHz = 120.0f; // Q ~ 87,000

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static void ProcessQuantumFeedback(
            in HomodyneRawTelemetry telemetry,
            ref SqueezingServoCommands output)
        {
            // 1. Calculate Instantaneous Variance of Quadratures
            float i = telemetry.QuadratureI;
            float q = telemetry.QuadratureQ;

            // 2. Optimum Homodyne Squeezing Angle Estimation
            // theta_opt = 0.5 * atan2(-2 * Cov(I,Q), Var(Q) - Var(I))
            float thetaOpt = 0.5f * MathF.Atan2(-2.0f * (i * q), (q * q) - (i * i));
            output.HomodyneLoPhaseShiftRad = thetaOpt;

            // 3. Noise Variance in Squeezed Quadrature
            float cosT = MathF.Cos(thetaOpt);
            float sinT = MathF.Sin(thetaOpt);
            float xSqueezed = i * cosT + q * sinT;
            float varianceSqueezed = xSqueezed * xSqueezed;

            // Shot-Noise Vacuum Reference Normalized to 1.0
            float shotNoiseRef = 0.050f; // calibrated shot noise power
            float normalizedNoise = varianceSqueezed / shotNoiseRef;

            // Squeezing in dB: -10 * log10(variance / shot_noise)
            float squeezingDb = -10.0f * MathF.Log10(MathF.Max(0.01f, normalizedNoise));
            output.SqueezingLevelDb = squeezingDb;
            output.BelowStandardQuantumLimit = (squeezingDb > 0.0f);

            // 4. Cold-Damping Feedback Force Computation
            // Active damping proportional to velocity (d xSqueezed / dt)
            float kFeedback = Math.Clamp(squeezingDb * 0.15f + 0.5f, 0.1f, 3.0f);
            output.ColdDampingFeedbackGain = kFeedback;

            // 5. Thermal Occupancy Number n_th under 12 mK cryostat
            // n_th = k_B * T / (hbar * Omega_m)
            float tempK = telemetry.CryostatTempMillikelvin * 1.0e-3f;
            float hbarOmega = 1.054e-34f * (2.0f * MathF.PI * MechResonanceBaseHz);
            float nThermal = (1.38e-23f * tempK) / hbarOmega;
            output.MechanicalThermalOccupancyNth = nThermal;
        }
    }
}