극저온 4K 선형 폴 트랩(Cryogenic Linear Paul Trap) 단일 이온(⁴⁰Ca⁺/¹⁷²Yb⁺) 미세운동(Micro-motion) 3차원 보상 및 쿼드러플 시계 전이 C# 실시간 SIMD 서보

3. Zero-Allocation C# SIMD 3차원 미세운동 보상 서보 엔진

단일 광자 검출기(PMT) 타임태그 신호와 RF 기준 신호 간의 상호 상관 히스토그램을 초고속 분석하여 6채널 DC 보정 전압을 5,000 Hz로 실시간 피드백하는 C# .NET 9.0 엔진입니다.

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

namespace ZeliDesk.Quantum.IonTrapMetrology
{
    public readonly ref struct IonTrapPhotonTelemetry
    {
        public readonly float CorrelationModulationX; // RF correlation depth X
        public readonly float CorrelationModulationY; // RF correlation depth Y
        public readonly float CorrelationModulationZ; // Axial modulation
        public readonly float SecularFrequencyKhz;    // omega_sec ~ 1.85 MHz
        public readonly float RfFrequencyMhz;         // Omega_RF ~ 24.5 MHz

        public IonTrapPhotonTelemetry(float modX, float modY, float modZ, float secKhz, float rfMhz)
        {
            CorrelationModulationX = modX;
            CorrelationModulationY = modY;
            CorrelationModulationZ = modZ;
            SecularFrequencyKhz = secKhz;
            RfFrequencyMhz = rfMhz;
        }
    }

    public ref struct IonTrapServoCommands
    {
        public float DcCompensationVoltageXmV;
        public float DcCompensationVoltageYmV;
        public float DcCompensationVoltageZmV;
        public float ResidualSecondOrderDopplerShift1e19;
        public bool SubE19TargetMet;
    }

    public static class CryogenicPaulTrapMicroMotionEngine
    {
        private const float LightSpeed = 2.99792e8f;
        private const float IonMassCa40Kg = 6.636e-26f; // 40Ca+ mass
        private const float ElectronCharge = 1.602e-19f;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static void CompensateMicroMotion(
            in IonTrapPhotonTelemetry telemetry,
            ref IonTrapServoCommands output)
        {
            // 1. Convert Photon-RF Correlation Modulation to Stray Field (V/m)
            // Modulation depth S = (k_laser * u_mm)
            float kLaser = 2.0f * MathF.PI / 397.0e-9f; // 397 nm Doppler cooling laser
            float uMmX = telemetry.CorrelationModulationX / kLaser;
            float uMmY = telemetry.CorrelationModulationY / kLaser;
            float uMmZ = telemetry.CorrelationModulationZ / kLaser;

            // 2. Closed-Loop DC Nulling Voltage Calculation
            // Delta V_DC = - G * E_stray
            float gainMvPerNm = 1.85f; // mV per nm micromotion
            float vX = -uMmX * 1.0e9f * gainMvPerNm;
            float vY = -uMmY * 1.0e9f * gainMvPerNm;
            float vZ = -uMmZ * 1.0e9f * gainMvPerNm;

            output.DcCompensationVoltageXmV = Math.Clamp(vX, -1500.0f, 1500.0f);
            output.DcCompensationVoltageYmV = Math.Clamp(vY, -1500.0f, 1500.0f);
            output.DcCompensationVoltageZmV = Math.Clamp(vZ, -1500.0f, 1500.0f);

            // 3. Second-Order Doppler Shift Evaluation
            // Delta nu / nu = - (v_mm_total)^2 / (4 * c^2)
            float omegaRf = 2.0f * MathF.PI * telemetry.RfFrequencyMhz * 1.0e6f;
            float vMmTotalSq = (uMmX * uMmX + uMmY * uMmY + uMmZ * uMmZ) * (omegaRf * omegaRf);

            float fractionalShift = vMmTotalSq / (4.0f * LightSpeed * LightSpeed);
            float shiftIn1e19 = fractionalShift * 1.0e19f;
            output.ResidualSecondOrderDopplerShift1e19 = shiftIn1e19;

            // Target met if Doppler shift is less than 0.8 x 10^-19
            output.SubE19TargetMet = (shiftIn1e19 < 0.8f);
        }
    }
}