극저온 광학 쌍극자 트랩(ODT) 기반 보스-아인슈타인 응축(BEC) 양자 와류(Quantized Vortex) 격자 형성 피에조 위상 제어 C# SIMD 엔진

3. Zero-Allocation C# SIMD 양자 와류 격자 서보 구현

흡수 이미징 카메라의 와류 코어 점군 좌표를 10,000 Hz로 실시간 분석하여 AOD 회전 교반 레이저의 주파수와 위상을 피드백하는 C# .NET 9.0 엔진입니다.

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

namespace ZeliDesk.Quantum.BecVortexLattice
{
    public readonly ref struct BecImagingTelemetry
    {
        public readonly int DetectedVortexCount;       // Count of vortex cores
        public readonly float CondensateRadiusMicrons; // Thomas-Fermi radius
        public readonly float TrapStirringFreqHz;      // Rotation freq Omega / 2pi
        public readonly float MeasuredHexagonalOrder;  // Psi_6 structural order
        public readonly float CondensateTempNanoK;     // Bath temp ~ 35 nK

        public BecImagingTelemetry(int count, float rTf, float fStir, float psi6, float tempNk)
        {
            DetectedVortexCount = count;
            CondensateRadiusMicrons = rTf;
            TrapStirringFreqHz = fStir;
            MeasuredHexagonalOrder = psi6;
            CondensateTempNanoK = tempNk;
        }
    }

    public ref struct VortexServoCommands
    {
        public float TargetAodStirringFreqHz;
        public float TrapEllipticityEpsilon;
        public float LatticeConstantMicrons;
        public float FeynmanVortexDeficit;
        public bool AbrikosovLatticeCrystallized;
    }

    public static class OpticalDipoleTrapVortexEngine
    {
        private const float Rubidium87MassKg = 1.443e-25f;
        private const float Hbar = 1.05457e-34f;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static void RegulateVortexLattice(
            in BecImagingTelemetry telemetry,
            ref VortexServoCommands output)
        {
            float omegaRad = 2.0f * MathF.PI * telemetry.TrapStirringFreqHz;

            // 1. Theoretical Feynman Equilibrium Vortex Density & Count
            // n_v = m * Omega / (pi * hbar)
            float nvPerM2 = (Rubidium87MassKg * omegaRad) / (MathF.PI * Hbar);
            float rM = telemetry.CondensateRadiusMicrons * 1.0e-6f;
            float areaM2 = MathF.PI * rM * rM;
            float expectedVortices = nvPerM2 * areaM2;

            output.FeynmanVortexDeficit = expectedVortices - telemetry.DetectedVortexCount;

            // 2. Equilibrium Triangular Lattice Spacing d_vortex
            float dVortexM = MathF.Sqrt((2.0f * Hbar) / (MathF.Sqrt(3.0f) * Rubidium87MassKg * MathF.Max(1.0f, omegaRad)));
            output.LatticeConstantMicrons = dVortexM * 1.0e6f;

            // 3. Closed-Loop Ellipticity & Frequency Servo
            // Once crystallized (Psi_6 > 0.85), drop ellipticity epsilon -> 0 to prevent shear
            float psi6 = telemetry.MeasuredHexagonalOrder;
            if (psi6 > 0.85f)
            {
                output.TrapEllipticityEpsilon = 0.005f; // Nearly circular symmetric trap
                output.TargetAodStirringFreqHz = telemetry.TrapStirringFreqHz; // Steady rotation lock
                output.AbrikosovLatticeCrystallized = true;
            }
            else
            {
                // Active stirring to nucleate more vortices
                float epsilonDemand = 0.085f * (1.0f - psi6);
                output.TrapEllipticityEpsilon = Math.Clamp(epsilonDemand, 0.01f, 0.12f);
                output.TargetAodStirringFreqHz = telemetry.TrapStirringFreqHz + 0.15f; // Accelerate stirring
                output.AbrikosovLatticeCrystallized = false;
            }
        }
    }
}