# -*- coding: utf-8 -*- """ Experimentul 3 — "Ghost Interference" (grupul Shih, 1995) Descris in documentul DIRD (DIA-08-1003-016), sectiunile IV-V, Fig. 2-4 si 6. O pereche de fotoni intricati in impuls (SPDC in BBO): fotonul "e" trece printr-o fanta dubla (sau simpla) si este detectat de D1 (punctual, fix); fotonul "o" merge direct si este scanat in pozitie de D2. Modelul foloseste propagatoare Fresnel de la un punct comun de nastere x_s in cristal (imaginea "desfasurata" Klyshko, Fig. 4), integrand numeric peste volumul sursei (efectul de "sursa groasa", Fig. 6): A(y1, x2) = suma_fante integrala dxs G(xs) * exp[ik((x_f - x_s)^2/2L1 + (y1 - x_f)^2/2Ld + (x2 - x_s)^2/2L2)] - IN COINCIDENTA cu D1 fix la y1: p(x2) = |A(y1, x2)|^2 -> franje "fantoma" - FARA coincidente (singles): suma peste toate y1 + fotonii ale caror perechi au fost absorbite de partile opace ale fantelor -> distributie neteda, fara franje. Reproduce Fig. 3 (pieptene / cocoasa) si complementaritatea coerenta-intricare (sectiunea V): franjele fantoma cer o sursa larga (intricare in impuls); o sursa ingusta (coerenta) le distruge — niciun regim nu pune franjele in "singles". """ import sys import numpy as np import tkinter as tk from tkinter import ttk import matplotlib matplotlib.use("TkAgg") from matplotlib.figure import Figure from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg LAM = 702e-6 # mm K = 2 * np.pi / LAM D_F = 0.4 # mm separare fante A_F = 0.08 # mm latime fanta LD = 400.0 # mm fante -> D1 L2 = 600.0 # mm cristal -> D2 X2 = np.linspace(-4, 4, 401) Y1G = np.linspace(-4, 4, 61) # pozitii D1 pentru integrarea "singles" FRAC_BLOCAT = 0.6 # fractiunea perechilor pierdute pe partile opace (calitativ) def calculeaza(nr_fante, w_s, L1): xs = np.linspace(-3 * w_s, 3 * w_s, 401) G = np.exp(-xs ** 2 / (2 * w_s ** 2)) G /= G.sum() centre = [0.0] if nr_fante == 1 else [-D_F / 2, D_F / 2] xf = np.concatenate([c + np.linspace(-A_F / 2, A_F / 2, 9) for c in centre]) F2 = np.exp(1j * K * (xf[:, None] - xs[None, :]) ** 2 / (2 * L1)) # [xf, xs] F1 = np.exp(1j * K * (Y1G[:, None] - xf[None, :]) ** 2 / (2 * LD)) # [y1, xf] F3 = np.exp(1j * K * (X2[:, None] - xs[None, :]) ** 2 / (2 * L2)) # [x2, xs] C = F1 @ F2 # [y1, xs] A = (C * G[None, :]) @ F3.T # [y1, x2] p_coinc = np.abs(A) ** 2 # p(x2 | D1 la y1), pe linii singles = p_coinc.sum(axis=0) singles /= singles.max() + 1e-30 # perechile idler absorbite de partile opace: twinul lor ajunge oricum la D2 # (distributie neteda ~ propagare libera a sursei) — pedestal fara franje sigma = max(w_s, LAM * L2 / (2 * np.pi * max(w_s, 1e-3))) + 0.5 fundal = np.exp(-X2 ** 2 / (2 * sigma ** 2)) fundal /= fundal.max() singles = (1 - FRAC_BLOCAT) * singles + FRAC_BLOCAT * fundal return p_coinc, singles / singles.max() def perioada_ghost(L1): """Perioada franjelor fantoma la D2: in imaginea Klyshko desfasurata, fantele sunt la distanta L1 + L2 de planul lui D2.""" return LAM * (L1 + L2) / D_F def contrast(p, perioada): """Contrastul componentei oscilante la perioada data, in [0, 1].""" tot = p.sum() if tot <= 0: return 0.0 z = (p * np.exp(2j * np.pi * X2 / perioada)).sum() / tot return float(min(1.0, 2 * np.abs(z))) class AppGhost: def __init__(self, root): self.root = root root.title("Exp. 3 — Ghost Interference (Shih 1995, DIRD Fig. 2-4, 6)") ctl = ttk.Frame(root, padding=8) ctl.pack(side=tk.LEFT, fill=tk.Y) ttk.Label(ctl, text="Interferenta 'fantoma'", font=("Segoe UI", 12, "bold")).pack(pady=(0, 8)) self.v_fante = tk.IntVar(value=2) ttk.Label(ctl, text="Sistem de fante (inaintea lui D1):").pack(anchor="w") ttk.Radiobutton(ctl, text="2 fante -> 'pieptene' (Fig. 3a)", variable=self.v_fante, value=2, command=self.actualizeaza).pack(anchor="w") ttk.Radiobutton(ctl, text="1 fanta -> 'cocoasa' (Fig. 3b)", variable=self.v_fante, value=1, command=self.actualizeaza).pack(anchor="w") ttk.Label(ctl, text="Pozitia detectorului D1, y1 [mm]:").pack(anchor="w", pady=(10, 0)) self.v_y1 = tk.DoubleVar(value=0.0) ttk.Scale(ctl, from_=-3, to=3, variable=self.v_y1, command=lambda e: self.actualizeaza()).pack(fill=tk.X) ttk.Label(ctl, text="Largimea pompei w_s [mm]\n(mare = intricare in impuls,\nmica = sursa coerenta):").pack( anchor="w", pady=(10, 0)) self.v_ws = tk.DoubleVar(value=0.4) ttk.Scale(ctl, from_=0.02, to=0.8, variable=self.v_ws, command=lambda e: self.actualizeaza()).pack(fill=tk.X) ttk.Label(ctl, text="Distanta sursa-fante L1 [mm]:").pack( anchor="w", pady=(10, 0)) self.v_L1 = tk.DoubleVar(value=200.0) ttk.Scale(ctl, from_=100, to=800, variable=self.v_L1, command=lambda e: self.actualizeaza()).pack(fill=tk.X) self.lbl = ttk.Label(ctl, text="", font=("Consolas", 10)) self.lbl.pack(anchor="w", pady=10) ttk.Label(ctl, wraplength=230, justify="left", foreground="#555", text=( "Sus: distributia lui D2 IN COINCIDENTA cu D1 — modificand fantele " "din bratul lui D1, modelul de pe D2 se schimba nelocal.\n\n" "Jos: distributia fara coincidente (singles) — neteda, fara franje. " "Fara legatura clasica de coincidenta nu se transmite nimic.\n\n" "Complementaritatea coerenta-intricare (sectiunea V din DIRD): " "micsorand w_s sursa devine coerenta dar isi pierde intricarea " "in impuls -> franjele fantoma dispar si din coincidente; " "marind w_s, franjele exista DOAR in coincidente. Nu exista " "regim in care 'singles' sa poarte semnalul.")).pack(anchor="w") self.fig = Figure(figsize=(8.5, 6.5), dpi=100) self.ax1 = self.fig.add_subplot(211) self.ax2 = self.fig.add_subplot(212) self.fig.subplots_adjust(hspace=0.4) self.canvas = FigureCanvasTkAgg(self.fig, master=root) self.canvas.get_tk_widget().pack(side=tk.RIGHT, fill=tk.BOTH, expand=True) self.actualizeaza() if "--test" in sys.argv: root.after(2500, root.destroy) def actualizeaza(self): p_coinc, singles = calculeaza(self.v_fante.get(), self.v_ws.get(), self.v_L1.get()) iy = int(np.argmin(np.abs(Y1G - self.v_y1.get()))) pc = p_coinc[iy] pc = pc / (pc.max() + 1e-30) self.ax1.clear() self.ax1.plot(X2, pc, color="#1f77b4") self.ax1.fill_between(X2, pc, alpha=0.3, color="#1f77b4") self.ax1.set_title(f"D2 in coincidenta cu D1 fixat la y1 = {Y1G[iy]:+.2f} mm") self.ax1.set_ylabel("rata normata") self.ax2.clear() self.ax2.plot(X2, singles, color="#555") self.ax2.fill_between(X2, singles, alpha=0.3, color="#888") self.ax2.set_title("D2 fara coincidente (singles) — nu apare niciun semnal") self.ax2.set_xlabel("pozitia x2 pe D2 [mm]") self.ax2.set_ylabel("rata normata") per = perioada_ghost(self.v_L1.get()) self.lbl.config(text=(f"contrast franje (coincid.): {contrast(pc, per):.2f}\n" f"contrast franje (singles): {contrast(singles, per):.2f}")) self.canvas.draw_idle() if __name__ == "__main__": root = tk.Tk() AppGhost(root) root.mainloop()