# -*- coding: utf-8 -*- """ Experimentul 4 — Experimentul Dopfer (Innsbruck, 1998) Descris in documentul DIRD (DIA-08-1003-016), sectiunea IV, Fig. 5. Fotoni intricati in impuls (SPDC, LiIO3). Fotonul de jos trece prin doua fante si este scanat de D1. Fotonul de sus trece printr-o lentila "Heisenberg" (focala f); detectorul D2 poate fi mutat in spatele lentilei: - la distanta z = f (planul Fourier): D2 masoara IMPULSUL -> nu exista informatie which-way -> in coincidenta apar franje la D1; - la distanta z = 2f (planul imagine, cu cristalul ca "oglinda" Klyshko si distanta obiect totala d_a + d_b = 2f): D2 vede PRIN care fanta a trecut fotonul pereche -> franjele dispar. Fara coincidente (singles la D1) nu apar franje NICIODATA, indiferent unde sta D2 -> mutarea lui D2 nu poate transmite un semnal (teorema de ne-semnalizare). Model: propagatoare Fresnel + faza lentilei exp(-ik x^2/2f), integrare numerica peste sursa, apertura lentilei si fante (imagine desfasurata Klyshko). """ 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 K = 2 * np.pi / LAM F = 300.0 # mm focala lentilei Heisenberg DA = 350.0 # mm cristal -> lentila DB = 250.0 # mm cristal -> fante (DA + DB = 2F -> imagine la z = 2F) DD = 300.0 # mm fante -> D1 D_F = 0.35 # mm separare fante A_F = 0.07 # mm latime fanta W_S = 0.3 # mm largimea sursei (pompa larga -> intricare in impuls buna) X1 = np.linspace(-4, 4, 401) XLGRID = np.linspace(-3, 3, 41) # pozitii D2 pentru integrarea "singles" PER_F1 = LAM * DD / D_F # perioada franjelor la D1 (fante la dist. DD) xs = np.linspace(-3 * W_S, 3 * W_S, 301) G = np.exp(-xs ** 2 / (2 * W_S ** 2)) G /= G.sum() xl = np.linspace(-4, 4, 1601) # apertura lentilei (esantionare fina anti-aliasing) xf = np.concatenate([c + np.linspace(-A_F / 2, A_F / 2, 9) for c in (-D_F / 2, D_F / 2)]) # bratul fantelor: M[xs, x1] M = (np.exp(1j * K * (xf[None, :, None] - xs[:, None, None]) ** 2 / (2 * DB)) * np.exp(1j * K * (X1[None, None, :] - xf[None, :, None]) ** 2 / (2 * DD)) ).sum(axis=1) def brat_lentila(z, xL): """Amplitudinea bratului cu lentila pentru D2 la (z, xL): vector peste xs.""" faza = (K * (xl[None, :] - xs[:, None]) ** 2 / (2 * DA) - K * xl[None, :] ** 2 / (2 * F) + K * (xL - xl[None, :]) ** 2 / (2 * z)) return np.exp(1j * faza).sum(axis=1) def coincidenta(z, xL): A = ((G * brat_lentila(z, xL))[None, :] @ M).ravel() p = np.abs(A) ** 2 return p / (p.max() + 1e-30) def singles(z): tot = np.zeros_like(X1) for xL in XLGRID: A = ((G * brat_lentila(z, xL))[None, :] @ M).ravel() tot += np.abs(A) ** 2 return tot / (tot.max() + 1e-30) def contrast(p): """Contrastul componentei de franje (perioada PER_F1) la D1, in [0, 1].""" tot = p.sum() if tot <= 0: return 0.0 z = (p * np.exp(2j * np.pi * X1 / PER_F1)).sum() / tot return float(min(1.0, 2 * np.abs(z))) class AppDopfer: def __init__(self, root): self.root = root root.title("Exp. 4 — Experimentul Dopfer 1998 (DIRD Fig. 5)") ctl = ttk.Frame(root, padding=8) ctl.pack(side=tk.LEFT, fill=tk.Y) ttk.Label(ctl, text="Lentila Heisenberg\n(Dopfer / Zeilinger)", font=("Segoe UI", 12, "bold")).pack(pady=(0, 8)) ttk.Label(ctl, text="Pozitia lui D2 dupa lentila, z [mm]:").pack(anchor="w") self.v_z = tk.DoubleVar(value=F) self.s_z = ttk.Scale(ctl, from_=150, to=750, variable=self.v_z, command=lambda e: self.actualizeaza()) self.s_z.pack(fill=tk.X) fr = ttk.Frame(ctl) fr.pack(fill=tk.X, pady=2) ttk.Button(fr, text="z = f (impuls)", command=lambda: self.seteaza_z(F, 0.0)).pack(side=tk.LEFT, expand=True, fill=tk.X) ttk.Button(fr, text="z = 2f (imagine)", command=lambda: self.seteaza_z(2 * F, D_F / 2)).pack(side=tk.LEFT, expand=True, fill=tk.X) ttk.Label(ctl, text="Pozitia transversala a lui D2 [mm]:").pack(anchor="w", pady=(10, 0)) self.v_xL = tk.DoubleVar(value=0.0) ttk.Scale(ctl, from_=-2, to=2, variable=self.v_xL, 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: rata D1 in coincidenta cu D2.\n" "z = f: D2 in planul Fourier -> impuls, fara which-way -> franje.\n" "z = 2f: D2 in planul imagine al fantelor -> which-way -> fara franje.\n\n" "Jos: singles la D1 — mereu fara franje, oriunde ar fi D2. " "'Emitatorul' care muta D2 nu poate trimite nimic fara canalul " "clasic de coincidenta.")).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(3000, root.destroy) def seteaza_z(self, z, xL=None): self.v_z.set(z) if xL is not None: self.v_xL.set(xL) # la z=2f, D2 se pune pe imaginea unei fante self.actualizeaza() def actualizeaza(self): z, xL = self.v_z.get(), self.v_xL.get() pc = coincidenta(z, xL) ps = singles(z) self.ax1.clear() self.ax1.plot(X1, pc, color="#d62728") self.ax1.fill_between(X1, pc, alpha=0.3, color="#d62728") self.ax1.set_title(f"D1 in coincidenta cu D2 (z = {z:.0f} mm, x_D2 = {xL:+.2f} mm)") self.ax1.set_ylabel("rata normata") self.ax2.clear() self.ax2.plot(X1, ps, color="#555") self.ax2.fill_between(X1, ps, alpha=0.3, color="#888") self.ax2.set_title("D1 fara coincidente (singles)") self.ax2.set_xlabel("pozitia x1 pe D1 [mm]") self.ax2.set_ylabel("rata normata") self.lbl.config(text=(f"z/f = {z / F:.2f}\n" f"contrast franje (coincid.): {contrast(pc):.2f}\n" f"contrast franje (singles): {contrast(ps):.2f}")) self.canvas.draw_idle() if __name__ == "__main__": root = tk.Tk() AppDopfer(root) root.mainloop()