Experimental Realization of the Einstein-Podolsky-Rosen Paradox with Entangled Photons

📌 Project Overview

This repository contains the analysis code and final laboratory report for the experimental verification of the Einstein-Podolsky-Rosen (EPR) paradox. The experiment utilized Spontaneous Parametric Down-Conversion (SPDC) to generate spatially entangled photon pairs and measured their correlations in conjugate bases to test the Heisenberg uncertainty limit.

🎯 Objectives

• Generate Entanglement: Construct an optical setup using a Type-I BBO crystal to create correlated photon pairs via SPDC.
• Measure Correlations: Record spatial correlations in two conjugate bases using a SPAD camera:
  • Position (Near Field)
  • Momentum (Far Field)
• Test the Paradox: Calculate the product of the conditional variances to check for a violation of the inequality: $$\Delta^{2}(x_{-})\Delta^{2}(k_{+}) < 0.25$$ where a violation ($< 0.25$) indicates quantum steering.

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🔬 Experimental Methodology

🛠️ Setup

• Source: A Type-I $\beta$-Barium Borate (BBO) crystal pumped by a 405 nm continuous-wave diode laser (50 mW).
• Detector: A Hermes SPAD (Single-Photon Avalanche Diode) camera operating in Geiger mode for single-photon detection.
• Optics: A configurable lens system allowed switching between:
  • Imaging Mode: Imaging the crystal plane to measure position ($x$) correlations.
  • Fourier Mode: Imaging the focal plane to measure momentum ($k$) correlations.

📊 Analysis Technique

Raw data consisted of thousands of binary frames. We constructed coincidence matrices and performed coordinate projections (Sum and Minus coordinates). To quantify the correlations, we applied a Gaussian background subtraction method to isolate the signal width from the noise floor.

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📈 Key Results

Despite observing the characteristic signatures of SPDC (position correlation peak and momentum anti-correlation ring), the quantitative analysis yielded the following results:

Metric	Measurement (approx.)
Position Variance $\Delta^{2}(x_{-})$	$137.95$
Momentum Variance $\Delta^{2}(k_{+})$	$131.02$
Final EPR Product	18,073
Quantum Limit	0.25

📝 Conclusion

The calculated product (18,073) is significantly higher than the quantum bound of 0.25. Therefore, we were unable to violate the inequality with this specific dataset.

Interpretation of Failure:

• Low SNR: The measurements were dominated by classical noise rather than quantum correlations.
• Accidental Coincidences: Uncorrelated events from stray light and detector dark counts created a high background floor.
• Defocusing: Even minor longitudinal misalignments of the crystal acted as a "quantum defocus," blurring the spatial correlations.

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🚀 Future Improvements

To successfully observe the violation, the following improvements were identified:

1. Stricter Alignment: Finer control over beam walking and crystal tilt to maximize collection efficiency.
2. Enhanced Temporal Gating: Reducing the coincidence time window to reject accidental noise.
3. Extended Integration: Increasing exposure time to allow quantum statistics to emerge above Poissonian noise.

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📂 Repository Structure

EPR-Paradox-Verification/
├── README.md               # Project overview (this file)
├── Final_Report.pdf        # Complete lab report with theory and results
├── analysis_script.py      # Python code for correlation analysis
└── LICENSE                 # MIT License