[Paper Review] Entanglement between two macroscopic fields by coherent atom-mediated exchange of photons

Carlos L. Garrido Alzar, Marcelo F. Santos+1 more|ArXiv.org|May 19, 2002

Quantum Information and Cryptography3 citations

TL;DR

This paper demonstrates that two macroscopic light beams—pump and probe—can become entangled via coherent atom-mediated photon exchange in a 85 Rb atomic medium under Electromagnetically Induced Transparency (EIT) conditions. Using two continuous-variable entanglement criteria, the authors show that quantum correlations emerge between the beams despite initial uncorrelated states, with up to 40% entanglement observed due to strong atomic coherence, enabling practical quantum information applications with intense, macroscopic fields.

ABSTRACT

Using two different criteria for continuous variable systems we demonstrated that pump and probe beams became quantum correlated in a situation of Electromagnetically Induced Transparency in a sample of Rb atoms. Our result combines two important features for practical implementations in the field of quantum information processing. Namely, we proved the existence of entanglement between two macroscopic light beams, and this entanglement is intrinsically associated to a strong coherence in an atomic medium.

Motivation & Objective

• To investigate whether two intense, macroscopic light beams can become entangled in a coherently prepared atomic medium.
• To explore the feasibility of combining continuous-variable quantum systems with EIT for scalable quantum information processing.
• To determine if entanglement can emerge in a system with environmental coupling, given strong atomic coherence.
• To validate entanglement using two independent continuous-variable criteria, ensuring robustness of the result.

Proposed method

• Modeling a three-level Λ-type atomic system in 85 Rb with two copropagating laser fields (pump and probe) treated quantum-mechanically.
• Deriving Heisenberg equations of motion for the system, leading to twelve coupled quantum Langevin equations for field and atomic operators.
• Linearizing quantum fluctuations around steady-state values to obtain a matrix linear stochastic differential equation describing the dynamics of fluctuations.
• Applying two entanglement criteria: the Duan et al. criterion (DGCZ) and the positive partial transpose (PPT) criterion, both based on quadrature variance and correlation measurements.
• Using a Lorentzian spectral profile for laser fields and incorporating Markov approximation to model laser linewidth and input noise.
• Designing an experimental setup using polarizing beam splitters, homodyne detectors, and local oscillators to measure quadrature variances and infer entanglement.

Experimental results

Research questions

• RQ1 Can two macroscopic light beams become entangled through coherent atom-mediated photon exchange in an EIT medium?
• RQ2 Does the presence of strong atomic coherence in EIT lead to measurable quantum correlations between intense light fields despite environmental coupling?
• RQ3 Can entanglement be verified using two independent continuous-variable entanglement criteria in a realistic, non-pure system?
• RQ4 What is the maximum degree of entanglement achievable between the pump and probe beams under EIT conditions, and what limits it?
• RQ5 How does the bistability response of the system relate to the generation of phase quadrature squeezing and quantum noise correlations?

Key findings

• Entanglement between the pump and probe beams is confirmed using both the Duan et al. (DGCZ) and positive partial transpose (PPT) criteria, demonstrating robustness of the result.
• The degree of entanglement reaches approximately 40%, limited by the decay rate of coherence between the two ground states in the atomic medium.
• Quantum correlations emerge even when the fields are initially uncorrelated, due to coherent photon exchange mediated by the atomic medium under EIT.
• Phase quadrature squeezing is observed at the turning point of the bistability curve, indicating non-classical noise reduction in the conjugate quadrature.
• The EIT condition induces measurable modifications in field quantum fluctuations, contradicting the common belief that EIT preserves field noise at high intensities.
• The system enables detection of the natural width of the EIT resonance through statistical analysis of field fluctuations, offering a sensitive probe for coherent effects in atomic media.