Characterizing propagation-dependent spatial entanglement for structured laser beams generated by an astigmatic mode...

Area of Science:

• Quantum optics
• Laser physics
• Information theory

Background:

• Structured laser beams, such as Hermite-Gaussian (HG) modes, are crucial in various optical applications.
• Astigmatic mode converters (AMCs) are used to alter the spatial properties of laser beams.
• Understanding the evolution of quantum properties like spatial entanglement during propagation is essential for quantum information processing.

Purpose of the Study:

• To theoretically investigate the propagation-dependent spatial entanglement of structured laser beams.
• To analyze the effect of an astigmatic mode converter (AMC) on the spatial entanglement of Hermite-Gaussian (HG) modes.
• To quantify the entanglement using von Neumann entropy and analyze the underlying mode distributions.

Main Methods:

• Analytical decomposition of output beams into Hermite-Gaussian (HG) mode expansions for arbitrary AMC rotation angles.
• Application of Schmidt decomposition to quantify spatial entanglement.
• Calculation of von Neumann entropy to measure entanglement.
• Quantitative analysis of the probability distribution of expanded HG modes.

Main Results:

• The spatial entanglement of structured laser beams is shown to be dependent on propagation distance.
• The astigmatic mode converter (AMC) introduces controllable changes in the spatial entanglement.
• The von Neumann entropy provides a reliable measure for quantifying this propagation-dependent entanglement.
• The probability distribution of HG modes reveals the mechanisms behind entanglement evolution.

Conclusions:

• Spatial entanglement in structured laser beams is dynamic and evolves with propagation.
• AMCs offer a method to tailor and control the spatial entanglement properties of laser beams.
• The theoretical framework provides a means to predict and understand entanglement dynamics in optical systems.