Photonic Circuits with Time Delays and Quantum Feedback

Area of Science:

• Quantum optics
• Quantum information science
• Condensed matter physics

Background:

• Photonic quantum circuits involve nodes connected by quantum channels.
• Significant time delays in communication are critical for quantum feedback and non-Markovian dynamics.
• Existing methods struggle with the complexity of delayed quantum systems.

Purpose of the Study:

• To develop an efficient computational approach for quantum systems with time delays.
• To accurately model the entanglement between quantum nodes and emitted photons.
• To investigate the non-Markovian dynamics in delayed quantum optical systems.

Main Methods:

• Developed a matrix product state approach.
• Solved the quantum stochastic Schrödinger equation with time delays.
• Applied the method to paradigmatic quantum optical examples.

Main Results:

• The matrix product state approach efficiently accounts for entanglement and non-Markovian dynamics.
• Successfully simulated two-atom and single-atom systems with time-delayed feedback.
• Demonstrated the method's applicability to quantum feedback problems.

Conclusions:

• The matrix product state method provides an efficient tool for studying delayed quantum dynamics.
• This approach is valuable for understanding quantum feedback and complex photonic circuits.
• The findings pave the way for designing and controlling quantum systems with time delays.