Multiple Davydov Ansätze as solutions to Lindblad master equations

Area of Science:

• Quantum Optics
• Quantum Information Theory
• Computational Physics

Background:

• Lindblad master equations are crucial for modeling driven quantum systems coupled to bosonic modes.
• These equations are fundamental in cavity quantum electrodynamics and pseudomode models.
• Accurate simulation of these systems is computationally challenging.

Purpose of the Study:

• To develop an accurate and computationally efficient method for solving Lindblad master equations.
• To apply the Dirac-Frenkel time-dependent variational principle with the Davydov D2Ansatz.
• To provide optimal solutions for driven and multimode quantum systems.

Main Methods:

• Employed the density-operator-based Dirac-Frenkel time-dependent variational principle.
• Utilized the multiple Davydov D2Ansatz for optimal solutions.
• Benchmarked against numerically exact methods in representative quantum models.

Main Results:

• Achieved excellent agreement between the variational approach and numerically exact results.
• Validated the method on a driven qubit coupled to a lossy cavity.
• Successfully applied to a complex pseudomode Lindblad master equation with seven discrete pseudomodes.
• Analyzed solution accuracy using a Frobenius norm error metric, confirming reliability.

Conclusions:

• The proposed variational method offers an accurate and computationally efficient framework.
• This approach is suitable for simulating complex open quantum systems described by Lindblad master equations.
• The method provides reliable solutions for multimode and driven quantum scenarios.