Sixth-order schemes for laser-matter interaction in the Schrödinger equation

Area of Science:

• Quantum mechanics
• Computational physics
• Laser-matter interactions

Background:

• Accurate numerical solutions of the Schrödinger equation are crucial for controlling quantum systems with lasers.
• Existing methods may struggle with highly oscillatory or discretely defined laser potentials.

Purpose of the Study:

• To develop novel sixth-order numerical schemes for the Schrödinger equation with time-dependent laser potentials.
• To extend existing sixth-order methods for time-independent potentials to handle laser interactions.

Main Methods:

• Exploiting the linear-in-space form of the time-dependent potential under the dipole approximation.
• Utilizing the Magnus expansion with intact integrals to separate time-stepping from laser field resolution.
• Employing carefully designed splittings to eliminate unfavorable terms.

Main Results:

• Three distinct sixth-order schemes were successfully derived and validated.
• The proposed methods demonstrate effectiveness in both atomic and semiclassical regimes.
• These schemes provide a superior alternative to time-ordered exponential splittings for specific laser potential characteristics.

Conclusions:

• The developed sixth-order schemes offer a robust and efficient approach for simulating quantum systems under laser control.
• These methods are particularly advantageous for problems involving highly oscillatory or discretely known laser fields.
• The strategies enhance the numerical solution of the Schrödinger equation, advancing applications in quantum control.