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Theory for the optimal control of time-averaged quantities in quantum systems
Ilia Grigorenko1, Martin E Garcia, K H Bennemann
1Institut für Theoretische Physik der Freien Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.
Physical Review Letters
|December 18, 2002
Summary
We developed a new theory for controlling quantum systems with relaxation. This approach uses a high-order Euler-Lagrange equation to find unique solutions, revealing how relaxation impacts quantum control.
Area of Science:
- Quantum mechanics
- Quantum control theory
- Theoretical physics
Background:
- Optimal control of quantum systems is crucial for quantum technologies.
- Existing theories often struggle with systems exhibiting relaxation.
- A robust theoretical framework is needed to account for dissipative effects.
Purpose of the Study:
- To develop a generalized variational theory for optimal quantum control with relaxation.
- To derive a unique solution for the optimal control field.
- To quantitatively assess the impact of relaxation on quantum system control.
Main Methods:
- Formulation of a generalized variational theory.
- Derivation of a high-order Euler-Lagrange differential equation for the optimal control field.
- Numerical and analytical solutions of the derived equation.
- Application to two-level quantum systems with relaxation.
Main Results:
- A novel variational theory for optimal quantum control with relaxation was established.
- The theory guarantees a unique solution for the optimal control field via a high-order Euler-Lagrange equation.
- Quantitative analysis demonstrated how relaxation effects limit the control of two-level quantum systems.
Conclusions:
- The presented variational theory offers a powerful and generalizable framework for optimal quantum control.
- The derived Euler-Lagrange equation provides a unique and solvable path to optimal control fields.
- Understanding relaxation's impact is essential for designing effective quantum control strategies.
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