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Superposition principle for the simultaneous optimization of collective responses
S Dong1,2, R Flores1, J Unger1
1Intense Laser Physics Theory Unit and Department of Physics, Illinois State University, Normal, Illinois 61790-4560, USA.
Physical Review. E
|August 17, 2018
Summary
Researchers found an efficient way to control multiple systems simultaneously using optimal control theory. The optimal force for collective response can be a superposition of individual optimal forces, simplifying complex control problems.
Area of Science:
- Complex Systems Dynamics
- Optimal Control Theory
- Quantum Mechanics
Background:
- Independent systems are often coupled to a common time-dependent external force.
- Simultaneously optimizing the collective response of multiple systems presents a significant challenge.
- Understanding how individual system responses contribute to the collective behavior is crucial.
Purpose of the Study:
- To compute the most efficient temporal pulse shape for an external force.
- To maximize the simultaneous collective response of multiple independent systems.
- To explore the relationship between collective optimal forces and individual optimal forces.
Main Methods:
- Application of optimal control theory to determine the most efficient force pulse shape.
- Analysis of weighted sums of system amplitudes at the final interaction time.
- Numerical and analytical solutions for sets of damped linear and nonlinear oscillators.
Main Results:
- A superposition principle was identified, relating the collective optimal force to individual optimal forces for certain systems.
- This principle simplifies the simultaneous optimization of collective responses.
- The method was successfully applied to optimize laser pulse profiles for quantum systems.
Conclusions:
- The superposition principle offers an efficient strategy for controlling the collective dynamics of multiple systems.
- This approach has practical implications in fields like quantum optics and macroscopic polarization control.
- The findings provide a new framework for designing complex control protocols.
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