Driving at the quantum speed limit: optimal control of a two-level system

Area of Science:

• Quantum mechanics
• Quantum control
• Atomic physics

Background:

• Understanding quantum dynamics is crucial for quantum technologies.
• Landau-Zener transitions describe non-adiabatic processes in quantum systems.
• Controlling quantum states requires precise manipulation of system parameters.

Purpose of the Study:

• Derive the minimal time to drive quantum states to a target state.
• Investigate the impact of bounded interaction strength on optimal driving protocols.
• Explore the concept of quantum speed limit time.

Main Methods:

• Analytical derivation of minimal time and protocols for Landau-Zener-type Hamiltonians.
• Analysis of time-dependent laser driving as an equivalent method.
• Examination of optimal driving strategies under bounded interaction strength (c).

Main Results:

• A simple formula for minimal driving time (Tmin) is derived.
• Optimal driving protocols can switch between bang-off-bang and bang-bang types depending on interaction strength.
• For large interaction strength (c), bang-off-bang driving is optimal, recovering unconstrained results.

Conclusions:

• The study provides a fundamental result for quantum state control.
• Optimal quantum control strategies are sensitive to interaction strength constraints.
• The findings offer insights into the fundamental limits of quantum dynamics and the quantum speed limit.