Quantum localization of the kicked rydberg atom

Area of Science:

• Quantum physics
• Atomic physics
• Nonlinear dynamics

Background:

• Rydberg atoms are highly excited atoms with unique properties.
• Classical systems can exhibit chaotic behavior and ionization under periodic impulses.
• Quantum systems may display different stability characteristics.

Purpose of the Study:

• To investigate quantum localization in a one-dimensional Rydberg atom.
• To compare the behavior of classical and quantum systems under periodic impulses.
• To understand the role of unstable periodic orbits in quantum stability.

Main Methods:

• Simulating a one-dimensional Rydberg atom subjected to a unidirectional periodic impulse train.
• Analyzing the classical system's response to high-frequency impulses.
• Examining the quantum system's stability and localization phenomena.
• Identifying "scars" of unstable periodic orbits.

Main Results:

• The classical system exhibits chaotic behavior and rapid ionization at high frequencies.
• The quantum system demonstrates remarkable stability and quantum localization.
• Quantum localization is directly linked to the presence of "scars" from unstable periodic orbits.
• The localization length is determined by the energy excursion along these periodic orbits.

Conclusions:

• Quantum localization provides a mechanism for stabilizing Rydberg atoms against ionization.
• Unstable periodic orbits and their "scars" play a crucial role in quantum localization.
• The energy excursion along periodic orbits quantifies the localization length in this system.