Quantum Kicked Rotor / Dynamical Localization

Periodic delta-like kicks first drive chaotic momentum diffusion, then quantum interference arrests the growth and localizes the momentum distribution.

QPE preset #35

This page describes the phenomenon using the current QPE preset and numerical modules as its primary source.

Physical idea

The surprise is temporal: kicks initially broaden momentum as if by diffusion, then interference among many kick histories arrests the growth. Localization occurs in momentum space.

Key relation. H=p²/(2m)+K cos(x) Σₙδ(t−nT). Classically the kicked rotor can diffuse chaotically in momentum; quantum phase coherence can halt that diffusion and produce dynamical localization.

Guided protocol from the preset

Press Play and watch momentum space. The state starts near momentum mode n=0. Each kick multiplies psi by exp[-i k cos(theta)], producing rapid momentum spreading.

Then quantum interference takes over. The spread stops growing diffusively: <n^2> remains bounded while the classical standard-map reference continues to diffuse.

Analysis -> Kicked Rotor. The upper panel is the stroboscopic momentum carpet P(n). The lower panel compares the real 2D quantum <n^2> with a classical ensemble using the same parameters.

History. Fishman, Grempel and Prange connected the quantum kicked rotor to Anderson localization in 1982. Direct atomic observations of dynamical localization were reported by Moore et al. in 1994, followed by an explicit atom-optics delta-kicked-rotor realization with ultracold sodium in 1995.

Model boundary. X is the periodic rotor angle and Y is a harmonically confined spectator coordinate. Kicks are ideal instantaneous unitary impulses rather than finite laser pulses.

What to observe and how to study it

  1. Run the guided preset unchanged and first identify the observable that changes.
  2. Change one parameter at a time, then Reset and repeat.
  3. Always compare rendering with the Analysis readouts: the image is a view, not a complete measurement.

History and experimental status

The quantum kicked rotor became a model system for quantum chaos. In 1995 Moore and collaborators realized the δ-kicked rotor with ultracold sodium atoms in a pulsed standing wave and observed dynamical localization.

Representative physical scale

Representative platformultracold Na atoms in a pulsed 589 nm standing wave
Mapping basisNa-23 kicked-rotor mapping with m_sim=0.10
1 QPE length unit14.4 nm
1 QPE time unit0.749 µs
Energy scale E0=ħ/T00.879 neV
Equivalent frequency E0/h0.213 MHz
NoteOne full 20.48-unit periodic X domain maps to one 589 nm/2 standing-wave period. Because the guided rotor uses m_sim=0.10, T0=m_phys L0^2/(m_sim hbar), giving about 0.749 us rather than the m_sim=1 kinetic time.
The scale is an order-of-magnitude bridge from QPE dimensionless units to one plausible platform; it does not turn the preset into a quantitative simulation of that specific apparatus.

Essential references

Continue studying

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