Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Branch points in the complex plane and geometric phases.

I Rotter1

  • 1Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
Summary

Laser-induced degenerate states (LIDS) are branch points in the complex plane causing geometric phase changes. Encircling these points or diabolic points leads to distinct wave function exchanges and phase shifts, with implications for quantum interference.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

The effect of repeated whole-body cryostimulation on the HSP-70 and lipid metabolisms in healthy subjects.

Physiological research·2019
Same author

Lipid Accumulation Product (LAP) as an Index of Metabolic and Hormonal Disorders in Aging Men.

Experimental and clinical endocrinology & diabetes : official journal, German Society of Endocrinology [and] German Diabetes Association·2016
Same author

The inflammatory effect of infection with Hymenolepis diminuta via the increased expression and activity of COX-1 and COX-2 in the rat jejunum and colon.

Experimental parasitology·2016
Same author

A review of progress in the physics of open quantum systems: theory and experiment.

Reports on progress in physics. Physical Society (Great Britain)·2015
Same author

[Influence of Selected Reproductive Factors and Smoking on Age at Menopause].

Gesundheitswesen (Bundesverband der Arzte des Offentlichen Gesundheitsdienstes (Germany))·2015
Same author

Immunohistochemical identification of aquaporin 2 in the kidneys of young beef cattle.

Biotechnic & histochemistry : official publication of the Biological Stain Commission·2013

Area of Science:

  • Quantum mechanics
  • Atomic physics
  • Mathematical physics

Background:

  • Laser-induced degenerate states (LIDS) are mathematically equivalent to double poles of the S matrix, manifesting as branch points in the complex plane (BPCP).
  • These critical points are associated with non-adiabatic geometric phase changes in quantum systems.
  • Understanding these phenomena is crucial for controlling quantum states and predicting interference patterns.

Purpose of the Study:

  • To elucidate the distinct geometric phase changes caused by encircling branch points in the complex plane (BPCP) versus diabolic points (DP).
  • To analyze the consequences of these phase changes on wave function evolution and quantum interference.
  • To extend the foundational work by Berry on geometric phases in quantum mechanics.

Main Methods:

Related Experiment Videos

  • Theoretical analysis of S matrix poles and their relation to branch points.
  • Adiabatic approximation to study wave function evolution around critical points.
  • Comparison of phase accumulation when encircling BPCPs and DPs in parameter space.

Main Results:

  • Branch points in the complex plane (BPCP) and diabolic points (DP) lead to different phase shifts due to the number of times the critical point is encircled.
  • Wave functions undergo exchange (Phi(i) --> +/- iPhi(j not equal i)) at critical parameters where states avoid crossing.
  • A second encircling of a BPCP restores the original wave functions and phases, provided the BPCP is isolated and encircling time is short.

Conclusions:

  • The distinct phase changes associated with BPCPs and DPs arise from the topology of the parameter space and the nature of the singularity.
  • Interference patterns are shown to be sensitive to the direction of encircling LIDS, offering a new perspective on quantum phase phenomena.
  • This work provides a comprehensive understanding of geometric phases in systems exhibiting laser-induced degenerate states.