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Updated: May 23, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Geometric phase contribution to quantum nonequilibrium many-body dynamics.

Michael Tomka¹, Anatoli Polkovnikov, Vladimir Gritsev

¹Physics Department, University of Fribourg, Fribourg, Switzerland.

Physical Review Letters

|April 3, 2012

Summary

The geometry of quantum states influences many-body dynamics. An interplay between dynamical and geometric phases can cause nonequilibrium phase transitions and affect defect generation near quantum critical points.

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Area of Science:

Quantum physics
Condensed matter theory
Quantum many-body systems

Background:

Quantum systems exhibit complex dynamics influenced by their underlying geometry.
Understanding quantum nonequilibrium dynamics is crucial for quantum technologies.
The interplay between dynamical and topological properties is a key area of research.

Purpose of the Study:

To investigate how the geometry of the quantum state space affects quantum many-body dynamics.
To explore the role of dynamical and geometric phases in quantum nonequilibrium processes.
To analyze the impact of geometric phase on defect generation across quantum critical points.

Main Methods:

Theoretical analysis of quantum many-body dynamics.
Study of an anisotropic XY ring model with a time-dependent flux.
Investigation of nonadiabatic transitions and phase transitions.

Main Results:

An interplay between dynamical and geometric phases governs quantum nonequilibrium dynamics.
Slow flux insertion favors dynamical phase dominance; fast insertion emphasizes geometric phase.
This interplay can induce a nonequilibrium phase transition.
Geometric phase influences defect generation when crossing quantum-critical points.

Conclusions:

The geometry of quantum state space is a critical factor in quantum many-body dynamics.
Dynamical and geometric phases offer distinct regimes of control for quantum systems.
Understanding these effects is essential for controlling quantum dynamics and minimizing defects in quantum critical phenomena.