Defect production in nonlinear quench across a quantum critical point

Area of Science:

• Condensed Matter Physics
• Quantum Critical Phenomena
• Nonlinear Dynamics

Background:

• Understanding defect formation is crucial for controlling quantum systems.
• Previous studies primarily focused on linear quenches, leaving nonlinear dynamics less explored.
• Quantum critical points offer unique opportunities for defect engineering.

Purpose of the Study:

• To theoretically investigate defect density scaling in nonlinear quenches across quantum critical points.
• To establish new scaling laws applicable to a broader range of quench protocols.
• To provide a theoretical framework for experimental verification.

Main Methods:

• Development of theoretical scaling laws for defect density (n) under nonlinear power-law quenches.
• Analysis of defect production across critical points characterized by correlation length (nu) and dynamical critical exponents (z).
• Comparison with existing theories for linear quenches (alpha=1).

Main Results:

• Derived defect density scaling laws: n ~ tau^(-alphanud/(alphaznu+1)) for nonlinear quenches.
• The derived laws encompass linear quench results as a special case (alpha=1).
• Numerical studies of established models corroborate the theoretical predictions.

Conclusions:

• The study presents the first theoretical scaling laws for defect production in nonlinear quenches across quantum critical points.
• The findings offer a generalized understanding of defect dynamics in driven quantum systems.
• The work paves the way for experimental validation and applications in quantum control.