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We investigated quantum kicked top dynamics in a large qubit system. A universal period-doubling behavior was observed as damping increased, characteristic of chaotic systems.

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Area of Science:

  • Quantum Information Science
  • Quantum Chaos
  • Quantum Dynamics

Background:

  • The kicked top model is a paradigmatic model for studying quantum chaos.
  • Understanding the transition from regular to chaotic dynamics in quantum systems is a key challenge.
  • Investigating the role of dissipation in quantum chaotic systems is crucial for realistic applications.

Purpose of the Study:

  • To explore the dynamics of a damped kicked top model for a large number of qubits (N→∞).
  • To analyze the evolution of a reduced single-qubit subsystem under amplitude damping.
  • To identify universal behaviors and bifurcations in the quantum chaotic regime.

Main Methods:

  • Simulation of a large qubit system (N→∞) undergoing damped kicked top dynamics.
  • Focus on the evolution of a reduced single-qubit subsystem subjected to an amplitude damping channel.
  • Analysis of the control parameter (damping constant r) and its effect on system dynamics.

Main Results:

  • Observed universal period-doubling behavior characteristic of one-dimensional maps in the chaotic regime.
  • Identified critical damping constants for period-doubling bifurcations (r₁≈0.3181, r₂≈0.5387).
  • Discovered a secondary bifurcation diagram around r≈0.544, leading to small-scale chaos, and noted the onset of full-scale chaos at r∞∼0.578.

Conclusions:

  • The damped kicked top model exhibits universal period-doubling bifurcations analogous to classical chaotic systems.
  • Dissipation introduces rich dynamics, including secondary bifurcations and windows of oscillatory behavior within the chaotic regime.
  • The study provides insights into the interplay between quantum chaos and dissipation in multi-qubit systems.