Geometry and quantum brachistochrone analysis of multiple entangled spin-1/2 particles under all-range Ising...

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Quantum information

Background:

• Understanding quantum system dynamics is crucial for quantum technologies.
• The geometry of quantum state space influences system evolution.
• Entanglement plays a key role in quantum phenomena.

Purpose of the Study:

• To establish a unified geometric and dynamical framework for n spin-1/2 particles with Ising interaction.
• To investigate the impact of state space geometry and topology on quantum phases and dynamics.
• To explore the role of entanglement in shaping quantum state space and controlling evolution.

Main Methods:

• Utilizing the Fubini-Study formalism to derive the metric tensor and Riemann curvature of the quantum state manifold.
• Analyzing the geometric and topological properties of the state space.
• Applying the framework to the quantum brachistochrone problem for optimal evolution time.

Main Results:

• The system evolves on a two-dimensional spherical manifold with a dumbbell-like structure.
• Quantum geometric and topological phases are influenced by state space curvature.
• Entanglement modulates evolution speed and geometric phase, with critical effects beyond a threshold.

Conclusions:

• The geometric framework provides insights into quantum dynamics and phase acquisition.
• Entanglement is a sensitive indicator of quantum state geometry and can steer quantum evolution.
• This approach guides the development of time-efficient quantum control strategies.