Enhanced Quantum Metrology via Saddle-Point Scrambling in Phase Space

Area of Science:

• Quantum Physics
• Quantum Metrology
• Nonlinear Dynamics

Background:

• Nonlinear effects are crucial for enhancing measurement precision in quantum metrology.
• Leveraging complex dynamical behaviors and phase space geometry is key to optimizing quantum measurements.

Purpose of the Study:

• To propose a quantum scrambling-integrated scheme for optimizing initial states and parameter encoding.
• To enhance measurement precision in quantum systems by exploiting nonlinear dynamical trajectories.

Main Methods:

• Utilizing nonlinear dynamical trajectories and geometric properties in phase space.
• Applying a quantum scrambling-integrated scheme to a two-mode Bose-Einstein condensate.
• Analyzing quantum Fisher information under long-time evolution.

Main Results:

• Achieving Heisenberg scaling in measurement precision by selecting specific initial states (uncorrelated spin coherent states at saddle points and separatrices).
• Demonstrating that the enhancement mechanism is driven by the energy spectrum's sensitivity to parameter variations.
• Providing an analytical expression for quantum Fisher information.

Conclusions:

• The proposed scheme enhances parameter estimation precision in quantum systems over a broader parameter range compared to criticality-enhanced protocols.
• The method is applicable to various models, including those with one- and two-axis countertwisting interactions and chaotic dynamics.
• This work offers a new perspective on applying nonlinear dynamics for advanced quantum metrology.