Analytic RF Pulse Design via Spin-Spring Mapping
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Solution Overview
Problem
Current methods for designing broadband radiofrequency pulses in quantum systems are inefficient due to nonlinearity and complexity, leading to suboptimal performance and high computational requirements, particularly in achieving uniform excitation or inversion across a range of frequencies.
Innovation Solution
A method is developed to design analytic broadband pulses by establishing a dynamic connection between nonlinear spin and linear spring systems, allowing for the conversion of nonlinear pulse design problems into linear control problems, enabling precise control of quantum systems with minimal numerical computation and achieving high-fidelity excitation or inversion across a defined bandwidth.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If current methods for designing broadband RF pulses are used, then excitation or inversion can be achieved across a range of frequencies, but the methods are inefficient due to nonlinearity and complexity, leading to suboptimal performance and high computational requirements
Solution Approach 1:
The patent introduces an intermediary mapping between the nonlinear spin system and a linear spring system. By defining a dynamic connection where spin trajectories are mapped to spring trajectories through a transformation function, the complex nonlinear pulse design problem is converted into a simpler linear control problem. This intermediary mapping allows analytical solutions to be derived without direct numerical optimization of the nonlinear system.
Solution Approach 2:
The patent replaces the mechanical/physical spin system with a mathematical spring system model. The nonlinear Bloch equations governing spin dynamics are substituted with linear harmonic oscillator equations. This substitution enables the use of analytical methods from linear systems theory to solve the pulse design problem, avoiding the need for computationally intensive numerical optimization while maintaining the essential dynamics through the trajectory mapping.
2Manufacturing precision
If numerical optimization methods are used to design broadband RF pulses, then uniform excitation across bandwidth can be achieved, but computational time and resources are excessively high
Solution Approach 1:
The patent performs preliminary action by establishing the analytical mapping between spin and spring systems before solving the pulse design problem. The transformation relationships and boundary conditions are pre-defined, allowing the linear spring system to be solved analytically. This preliminary setup eliminates the need for iterative numerical optimization during the actual pulse design process, significantly reducing computational time while maintaining excitation uniformity across the bandwidth.
3Adaptability or versatility
If high power RF pulses are used to achieve broadband excitation, then coverage across frequency range improves, but energy consumption and amplitude constraints are violated
Solution Approach 1:
The patent changes the fundamental parameters of the problem by transforming it from a high-energy spin control problem to a low-energy spring control problem. The analytical solution for the spring system naturally provides pulse parameters that satisfy amplitude constraints. By working in the transformed parameter space of the linear system, the method achieves broadband coverage without requiring high RF power, as the linear system's solution inherently respects energy constraints that would be violated in direct nonlinear optimization.
Data Source
AI summary
The present disclosure provides for a method of designing a radiofrequency or broadband pulse sequence. The method can comprise a qubit (e.g., nuclear spin, photon, electron, atomic spin, dot spin) and a harmonic oscillator wherein a flip angle is controlled by steering a spring between specific states.