Evolutionary Algorithm Optimization of Zeeman Deceleration: Is It Worthwhile for Longer Decelerators?

In Zeeman deceleration, only a small subset of low-field-seeking particles in the incoming beam possess initial velocities and positions that place them within the phase-space acceptance of the device. In order to maximize the number of particles that are successfully decelerated to a selected final velocity, we seek to optimize the phase-space acceptance of the decelerator. Three-dimensional particle trajectory simulations are employed to investigate the potential benefits of using a covariance matrix adaptation evolutionary strategy (CMA-ES) optimization method for decelerators longer than 12 stages and for decelerating species other than H atoms. In all scenarios considered, the evolutionary algorithm-optimized sequences yield vastly more particles within the target velocity range. This is particularly evident in scenarios where standard sequences are known to perform poorly; simulations show that CMA-ES optimization of a standard sequence decelerating H atoms from an initial velocity of 500 ms down to a final velocity of 200 ms in a 24-stage decelerator produces a considerable 5921% (or 60-fold) increase in the number of successfully decelerated particles. Particle losses that occur with standard pulse sequences-for example, arising from the coupling of longitudinal and transverse motion-are overcome in the CMA-ES optimization process as the passage of all particles through the decelerator is explicitly considered and focusing effects are accounted for in the optimization process.