Nonadiabatic Processes in Dynamical Controls Reveal Mechanisms Impacting Particle Conveyance and Adiabatic Tunneling during Acceleration

Controlling the movement of particles requires precise manipulation of the forces acting upon them, a task complicated by the potential for particles to escape their intended paths. Yoshiaki Teranishi from National Yang Ming Chiao Tung University, Satoshi Morita from Keio University, and Seiji Miyashita from the University of Tokyo investigate the factors governing a particle’s survival within a trapping potential during controlled movement. Their work reveals that escape arises from two primary mechanisms: initial disturbances caused by abrupt changes in control parameters, and adiabatic tunneling during acceleration. The team develops a formula to predict survival probability based on these factors, demonstrating that the combined effects of initial and final disturbances, alongside continuous tunneling, accurately explain particle behaviour across various acceleration protocols. This achievement allows scientists to estimate survival probabilities for any control strategy without detailed dynamic calculations, representing a significant step forward in the precise control of particle dynamics.

Adiabatic and Non-Adiabatic Potential Transitions

This research explores the quantum mechanical behavior of a particle within a harmonic potential that changes over time, a more complex scenario than a static potential. When a potential changes slowly, the particle remains in the instantaneous quantum state dictated by that potential, a concept known as the adiabatic approximation. However, when the potential changes rapidly, the adiabatic approximation breaks down, and the particle can transition between different quantum states. The Morita effect describes transitions induced by changes in the derivatives of the parameters governing the potential’s motion.

Understanding these transitions is crucial for controlling quantum systems. The research details a theoretical treatment of these non-adiabatic transitions, focusing on how the time-varying potential influences particle behavior. Scientists derive formulas to calculate the probability of transitions between quantum states, demonstrating that even higher-order changes in the potential can induce these transitions. The team specifically investigates the Morita effect, providing a mathematical description of the transition probability. To illustrate the theory, they consider a specific example where the potential moves sinusoidally, allowing for concrete calculations. The results connect to existing theoretical frameworks and build upon previous work on related phenomena.

Survival Probability Governed by Acceleration Protocols

Scientists have achieved a precise understanding of how to control particle conveyance within a trapping potential, quantifying the factors that cause a particle to escape. The research focuses on survival probability during conveyance, identifying two key mechanisms: initial disturbance caused by abrupt changes in parameters and adiabatic tunneling, a process occurring during acceleration. Through detailed analysis, the team proposes a formula to calculate survival probability as a function of the acceleration protocol, incorporating both disturbance mechanisms and adiabatic tunneling. Experiments reveal that the decay of survival probability under different acceleration protocols is accurately explained by combining the effects of initial and final disturbances with an integral form of adiabatic tunneling throughout the transport process.

This breakthrough delivers a method to estimate survival probability for any acceleration protocol without performing individual dynamical simulations, once the disturbance factors and adiabatic tunneling rate are known. The team demonstrated this by successfully fitting the survival probability to analytical formulas, confirming the accuracy of their approach. Measurements confirm that the decay rate is a smooth function of acceleration, and the team obtained a precise analytical form to describe this dependence.

Particle Loss Prediction in Trapping Potentials

Scientists have developed a comprehensive model to predict the survival probability of a particle undergoing conveyance within a trapping potential. The research demonstrates that particle loss arises from two primary mechanisms: initial disturbances caused by abrupt changes in parameters, and adiabatic tunneling, a quantum mechanical effect occurring during acceleration. The team proposes a formula incorporating both factors, allowing for accurate estimation of survival probability across various acceleration protocols without requiring detailed dynamic simulations for each case. The researchers validated their model through extensive comparison with numerical data, successfully predicting particle behavior under cosine, sine, and combined acceleration protocols.

Notably, the model accurately accounts for the influence of initial and final disturbances, as well as the integral contribution of adiabatic tunneling throughout the conveyance process. The findings reveal that the model remains effective even when acceleration rates are low, indicating its broad applicability. This research provides a valuable theoretical framework for understanding and predicting particle dynamics in trapping potentials, with potential implications for fields such as quantum control and precision measurement.