Exploring the effect of correlations on quantum speed limits in interacting cold atom systems

在过去的一年里，我已经发表了3篇关于这个项目的主要论文。其中两篇论文关注的是超对称（SUSY）势下量子系统的动力学。SUSY允许建立一个退化势的层次结构，这些势可以通过SUSY算子相互映射。在第一篇文章中，我探索了不同SUSY电位之间多体态的猝灭动力学，表明与任意电位之间的猝灭相比，初始状态的恢复在周期性时间内持续[PRR 4 033014(2022)]。对绝热捷径（STAs）的后续研究表明，SUSY可以帮助量子控制，允许仅使用其相互SUSY算子的信息来设计SUSY势族的STAs [NJP 24 095001(2022)]。这也允许将状态的量子速度限制（qsl）与其SUSY算子联系起来，表明同一层次中的状态具有密切相关的qsl，因此具有动力学。qsl在量子热机中使用的相互作用的少体系统中的作用被进一步探索[PRR 5 013088(2023)]。在这里，陷阱频率和相互作用是动态控制的，允许实现由于相互作用而增强性能的奥托循环。虽然动态控制相互作用增加了QSL时间并限制了功率输出，但从相互作用中获得的增强仍然使其优于非相互作用周期。

In the past year I have published 3 main papers on this project. Two of these papers focussed on dynamics of quantum systems in supersymmetric(SUSY) potentials. SUSY allows to build a hierarchy of degenerate potentials that can be mapped to one another through SUSY operators. In the first work I explored the quench dynamics of many-body states between different SUSY potentials showing that revivals of the initial state are persevered at periodic times, in comparison to quenches between arbitrary potentials [PRR 4 033014 (2022)]. Follow up work on shortcuts to adiabaticity (STAs) showed that SUSY can aid in quantum control, allowing to design STAs for a family of SUSY potentials using only information on their mutual SUSY operators [NJP 24 095001 (2022)]. This also allowed to relate the quantum speed limits (QSLs) of states with respect to their SUSY operators, showing that states in the same hierarchy have closely related QSLs and therefore dynamics.The role of QSLs was further explored in interacting few-body systems which are used in a quantum heat engine [PRR 5 013088 (2023)]. Here the trap frequency and interaction are dynamically controlled allowing to realize an Otto cycle with enhanced performance due to the interactions. While dynamically controlling the interaction increases the QSL time and limits the power output, the enhancement obtained from the interactions still allows it outperform non-interacting cycles.