非絕熱系統中的高效率中性原子傳輸

Abstract

可重組的中性原子陣列被視為建構大規模量子資訊處理器的一項極具潛力的平台。在此類架構中，高保真度的中性原子輸送是一項關鍵需求。儘管理論上絕熱過程可以實現無損且無最終激發的輸送，其所需的操作時間通常是長於量子態的相干時間，特別是在操作反覆多次時。因此，嚴格的絕熱輸送在實際操作中，無論在保真度或效率方面皆不具優勢。基於此動機，過去已有大量研究致力於發展非絕熱的輸送策略，此類方法統稱為「絕熱捷徑」（shortcuts to adiabaticity, STA），其目標是在顯著縮短操作時間的同時，仍能重現絕熱過程所達到的最終量子態。 本研究著重於以傅立葉分析為基礎的STA方法設計中性原子在調和勢阱中的高效率輸送方案。我們首先指出，合適的輸送時間可以透過速度或加速度軌跡的傅立葉轉換得到。在以數值方法分析數種代表性的速度函數後，我們發現可在僅有數個陷阱振盪週期的輸送時間內達成極高的最終運動態保真度。此外，我們亦分析了佛克態分佈，以及計算富比尼–施圖迪度量以量化量子態演化速率。基於以上分析，我們提出一種「不變運動態」（invariant motional state, IMS）輸送策略，能在有限的等速移動區間內，使運動態在隨著陷阱移動的參考系中保持不變。最後，我們討論了將IMS概念延伸至輸送中的離子阱系統之可能性，並指出由於質心模態與相對模態之間的解耦合，IMS型輸送可自然地被應用於輸送中的Mølmer–Sørensen 糾纏閘操作中。我們的研究提供了一套簡潔的方式用以評估非絕熱輸送方案，並可作為設計中性原子與離子阱系統的快速且穩健輸送方案的參考。

Reconfigurable atom arrays provide a promising platform for building large-scale quantum information processors. A key requirement for such architectures is the ability to transport neutral atoms with high fidelity. Although transport without loss and final excitation can in principle be achieved through adiabatic processes, the required timescales may be much longer than the coherence times of quantum states, especially when repeated operations are considered. As a result, strictly adiabatic transport is generally unfavorable in terms of both fidelity and operational efficiency. This has motivated extensive studies of non-adiabatic transport strategies, commonly referred to as shortcuts to adiabaticity (STA), which aim to reproduce the outcome of adiabatic protocols within significantly shorter times. In this work, we focus on constructing efficient transport protocols for neutral atoms confined in a harmonic trap using Fourier-based STA approaches. We first show that suitable transport times can be identified by analyzing the Fourier components of the acceleration or velocity profiles. Several representative profiles are examined numerically, and high final motional-state fidelities are obtained for transport durations of only a few trap oscillation periods. The motional dynamics during transport is further characterized through the population distribution in the Fock basis and the Fubini--Study metric, which quantifies the rate of quantum-state evolution. Based on these analyses, we propose an invariant motional state (IMS) protocol, in which the motional state remains stationary in the comoving frame during a finite constant-velocity interval. Finally, we discuss the extension of the IMS concept to transported trapped-ion systems, where the decoupling between center-of-mass and relative motional modes suggests a natural way to incorporate IMS-type transport into transported Mølmer--Sørensen gates. Our results provide a simple way to assess non-adiabatic transport protocols and may serve as a useful reference for designing fast and robust transport in neutral-atom as well as trapped-ion systems.