重新设计线性-二次-高斯代价函数用于量子谐振子的反馈冷却
Redesigning the linear--quadratic--Gaussian cost function for feedback cooling of a quantum harmonic oscillator
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中文总结 AI 辅助
针对量子谐振子反馈冷却，重新设计LQG代价函数以考虑势阱移动，推导最优反馈律，相比低通滤波在高效探测下显著降低声子占据数。
中文摘要 AI 辅助
线性-二次-高斯（LQG）控制仅相对于规定的代价函数而言是最优的，而代价函数的选择决定了控制的物理目标。我们考虑通过移动连续监测的量子谐振子的势阱最小值来实现反馈冷却。在此设置中，物理相关的冷却目标可定义为最小化振荡器相对于反馈移动势阱的能量。相比之下，传统LQG控制从固定原点评估能量，因此无法直接优化该量。为解决此问题，我们引入了一个重新设计的代价函数，该函数明确考虑了反馈引起的势阱移动。随后，我们推导了相应的最优反馈律，并获得了最小可达稳态声子占据数的解析表达式。重新设计的LQG控制实现了比针对相同冷却目标制定的低通滤波器（LPF）反馈更低的占据数。虽然这种改进在实验目前可达到的探测效率下很小——表明LPF反馈已提供接近最优的冷却性能——但随着探测效率趋近于1，该优势变得显著。在此区域，重新设计的LQG控制在有限测量强度下为达到运动基态提供了越来越大的优势。我们澄清，传统和重新设计的代价函数代表了不同的控制目标，而非同一优化问题的不同实现。
英文摘要
Linear--quadratic--Gaussian (LQG) control is optimal only with respect to a prescribed cost function, the choice of which dictates the physical objective of the control. We consider feedback cooling of a continuously monitored quantum harmonic oscillator by shifting the minimum of its trapping potential. In this setting, the physically relevant cooling objective can be defined as minimizing the oscillator's energy relative to the feedback-shifted potential. In contrast, conventional LQG control evaluates the energy from a fixed origin and thus fails to directly optimize this quantity. To address this problem, we introduce a redesigned cost function that explicitly accounts for the feedback-induced shift of the potential. We then derive the corresponding optimal feedback law and obtain an analytic expression for the minimum achievable steady-state phonon occupation number. The redesigned LQG control achieves a lower occupation number than low-pass-filter (LPF) feedback formulated for the same cooling objective. While this improvement is minor at detection efficiencies currently attainable in experiments---indicating that LPF feedback already delivers near-optimal cooling performance---the advantage becomes pronounced as the detection efficiency approaches unity. In this regime, the redesigned LQG control provides an increasing advantage for reaching the motional ground state at a finite measurement strength. We clarify that the conventional and redesigned cost functions represent distinct control objectives rather than different implementations of the same optimization problem.
发表机构
- University of Tokyo（东京大学）
- King’s College London（伦敦国王学院）
- RIKEN（理化学研究所）
机构由 AI 辅助整理，请以论文原文为准。
