Stochastic Thermodynamics of Nonlinear Quantum Systems

该奖项由材料研究部的凝聚态和材料理论项目以及物理系的原子、分子和光学物理理论项目资助。非技术摘要我们正处于一场技术革命的边缘。在过去的几年里，计算硬件已经商业化，有望充分利用量子优势。然而，由于硬件仍然容易出现退相干和线性量子力学的局限性，现有的系统都不能很好地用于实际应用。量子热力学是研究量子系统中热噪声效应的主流理论。这一新兴领域已经为量子计算机的设计带来了具有实际意义的见解和结果。虽然以前的大多数研究都集中在线性系统上，但光子或超冷原子气体中的非线性量子系统显示出独特而强大的计算能力。然而，为了设计高效的量子计算机，人们必须了解底层材料的热力学，因为写入和擦除都是以牺牲热力学功为代价的(兰道尔原理)。到目前为止，人们对非线性系统的非平衡热力学的了解还只处于初级水平。因此，该项目将把随机热力学的范围扩展到非线性量子系统，这将有助于为21世纪的信息技术奠定基础。通过研究计算的最终物理极限和权衡，它将有助于发展构建后摩尔定律计算机体系结构所必需的理论基础，并为未来节能计算机体系结构的设计和制造做出贡献。为了实现这些影响，该项目将让研究生和本科生参与尖端研究，为国家的下一代科学家做准备。技术概述经典和量子随机热力学的科学努力侧重于描述所谓的信息引擎，这些引擎也已经在实验中实现。信息引擎是一种通过处理信息来运行的热力学装置，因此可以被认为是任何(量子)计算机的热力学范例。该项目将量子随机热力学理论推广到非线性系统，从而为这一动态研究领域做出贡献。这项研究很有意义，因为要在非线性量子系统中建立量子计算机，就必须了解信息和熵产生的相互作用。为了实现这一目标，该项目将集中在三个主要主题上：将纳米尺度下的功、热和熵产生的基本概念从线性量子力学推广到非线性量子力学，研究(量子)信息和(量子)热力学的相互作用，推广量子速度极限及其应用，以确定具有最小耗散或最快信息处理的最佳量子过程。特别是，本项目将致力于(I)量子速度极限的数值研究，即量子状态在非线性动力学下演化的最大速率；(Ii)发展非线性量子系统中随机热力学的一致框架，包括识别和研究熵和信息产生，以及广义涨落定理的推导；(Iii)最小但自给自足的量子信息引擎的理论研究和设计，它以最佳方式利用非线性动力学产生的计算优势；以及(Iv)玻色-爱因斯坦凝聚体中量子信息引擎的概念框架的发展和实验设计。结果可能影响量子计算机的设计和对量子纳米技术的基本理解。此外，这项研究将为理解任意远离热平衡运行的含时量子信息处理系统开辟新的途径。最后，拟议的研究也具有基本的理论兴趣，因为包括量子光学和量子最优控制理论在内的方法论提供了概念上简单的模型和工具来描述同时受到热和量子波动影响的纳米设备。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award is being funded by the Condensed-Matter and Materials Theory program in the Division of Materials Research and by the Atomic, Molecular, and Optical Physics Theory program in the Division of Physics.Nontechnical summaryWe are on the verge of a technological revolution. Over the last few years, computational hardware has become commercially available that promises to take full advantage of quantum supremacy. However, none of the available systems is readily useful for practical application, since the hardware is still prone to decoherence and the limitations of linear quantum mechanics.The prevailing theory for studying effects of thermal noise in quantum systems is Quantum Thermodynamics. This emerging field has already delivered insights and results of practical consequence for the design of quantum computers. While most previous research has focused exclusively on linear systems, nonlinear quantum systems in photonic or ultracold atom gases exhibit unique and powerful capabilities for computing. However, to design efficient quantum computers, one has to understand the thermodynamics of the underlying material, since writing as well as erasing comes at the expense of thermodynamic work (Landauer's principle). To date, the nonequilibrium thermodynamics of nonlinear systems has been understood only at a rudimentary level. Therefore, this project will extend the scope of stochastic thermodynamics to nonlinear quantum systems.This project will help lay the groundwork for 21st-century information technology. By investigating the ultimate physical limits and tradeoffs of computation, it will help develop the theoretical foundation essential for constructing post-Moore's-Law computer architectures and contribute to future engineering and manufacturing of energy-efficient computer architectures. To achieve these impacts, the project will involve graduate and undergraduate students in cutting-edge research, preparing the nation's next generation of scientists.Technical summaryScientific efforts in classical as well as quantum stochastic thermodynamics have focused on the description of so-called information engines, which also have been realized experimentally. An information engine is a thermodynamic device that operates by processing information and can thus be considered the thermodynamic paradigm for any (quantum) computer.The project will contribute to this dynamic field of research by generalizing the theory of quantum stochastic thermodynamics to nonlinear systems. This research is of topical interest, since to build a quantum computer in a nonlinear quantum system, one must understand the interplay of information and entropy production. To achieve this goal, the project will focus on three main topics: generalizing fundamental notions of work, heat, and entropy production at the nanoscale from linear to nonlinear quantum mechanics, studying the interplay of (quantum) information and (quantum) thermodynamics, and generalizing the quantum speed limit and its applications in order to identify optimal quantum processes with minimal dissipation or maximally fast information processing.In particular, this project will aim at (i) the numerical study of the quantum speed limit, i.e., the maximal rate with which a quantum state can evolve under nonlinear dynamics; (ii) the development of a consistent framework for stochastic thermodynamics in nonlinear quantum systems, comprising the identification and study of entropy and information production, and the derivation of generalized fluctuation theorems; (iii) the theoretical study and design of minimal, yet self-contained, quantum information engines, which optimally exploit computational advantages arising from nonlinear dynamics; and (iv) the development of a conceptual framework and the design of experiments for quantum information engines in Bose-Einstein condensates.The results could impact the design of quantum computers and the fundamental understanding of quantum nanotechnology. Moreover, this research will open new avenues for the understanding of time-dependent quantum-information-processing systems operating arbitrarily far from thermal equilibrium. Finally, the proposed research is also of basic theoretical interest, since the methodology, including quantum optics and quantum optimal control theory, provides conceptually simple models and tools to describe nano-devices subjected to both thermal and quantum fluctuations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.