Novel non-equilibrium states of matter in periodically driven spin systems: from time crystals to integrated thermal machines

定时是循环机器运行的关键。例如，一个典型的汽车发动机使用一个周期性的四步过程将化学能转化为动力：燃料-空气混合物首先被注入气缸，然后被移动的活塞压缩;点燃流体导致爆炸，将活塞推到气缸底部，从而驱动汽车的车轴;当活塞返回到其初始位置并且燃烧过的流体从气缸排出时，该循环完成。为了平稳可靠地运行这一过程，发动机需要一个精确的外部时钟来确定燃油喷射、点火和排气的时刻。最近，人们对称为时间晶体的多体系统产生了很大的兴趣，这种系统表现出远离热平衡的秩序。时间晶体的特点是突发的，持续的，强大的振荡，打破时间平移对称性，形成“时间晶体”，就像标准的晶体材料打破空间中的平移不变性一样。如果这些系统具有连续的能量流，例如以光子的形式，则可以产生振荡电流或电磁场，并且可以充当自主时钟。这种时钟可以用来维持微观活塞的周期性运动，并取代发动机的经典工作流体。这些新的时间晶体引擎是自我控制的设备，其运行效率和稳定性不受外部时钟或反馈回路精度的限制。因此，它们有望成为需要超精确能量输入的未来纳米机器（例如量子传感器）的电机。通过这一提议，我们寻求支持一项新的理论实验计划，该计划位于诺丁汉大学，与图宾根大学密切合作。其目的是发展对时间晶体核心方面的基本理解，例如它们在远程相互作用和耗散存在下的鲁棒性，并探索实验实现及其在未来技术中的潜在应用的新途径。其中一个中心目标是建立可行的策略，用于设计和优化热机，利用时间结晶相的特殊性质用于机械发电和热力学目的，包括冷却和高精度泵送电荷和物质的小长度和能量尺度。我们将专注于基本理论和周期性驱动自旋系统的两个互补实验平台：固态纳米磁学（在诺丁汉进行理论和实验），以及相互作用的里德伯原子阵列（在诺丁汉进行理论和实验，通过我们与蒂宾根的合作伙伴关系，由BW基金会资助）。我们的研究团队由在实验和理论原子物理、统计物理、量子热力学和凝聚态物理方面具有丰富经验的研究人员组成，他们在开放量子系统、冷原子系统、量子磁体、光机械系统以及与该提议相关的其他主题方面做出了重要贡献。这个联合项目将使我们能够携手合作，使新的理论思想能够在实验中迅速得到检验，并直接反馈到理论发展中。量子技术有望以类似于工业革命改变19和20世纪世纪的方式塑造我们的世纪。量子时间晶体机器有可能成为这一令人兴奋的发展的发动机。它们不会移动我们未来的汽车，但它们很可能决定我们未来的量子计算机、传感器和通信设备的工作节奏。

Timing is key to the operation of cyclic machines. A typical car engine, for example, uses a periodic four-step process to convert chemical energy into motive power: a fuel-air mixture is first injected into a cylinder and then compressed by a moving piston; igniting the fluid leads to an explosion that pushes the piston to the bottom of the cylinder, thus driving the axle of the car; the cycle is completed as the piston returns to its initial position and the burned fluid is exhausted from the cylinder. To run this process smoothly and reliably, the engine requires a precise external clock to determine the instants of fuel injection, ignition, and exhaustion.Recently, there has been a lot of interest in many-body systems called time crystals that exhibit order far from thermal equilibrium. Time crystals are characterised by emergent, persistent, robust oscillations that break time-translation symmetry and form a "crystal in time", just like standard crystalline materials break translation invariance in space. If these systems are provided with a continuous flow of energy, e.g. in the form of photons, an oscillating current or electromagnetic field can be generated and can act as an autonomous clock. That clock can be used to sustain the periodic motion of a microscopic piston and replace the classical working fluid of an engine. These new time-crystal engines are self-controlled devices, whose efficiency and constancy of operation are not limited by the precision of external clocks or feedback loops. As a result, they are promising candidates to become the motors of future nano-machines that require ultra-precise energy input, e.g. quantum sensors.With this proposal, we seek support for a new theory-experiment initiative, based at the University of Nottingham in close collaboration with the University of Tübingen. The aim will be to develop the fundamental understanding of the central aspects of time crystals, e.g. their robustness in the presence of long-range interactions and dissipation, and to explore new avenues towards their experimental realisation and their potential application in future technologies. One of the central goals is to establish viable strategies for the design and optimization of thermal machines that utilize the exceptional properties of time-crystalline phases for mechanical power generation and thermodynamic purposes in general, including cooling and the high-accuracy pumping of charge and matter on small length and energy scales. We will focus on the fundamental theory and on two complementary experimental platforms of periodically driven spin systems: solid-state nanomagnetism (with both theory and experiments carried out in Nottingham), and arrays of interacting Rydberg atoms (with theory carried out in Nottingham and experiments via our partnership with Tübingen, supported by an awarded BW Foundation grant). Our work will allow a new perspective on solid-state and atomic physics for uncovering and exploiting complex collective behaviour.Our team comprises researchers with ample experience in experimental and theoretical atomic physics, statistical physics, quantum thermodynamics, and condensed matter, who have made central contributions to open quantum systems, cold atomic systems, quantum magnets, optomechanical systems, and other topics related to this proposal. This joint project will allow us to work hand-in-hand so that new theoretical ideas can quickly be tested in experiments which directly feed back into theoretical developments.Quantum technologies are expected to shape our century in a similar way as the industrial revolution changed 19th and 20th century. Quantum time-crystal machines have the potential to become the motors of this exciting development. They will not move our future cars, but they might well determine the working rhythm of our future quantum computers, sensors, and communication devices.