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

计时是循环机运转的关键。例如，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：首先将燃料-空气混合物注入气缸，然后由运动的活塞压缩；点燃液体会导致爆炸，将活塞推到气缸底部，从而驱动汽车的车轴；当活塞回到初始位置，燃烧的液体从气缸中排出时，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、点火和耗尽的时刻。最近，人们对被称为时间晶体的多体系统非常感兴趣，这些系统显示出远离热平衡的有序。时间晶体的特征是突然的、持续的、强劲的振荡，这种振荡打破了时间平移对称性，形成了“时间晶体”，就像标准晶体材料打破了空间的平移不变性一样。如果为这些系统提供连续的能量流，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。这个时钟可以用来维持微小活塞的周期性运动，并取代发动机的经典工作液体。这些新的时间晶体引擎是自控设备，其效率和运行稳定性不受外部时钟或反馈环路精度的限制。因此，他们很有希望成为未来纳米机器的发动机，这些机器需要超精确的能量输入，例如量子传感器。通过这项提议，我们寻求对诺丁汉大学与图宾根大学密切合作的一项新的理论实验倡议的支持。其目的将是加深对时间晶体中心方面的基本了解，例如它们在存在远程相互作用和耗散时的稳定性，并探索实现它们的实验和它们在未来技术中的潜在应用的新途径。中心目标之一是为热机的设计和优化制定可行的战略，这些热机利用时间晶相的特殊性质用于机械发电和一般的热力学目的，包括冷却和在小长度和能量尺度上高精度地泵送电荷和物质。我们将专注于基本理论和周期驱动自旋系统的两个互补实验平台：固态纳米磁性(在诺丁汉进行了理论和实验)，以及相互作用的里德堡原子阵列(通过我们与Tübingen的合作伙伴关系，由BW基金会授予的拨款支持，在诺丁汉进行了理论和实验)。我们的工作将为揭示和利用复杂的集体行为提供一个新的固态和原子物理视角。我们的团队包括在实验和理论原子物理、统计物理、量子热力学和凝聚态物质方面拥有丰富经验的研究人员，他们在开放量子系统、冷原子系统、量子磁铁、光学机械系统和其他与这一提议相关的主题方面做出了核心贡献。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迅速在实验中得到检验，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世纪和20世纪的方式塑造我们的世纪。量子时间晶体机器有潜力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.