Collaborative Research: Photonic Chip-Scale Time Crystals

各种各样的晶体，如盐粒和雪花，或硅晶体，构成现代电子产品的支柱，都是由大量的原子或分子组成的。就像雪花中的水分子一样有序而对称，六边形晶体代表的不是对称，而是它突破了空空间的完美对称性，变成了分子阵列的离散对称性。虽然少量的原子可以通过化学键形成具有新的物理和化学性质的分子，但只有真正大量（约10^23，数十万亿）的这种相互作用的构建块聚集在一起才能形成晶体。由此产生的晶体再次具有独特的性质，从而提高了它们的实用性。大约十年前，科学家们开始建立时间晶体的理论-由大量相互作用的构建块组成的系统，这些构建块打破了对称性，不是在空间中，而是在时间维度中。结果表明，与固态空间晶体平行，时间晶体提供了理想的特性（例如，时间鲁棒性），以及全新的物理效果（例如，避免当通常加热预期破坏晶体时晶体有序度的损失）。这些固有的时间晶体特性对于未来的应用至关重要，例如量子计算，其中数据的量子比特期望随着时间的推移和经过几次阅读操作后保留其信息。迄今为止，时间晶体的实验演示仍然很少，尤其局限于不利于现实世界应用的孤立系统。它们也主要局限于“小”晶体，通常只有2个颞基本细胞。拟议的研究旨在通过在小型化非线性光学器件中使用光子在非隔离系统中实现时间晶体来克服这些限制。该平台使时间晶体的未开发方面的调查和展示他们在精密计时的应用。此外，它可以容纳“大”时间晶体，从而提供了实现凝聚态物理效应的时间模拟的可能性，并使用成熟的光子技术解决了悬而未决的问题。为了进一步发挥影响力，我们提出的计划包括科学专业教育推广和研讨会组件，这些组件将为有抱负的高中生和工程师开发和提供课程。该团队将在耗散克尔非线性腔中演示离散时间晶体。利用集成光子结构的纳米纤维所提供的灵活性，时间晶体将在多色激光泵浦的氮化硅微腔谐振器中实现和研究。色散工程和谐振腔的合理设计和泵浦将确保实现大时间晶体。所产生的时间晶体的状态将被控制，并且不同相位之间的过渡将通过频率调制和扫描来实现。时间晶体的稳定将通过自注入锁定两个激光器的两个不相邻的同系列的光学模式的微谐振腔和跟踪通过监测的相位噪声的泵浦激光器之间的拍音与所产生的次谐波。在该平台中实现离散时间晶体所固有的分频导致相位噪声的降低。该系统可用于频率参考转移锁定泵激光器的外部频率参考。成功演示了结合光子学和凝聚态物理概念的拟议平台，大大加速了时间晶体作为物质新阶段的研究，并揭示了其一些实际应用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Garden variety crystals like salt grains and snowflakes, or silicon crystals forming the backbone of modern-day electronics all consist of large numbers of atoms or molecules. As orderly and symmetric as water molecules sit in a snowflake, the hexagonal crystal represents not symmetry but its breaking through the reduction of the perfect symmetry of empty space into the discrete symmetry of an array of molecules. While a small number of atoms can form molecules with new physical and chemical properties by chemical bonding, only a truly large number (~10^23, hundreds of thousands of billions of billions) of such interacting building blocks coming together can form crystals. The resultant crystals possess yet again unique properties, giving rise to their utility. About a decade ago, scientists started theorizing time crystals – systems consisting of a large number of interacting building blocks which break symmetry, not in space but in the time dimension. It was shown that, paralleling solid-state spatial crystals, time crystals offer desirable characteristics (e.g., temporal robustness), as well as totally new physical effects (e.g., avoiding loss of crystalline order when typically heating is expected to destroy a crystal). These inherent time crystal properties are crucial for future applications such as quantum computation where quantum bits of data are expected to preserve their information over time and after several reading operations. Experimental demonstrations of time crystals have thus far remained scarce and particularly limited to isolated systems which are not conducive to real-world applications. They have also been largely confined to “small” crystals, typically with only 2 temporal elementary cells. The proposed research aims to surmount these limitations by realizing time crystals in non-isolated systems using photons in miniaturized nonlinear optical devices. This platform empowers investigation of unexplored aspects of time crystals and demonstrating their application in precision timekeeping. Additionally, it accommodates “big” time crystals, hence offering the possibility of realizing temporal analogues of condensed matter physical effects and addressing open questions using the mature photonic technology. For further impact, our proposed program includes scientific professional education outreach and workshop components which will develop and deliver a curriculum to aspiring high school students and engineers.The team will demonstrate discrete time crystals in dissipative Kerr nonlinear cavities. Leveraging the flexibilities afforded by nanofabrication of integrated photonic structures, time crystals will be realized and investigated in silicon nitride microring resonators pumped by polychromatic lasers. Dispersion engineering and judicious design and pumping of the resonator will ensure realizing big time crystals. The state of the created time crystals will be controlled and transition between different phases will be achieved by means of frequency modulation and sweep. Stabilization of time crystals will be achieved by self-injection locking two lasers to two non-adjacent same-family optical modes of the microring resonator and tracked through monitoring the phase noise of the beatnote between the pump lasers versus that of the generated subharmonics. The frequency division inherent to the realization of discrete time crystals in this platform results in the reduction of the phase noise. The system can be used for frequency reference transfer by locking the pump lasers to external frequency references. Successful demonstration of the proposed platform combining concepts from photonics and condensed matter physics significantly accelerates the investigation of time crystals as a new phase of matter and reveals some of their practical applications.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.