Interacting Topological Matter in Synthetic Dimensions

综合维度中拓扑物质的相互作用

• 批准号: EP/W016141/1
• 负责人: Hannah Price
• 金额: $ 31.85万
• 依托单位: University of Birmingham
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW016141%2F1
• 关键词: Interacting; Topological; Matter; Synthetic; Dimensions

In recent years, the study of "topological states of matter" has reshaped our understanding of physics, allowing us to discover, study and classify many new physical effects. In mathematics, topology is a way to classify different surfaces; for example, doughnuts belong to a family of surfaces with one hole, while oranges belong to that with no holes. If we smoothly squish an orange, its shape changes but it does not become like a doughnut unless we tear a hole and change its topology. In physics, similar ideas can be used to classify the states of a quantum particle or of wave-like phenomena. Just like the squishable orange, these topological states are robust (e.g. unaffected by disorder or impurities), provided that changes do not affect the topological properties. This has raised both interesting fundamental questions and possibilities for future technologies in communications and computing, especially once interactions between particles are also included.However, engineering a topological state of matter is not always easy, particularly in systems of photons or cold atoms. One successful solution to this problem is based on the powerful and general approach of "synthetic dimensions". The essence of a "synthetic dimension" is to identify some property inherent to a system (such as, for example, the frequency, i.e. the colour, of light in a device), and then to carefully engineer the system such that this property can change over time (e.g. that the light can change its colour). In a certain well-defined sense, the change of this property is analogous to the change in the spatial coordinates of a particle as it moves left/right, up/down and forwards/backwards through real space. This motivates the re-interpretation of that property (e.g. the colour of light) as being like an extra "synthetic dimension" in the system. Although "synthetic dimensions" may initially seem to be very abstract, this approach actually has many advantages for engineering topological matter, as shown by a recent rapid rise in popularity in atomic and photonic experiments. However, so far, most of these experiments have only explored single-particle (i.e. non-interacting) physics, and big open questions remain as to how useful synthetic dimensions will be to investigate the more interesting regime of interacting topological matter, in which inter-particle interactions must be included. This theoretical project will tackle this challenge by exploring interacting topological matter in synthetic dimensions. We shall examine and evaluate interaction effects in promising synthetic-dimension schemes, and propose experiments to realise interacting states in 2D and even higher-dimensional 4D topological lattices. The latter, in particular, is an exciting opportunity opened up by synthetic dimensions, as this approach provides a way to artificially augment the effective dimensionality of a system beyond our 3D physical world. Throughout this project, we will aim to advance knowledge by addressing fundamental open questions, such as the role of interactions in different systems and in non-equilibrium settings, and by laying the groundwork for important future experiments in this field.

近年来，对物质拓扑态的研究重塑了我们对物理学的理解，使我们能够发现、研究和分类许多新的物理效应。在数学中，拓扑学是一种对不同曲面进行分类的方法；例如，甜甜圈属于有一个洞的曲面族，而橙子属于没有洞的曲面族。如果我们流畅地挤压橙子，它的形状会改变，但除非我们撕开一个洞并改变它的拓扑结构，否则它不会变得像甜甜圈。在物理学中，类似的概念可以用来对量子粒子或波状现象的状态进行分类。就像可压扁的橙子一样，这些拓扑态是健壮的(例如，不受无序或杂质的影响)，前提是变化不影响拓扑性质。这既提出了有趣的基本问题，也为未来通信和计算技术带来了可能性，特别是当粒子之间的相互作用也包括在内的时候。然而，设计物质的拓扑态并不总是容易的，特别是在光子或冷原子系统中。这个问题的一个成功的解决方案是基于“合成维度”这一强大而通用的方法。“合成维度”的本质是识别系统固有的某些属性(例如，光在设备中的频率，即颜色)，然后仔细设计系统，使得该属性可以随时间改变(例如，光可以改变其颜色)。在某种定义明确的意义上，这一性质的变化类似于粒子在真实空间中左/右、上/下和向前/向后移动时空间坐标的变化。这促使人们将该属性(例如光的颜色)重新解释为系统中的一个额外的“合成维度”。尽管“合成维度”一开始看起来很抽象，但这种方法实际上对工程拓扑物质有很多优势，最近在原子和光子实验中迅速流行起来就表明了这一点。然而，到目前为止，这些实验中的大多数只探索了单粒子(即非相互作用)物理，对于合成维度对于研究更有趣的相互作用拓扑物质(其中必须包括粒子间相互作用)有多大用处，仍然存在很大的悬而未决的问题。这个理论项目将通过探索合成维度中相互作用的拓扑物质来解决这一挑战。我们将检查和评估有前景的合成维度方案中的相互作用效应，并提出在2D甚至更高维的4D拓扑晶格中实现相互作用态的实验。尤其是后者，是一个由合成维度开启的令人兴奋的机会，因为这种方法提供了一种方法，可以在我们的3D物理世界之外人为地增加系统的有效维度。在整个项目中，我们将致力于通过解决基本的开放问题来促进知识的发展，例如不同系统和非平衡环境中相互作用的作用，并为这一领域未来的重要实验奠定基础。

项目成果

Measuring the adiabatic non-Hermitian Berry phase in feedback-coupled oscillators

• DOI: 10.1103/physrevresearch.5.l032026
• 发表时间: 2022-05
• 期刊: Physical Review Research
• 影响因子: 4.2
• 作者: Yaashnaa Singhal;Enrico Martello;S. Agrawal;T. Ozawa;H. Price;B. Gadway

Artificial gauge fields in the t-z mapping for optical pulses: Spatiotemporal wave packet control and quantum Hall physics.

• DOI: 10.1126/sciadv.adj0360
• 发表时间: 2023-10-20
• 期刊: SCIENCE ADVANCES
• 影响因子: 13.6
• 作者: Oliver, Christopher;Mukherjee, Sebabrata;Rechstman, Mikael C.;Carusotto, Iacopo;Price, Hannah M.
• 通讯作者: Price, Hannah M.