On Chip Generation and Characterization of Non-Gaussian States of light

光的非高斯态在量子技术中有着巨大的应用；特别是作为一种引入连续变量（CV）方法所需的非高斯元素的方法，以获得真正的量子优势。这个项目的目的是利用集成光子学研究它们的产生、探测和操纵。薛定谔猫态是这种非高斯态的一个例子（有关猫态的更多信息，请参阅[1]），可以通过多种方式生成。对于这个项目，生成的方法是通过光子减法。产生cat态是通过产生一个压缩态来实现的，从这个压缩态中可以移除并检测到单个光子。这是使用弱反射率分束器完成的。通过预告这些事件，人们知道状态的剩余部分已经从它那里移除了一个光子，并与期望的状态相匹配。这个过程比生成其他非高斯状态（如GKP状态[2]）的方法要简单得多，使这些状态成为实际实现的一个有吸引力的选择。虽然这些状态的产生已经通过光子减法（例如[3]）实现，但还没有使用集成光子学完成。Giacomo公司已经生产出一种芯片来实现这一功能，它能够在同一芯片上进行生成、减法和检测。如果这是成功的，这将标志着第一次使用集成光子学产生光子减去状态。集成光子学在稳定性、占地面积和可扩展性方面的巨大优势使该平台的选择变得明确。这个项目建立在我对项目B所做的工作的基础上，在那里我一直在寻找这个实验的检测方案。博士学位的第一部分将建立在这项工作的基础上，以找出操作该芯片的最佳方法，并从Beth在她的项目B中完成的工作中接管，以完成芯片的表征和设置。总的来说，这是该芯片的设置和操作，将形成博士的骨干。这个芯片能做什么？如前所述，该芯片产生并检测这些光子减去状态，可以在连续波（CW）或脉冲模式下操作。每种方法都有自己的操作考虑，必须与事件的模式塑造和定时同步等问题一起解决。即使该芯片在连续波和脉冲状态下产生cat状态，也可以产生更多的结果。由于该芯片具有生成这些状态所需的两个结构副本，因此可以将两个副本都泵入以生成多个状态。由于分束器和干涉仪的存在，连接这两种结构，有可能干扰这两种状态并使它们纠缠，从而为大量可能的实验打开了大门。这包括猫繁殖协议，其中两个猫状态连接在一起形成一个更大的状态[4,5]。通过这样做，一个大的状态可以由更容易产生的小状态组合而成。我希望一旦这个芯片被用来成功地演示这些状态的产生，我就会设计一个新的芯片来建立在这些结果的基础上——看看产生新的状态或以有趣的方式应用这些猫的状态。另一种可能的途径是建立一个集群状态[6]。簇态是使用基于测量的方法进行连续可变量子计算的起始块，当从非高斯态构建并且尚未在芯片上创建时具有显着的优势。虽然这些代表了可能的未来方向，但不可能肯定地说，现有芯片上的工作可能会带来什么，但我希望这足以激励这项工作可能采取的各种各样的可能方向。

Non-gaussian states of light have tremendous applications across quantum technologies; especially as a way of introducing the required non-gaussian elements for continuous variable (CV) methods to gain a true quantum advantage. The aim of this project is to work on their generation, detection and manipulation using integrated photonics. Schrodinger Cat states are an example of such a non-gaussian state (see [1] for more information on cat states) and can be generated in a plethora of ways. For this project the method of generation is via photon subtraction. Generation of cat states is achieved by producing a squeezed state from which a single photon is removed and detected. This is done using a weak reflectivity beam splitter. By heralding on these events, one knows that what remains of state has had a single photon removed from it and matches the desired state. This process is much simpler than methods proposed for generating other non-gaussian states such as GKP states [2] making these states an attractive option for practical implementations. Whilst the generation of these states has already been achieved via photon subtraction (for example [3]) it has not been done using integrated photonics. Giacomo has already produced a chip to do this, which is capable of generation, subtraction and detection all on the same chip. If this is successful it would mark the first time a photon subtracted state has been generated using integrated photonics. The huge advantage in terms of stability, footprint and scalability of integrated photonics makes the choice of this platform clear. This project builds on work I have done over project B, where I have been looking at detection schemes for exactly this experiment. The first part of the PhD would be building on top of this work in order to figure out the optimum way to operate this chip as well as taking over from the work Beth has done in her project B to finish the characterisation and setup of the chip. Overall, it is the setup and operation of this chip that would form the backbone of the PhD. What can this chip do? As already mentioned, this chip generates and detects these photon subtracted states and can be operated in a continuous wave (CW) or pulsed mode. Each of these has their own operational considerations which must be addressed alongside things including mode shaping and timing synchronisation for events. Even if/when cat state are generated from this chip in both the CW and pulsed regime there are more results that can be generated. As this chip has two copies of the structures needed to generate these states one can pump both copies to generate multiple states. Due to the presence of beam splitters and interferometers linking these two structure it is possible to interfere these two states and entangle them opening the door to a wealth of possible experiments. This includes the cat breeding protocol where two of these cat states are joined together to form a larger one [4,5]. By doing this one large state can be generated by combining smaller states which are easier to produce. It is hoped that once this chip has been used to successfully demonstrate the generation of these states that I would design a new chip to build upon these results- looking at generating new states or applying these cat states in fun ways. Another possible route is to look to build a cluster state [6]. Cluster states are the starting blocks of continuous variable quantum computing using the measurement-based approach and have significant advantages when constructed from non-gaussian states and have yet been created on chip. Whilst these represent possible future directions it is impossible to say with certainty what may follow on from work on the existing chip but I hope this motivates enough the large variety of possible directions that this work could take.