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以获得真正的量子优势的方式。这个项目的目的是利用集成的光子学来研究它们的产生、检测和操作。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，请参见[1])，并且可以以多种方式生成。对于这个项目，产生的方法是通过光子减法。CAT态的产生是通过产生压缩态来实现的，其中单个光子被移除并被检测到。这是使用弱反射率分束器完成的。通过对这些事件的预告，一个人知道状态的剩余部分已经从其中移除了单个光子，并与所需的状态匹配。这个过程比提出的生成其他非高斯态的方法要简单得多，例如GKP态[2]，使得这些态对于实际实现来说是一个有吸引力的选择。虽然这些态的产生已经通过光子减法(例如[3])实现了，但还没有使用集成光子学来实现。贾科莫已经生产了一种芯片来实现这一点，它能够在同一芯片上进行生成、减法和检测。如果成功，这将标志着第一次使用集成光子学产生了光子减去状态。集成光电子在稳定性、占地面积和可扩展性方面的巨大优势，让这一平台的选择变得清晰。这个项目建立在我在B项目上所做的工作的基础上，在B项目中，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式，并接替Beth在她的项目B中所做的工作，以完成芯片的表征和设置。总体而言，正是该芯片的设置和运行将构成PHD的主干。这个芯片能做什么？如前所述，该芯片生成并检测这些光子减去状态，并且可以在连续波(CW)或脉冲模式下工作。其中每一个都有自己的操作考虑因素，必须与事件的模式整形和定时同步一起解决。即使在CW和脉冲状态下从该芯片产生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结构的两个副本，因此可以泵送这两个副本以生成多个状态。由于分束器和干涉仪的存在连接了这两种结构，所以有可能干涉这两种状态并将它们纠缠在一起，从而为大量可能的实验打开了大门。这包括猫育种协议，其中两个猫状态结合在一起形成一个更大的猫状态[4，5]。通过这样做，可以通过组合更容易产生的较小的状态来产生一个大的状态。希望一旦这个芯片被成功地用来演示这些状态的产生，我就会设计一个新的芯片来建立这些结果--研究产生新的状态或以有趣的方式应用这些猫状态。另一种可能的途径是寻找建立一个集群状态[6]。团簇态是使用基于测量的方法进行连续变量量子计算的起点，当从非高斯态构建时具有显著的优势，并且尚未在芯片上创建。虽然这些代表了未来可能的方向，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.