Entanglement-enhanced sensing with quantum networks

纠缠是一种独特的量子现象，它使两个最初独立的量子系统能够相互链接。纠缠构成了量子技术相对于经典技术具有优势的基础，特别是在计算和网络方面。在牛津大学，我们开发了一个囚禁离子的量子网络，通过光子互连在两个宏观上分离的系统中产生离子之间的纠缠。虽然这个网络最初是为量子计算或密码学的应用而构建的，但在这个项目中，我的目标是利用这些离子的光学跃迁或它们的运动，将我们的量子网络用于纠缠增强传感。首先，我的目标是建立一个纠缠光学原子钟网络，用于增强两个不同陷阱中离子的频率比较。光学原子钟用于最精确的时间测量。精确计时对于全球定位卫星、精准农业的应用或金融交易的时间戳以确保安全至关重要。两个原子钟之间的频率比较也用于大地测量，并用于探测基本常数的变化，或暗物质的性质。然而，这样的频率测量通常受到标准量子限制的限制。纠缠提供了一条超越这一限制的途径，减少了实现给定精度所需的测量次数。纠缠在一起的时钟网络还将最大限度地利用计时资源，并具有潜在的安全好处。我们的实验是这种网络的第一次演示。从我们最初的原理证明开始，我们将加入另一个离子物种，展示我们系统的多功能性，将远程纠缠扩展到更稳定和可以探测更长时间的跃迁。此外，我们可以在最初演示的基础上，通过在每个网络中添加局域纠缠操作来进一步增强频率测量。第二，我想要产生离子运动态的远程纠缠。通过将离子的内态耦合到它们的运动，我们可以将初始的自旋-自旋纠缠映射到它们各自的运动。这将是两个离子在不同系统中的首次演示，即使它们之间相隔几米，也会在空间范围为几纳米的量子态之间产生纠缠。以前已经对单个陷阱中的两个离子进行了演示。我们可以利用这种远程纠缠来增强对每个离子中的位移的测量。当离子带电时，感应离子的微小位移可以用来测量微小的电场，并应用于探测暗物质。我们开发的用于纠缠远程机械振子并测量其位移的方案也将适用于其他光学机械系统。通过使用离子运动的非经典态，例如压缩态，可以获得进一步的增强。最后，我们可以利用离子的运动自由度来探索一种不同的量子计算方法，在这种方法中，我们将信息编码在离子的运动中，而不是它们的内态。在这里，离子运动提供了一个更大的希尔伯特空间来探索，具有纠错的潜在优势。我们可以利用我们系统独有的远程纠缠来开发用于连续变量量子计算的新协议，这也将适用于其他系统，如超导量子比特。

Entanglement, a uniquely quantum phenomenon, enables two initially independent quantum systems to be interlinked. Entanglement forms the basis of why quantum technologies have an advantage to their classical counterparts, in particular for computing and networking. At Oxford, we have developed a quantum network of trapped ions, generating entanglement between ions in two macroscopically separate systems via a photonic interconnect. While this network was originally built for applications in quantum computing or cryptography, in this project, I aim to use our quantum network for entanglement enhanced sensing, using either the optical transition of these ions or their motion.First, I aim to build a network of entangled optical atomic clocks for enhanced frequency comparisons of ions in two separate traps. Optical atomic clocks are used for the most precise measurements of time. Precision timing is essential for applications from global positioning satellites, precision agriculture, or for the timestamping of financial transactions to ensure security. Frequency comparisons between two atomic clocks are also used for geodesy, and to probe variations of fundamental constants, or the properties of dark matter. However, such frequency measurements are typically limited by the standard quantum limit. Entanglement provides a path beyond that limit, reducing the number of measurements required to achieve a given precision. An entangled network of clocks would also maximise the use of timekeeping resources and have potential security benefits as well. Our experiment is the first demonstration of such a network. Starting from our initial proof of principle demonstration, we will incorporate another ion species, showing the versatility of our system to extend the remote entanglement to transitions that are more stable and can be probed longer. In addition, we can build on our initial demonstration by adding local entangling operations in each network to further enhance the frequency measurements.Second, I want to generate remote entanglement of the motional states of the ions. By coupling the ions' internal states to their motion, we can map the initial spin-spin entanglement to their respective motions. This demonstration would be the first for two ions in separate systems, generating entanglement between quantum states that have a spatial extent of a few nm even though they are separated by metres. Previous demonstrations have been done for two ions in a single trap. We can use this remote entanglement to enhance measurements of displacements in each of the ions. As the ions are charged, sensing small displacements of the ion can be used to measure small electric fields, with applications to detecting dark matter. The protocols we develop for entangling remote mechanical oscillators and measuring their displacements would also be applicable to other optomechanical systems. Further enhancements could be obtained by using nonclassical states of the ion motion such as squeezed states. Finally, we can use the ions' motional degree of freedom to explore a different approach to quantum computing, where we encode the information in the ions' motion rather than their internal states. Here, the ion motion offers a larger Hilbert space to explore, with potential advantages for error correction. We can use the remote entanglement that is unique to our system to develop new protocols for continuous variable quantum computation, which would also be applicable to other systems such as superconducting qubits.