Light-Matter interface detection of the full correlations distribution of quantum many-body systems

在过去的50年里，科学技术取得了巨大的进步，对社会和经济产生了巨大的影响，导致了一场类似于工业革命的新的信息革命。尽管电子设备的复杂性、可控性和小型化已经达到了令人难以置信的水平，但信息处理依赖于20世纪30年代数学家(图灵、丘奇、冯·诺伊曼)阐述的相同的经典原理。20世纪80年代，包括R·P·费曼和D·多伊奇在内的理论物理学家以及后来的P·肖尔等计算机科学家提出的富有远见的想法，将量子力学的概念结合在一起，引发了另一场信息技术革命：量子信息理论的诞生。在经典世界中，位是最小的信息单位，可以取0或1的值，大致对应于电路是断开还是闭合。相反，在量子世界中，人们处理的是量子比特或量子比特，例如通过电子自旋或光子极化来体现。这些量子比特可以像在经典情况下那样假设两个值0和1，但它们也可以同时在这两个值的叠加中准备。这一明显令人震惊的特性已经在大量实验中得到验证，并导致某些任务的惊人速度，比如用量子计算机进行整数因式分解，即类似于传统计算机处理量子比特的设备。到目前为止，量子计算机只用少量量子比特--不超过10个--囚禁离子或中性原子、光子，但也有固态设备。因此，大规模量子计算机有望在几十年内实现。然而，被称为量子模拟器的特殊用途量子计算机目前正在实验室中生产，这些实验室的原子温度比绝对零度(超低温)高出十亿分之一。这类实验的目的是在可控的环境下再现难以获得的量子材料的物理学，例如高温超导体，从而允许科学家探索其性质并测试模型和理论。拥有超冷原子的量子模拟器面临的一大悬而未决的问题是，一旦样品在量子态下制备，如何检测其特征。基于高分辨率光学显微镜的成像或激光对样品的散射，正在使用几种技术。在这个项目中，我们建议使用一束偏振光来探测中性原子阵列。作为光-原子相互作用的结果，光的偏振根据原子的状态而旋转。因此，可以测量的出射光脉冲提供了关于原子状态的信息。这种方案的优点是，人们可以在不破坏原子样本的情况下进行测量，而不像在其他方案中那样。该项目的结果将揭示许多量子比特的量子态的亲密结构，这些量子比特由被电磁场俘获的原子所体现。因此，它不仅有望对量子信息论产生重大影响，而且将对原子物理、统计力学和凝聚态物理产生重大影响。与经典的量子比特相比，量子比特还有另一个特点：人们可以将一个量子比特的状态与另一个量子比特的状态关联起来，这样如果对两个量子比特进行测量，结果总是一致的。这种被称为纠缠的现象是量子信息应用的基础，比如量子隐形传态。该项目的另一个目标是提议将两个这样的超冷原子样本纠缠在一起，从而在由数百个原子组成的两个分离的大质量物体之间产生纠缠。我们提出的方案可以在下一代超冷原子实验中实现。

The last fifty years have witnessed tremendous advances in science and technology with a huge impact on society and economy leading to a new information revolution in analogy with the industrial one. Although electronic devices have reached an incredible level of complexity, control and miniaturisation, information processing relies on the same classical principles enunciated by mathematicians in the 1930s (Turing, Church, von Neumann). In the 1980s, visionary ideas from theoretical physicists, including R. P. Feynman and D. Deutsch, and later from computer scientists such as P. Shor, combining concepts from quantum mechanics led to another revolution of information technology: the birth of quantum information theory. In the classical world, a bit, the smallest unit of information, can assume values 0 or 1 corresponding roughly to an electrical circuit being open or closed. In the quantum world, instead, one deals with quantum bits or qubits, embodied for example by an electron spin or a photon polarisation. These qubits can assume the two values 0 and 1 as in the classical case but they can also be prepared in a superposition of the two values simultaneously. This, apparently shocking, property has been verified in numerous experiments and is responsible for the amazing speed-up of certain tasks like integer numbers factorisation with quantum computers, i.e. devices that process qubits in analogy with traditional computers.So far quantum computers have only been realised with a small number of qubits-no more than ten-with trapped ions or neutral atoms, photons but also solid state devices. Large scale quantum computers are therefore expected to be realised only in a few decades.However special purposes quantum computers, called quantum simulators are currently being produced in laboratories working with atoms at temperatures one billionth above the absolute zero (ultracold). Such experiments aim at reproducing, with a controlled environment, the physics of hard to access quantum materials, for example a high-temperature superconductor, thus allowing scientists to probe its properties and test models and theories.A big open question for quantum simulators with ultracold atoms is how, once the sample is prepared in a quantum state, to detect its features. Several techniques are being used based on imaging through a high resolution optical microscope or on scattering of laser light off the sample. In this project we propose the use of a beam of polarised light to probe arrays of neutral atoms. As a consequence of the light-atoms interaction, the light polarisation rotates depending on the state of the atoms. Therefore the outgoing pulse of light, that can be measured, gives information about the state of the atoms.The advantage of this scheme is that one can perform the measurement without destroying the atomic samples as in other proposals. The outcomes of this project will shed light on the intimate structure of the quantum state of many qubits embodied by atoms trapped by electromagnetic fields. For this reason, it is expected to have a strong impact not only in quantum information theory, but also in atomic physics, in statistical mechanics and in the condensed matter physics. Qubits have another peculiarity compared to their classical counterpart: one can correlate the state of one qubit with that of another one in such a way that if one performs a measurement of the two qubits the outcomes always coincide. This phenomenon called entanglement is at the basis of quantum information applications like quantum teleportation. Another goal of this project is a proposal to entangle two of these ultracold atomic samples thus creating entanglement between two separated massive objects composed of hundreds of atoms. The scheme we propose can be implemented in the next generation of experiments with ultracold atoms.