Study of Quantum Fields and entanglement using dilute quantum gases

在七十年代早期，人们认识到粒子的概念取决于用于探测它们的量子测量过程的具体细节，并且测量装置的运动状态可以决定是否观察到粒子。这一发现创造了一个新的观点，这一观点是由Fulling，Unruh和Hawking的工作所推动的，他们的工作表明，在一个区域中发现的粒子数量取决于测量设备的加速度。例如，真空，即一个根本不包含粒子的区域，将被加速的观察者视为有粒子的区域。粒子的数量和它们的能量会随着加速度的增加而增加。这种效应被称为安鲁效应。因为根据广义相对论，加速度和引力是等价的，一个类似的效应就是黑洞辐射。爱因斯坦、波多尔斯基和罗森在1935年的一篇论文中引入了一个格丹肯实验，论证量子力学不是一个完整的物理理论。它有时被称为EPR悖论。这个思想实验展示了量子力学的矛盾特征，展示了奇怪的相关性，有时被称为远距离的幽灵作用。这些相关性可以被量化。提出了各种量化方法，这些方法被称为纠缠度量。我建议用第一段介绍的观点来研究纠缠。我对研究纠缠被不同的观察者探测时的行为很感兴趣。特别是，我想探索这些想法的实验实现。由于实验困难，昂鲁效应从未被测量过，我将研究这种效应在玻色爱因斯坦凝聚体（BEC）中的实现。BEC是处于同一状态的原子的宏观集合。BEC可以被认为是位于同一点的宏观粒子数，但由于量子力学的规则，由于不确定性关系，这个点可能很大。人们发现，这种奇怪的状态在某种程度上与光的真空非常相似，也就是说，如果我们把真空想象成某种让光传播的以太，那么BEC就是信息传播的背景。在本课题中，我想研究在BEC中实验实现这些效应的可行性。首先，我将研究一个测量Unruh效应的方案。我将提出一个方案，在这个方案中，加速观察者将在真空中发现粒子，不是真正的真空，而是它的类比，非常低温度下的BEC。然后，我将提出两个在真空附近加速的可观测物会纠缠在一起的实验，即会显示EPR相关。这一理论的实验可行性是重要的，它不仅证明了人们相信的物理理论是正确的，而且作为研究一种无法计算的方案的手段。由加速度产生的纠缠是一个无法解析解决的问题。本实验的实现将为这一问题提供一个数值解。这里需要注意的是，这个问题，除了不能用解析方法解决之外，也不能用普通的计算机进行数值检验。量子计算机可以检查这个结果，但不幸的是，这样的计算机并不存在。模拟实验问题只能通过使用量子计算机进行数值检查，这正是量子模拟器背后的想法。这项技术的进步将成为创造量子计算机的重要垫脚石。

In the early seventies it was realized that the notion of particles depends on the specific details of the quantum measurement process used to detect them, and that the state of motion of the measuring device can determine whether or not particles are observed. This discovery has created a new viewpoint which was prompted by Fulling,Unruh and Hawking's work demonstrating that the number of particles found in a region depends on the acceleration of the measuring device. For example, the vacuum, i.e. a region that contains no particles at all, would be seen by an accelerated observer as aregion with particles. The number of particles and their energy would increase with increased acceleration. This effect is known as the Unruh effect. Since by general relativity acceleration and gravitation are equivalent, an analogical effect would be the black hole radiation.Einstein, Podolsky, and Rosen, introduced a Gedanken experiment in a 1935 paper to argue that quantum mechanics is not a complete physical theory. It is sometimes referred to as the EPR paradox. This thought experiment shows paradoxical features of quantum mechanics, demonstrating strange correlation sometimes referred to as spooky action from a distance. These correlations could be quantified. Various quantifications were suggested which are referred to as measures of entanglement.I propose to study entanglement using the view point introduced in the first paragraph. I am interested in studying the behavior of entanglement when it is probed by different observers. Especially, I would like to explore the experimental realization of these ideas.Since the Unruh effect was never measured due to experimental difficulties, I will study the realization of this effect in a Bose Einstein Condensate (BEC). A BEC is a macroscopic collection of atoms which are all located in the same state. BEC could be thought of as a macroscopic number of particles located at the same point, but this point, due to the rules of quantum mechanics could be quite big, due to uncertainty relations. It was found that this strange state, in some way, is very similar to the vacuum of light, i.e. if we think of the vacuum as some kind of ether which let the lightpropagate through, the BEC is a background in which information propagates.In this proposal I want to study the feasibility of the experimental realization of these effects in BEC. First I will study a scheme to measure the Unruh effect. I will propose a scheme in which an accelerated observer will find particles inside the vacuum, not thereal vacuum but its analogy, the BEC at very low temperature. Then I will propose experiments in which two observables which accelerate next to the vacuum would become entangled, i.e. would show EPR correlation. The experimental feasibility of this is important not only as a proof of physical theory which is believed to be true, butalso as a mean to study a scheme which cannot be calculated. The creation of entanglement by acceleration is a problem which cannot be solved analytically. The realization of this experiment would provide a numerical solution to this problem. It is important to note here, that this problem, in addition to not being analyticallysolvable can neither be checked numerically in a regular computer. A quantum computer could check this result, but unfortunately such a computer does not exist. Modeling experimentally problems that could be checked numerically only by using a quantum computer is just the idea behind the quantum simulator. The advance of this technology would serve as a major stepping stone to the creation of a quantumcomputer.