Study of Quantum Fields and entanglement using dilute quantum gases

在七十年代初，人们意识到粒子的概念取决于用于检测粒子的量子测量过程的具体细节，并且测量设备的运动状态可以确定是否观察到粒子。这一发现创造了一种新的观点，这是由富林、昂鲁和霍金的工作推动的，他们证明了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，将被加速观察者视为有粒子的区域。粒子的数量和能量会随着加速度的增加而增加。这种效应被称为Unruh效应。由于根据广义相对论，加速度和引力是等价的，所以类似的效应就是黑洞辐射。爱因斯坦、蒲多尔斯基和罗森在1935年的一篇论文中引入了格丹肯实验，以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。这个思维实验展示了量子力学的悖论特征，展示了奇怪的关联，有时被称为远距离的诡异作用。这些相关性是可以量化的。人们提出了各种量化方法，称为纠缠度量。我建议用第一段中介绍的观点来研究纠缠。我对研究不同观察者探测到的纠缠行为很感兴趣。由于由于实验上的困难，Unruh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是所有处于相同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数量的粒子，但由于量子力学的规则，由于不确定关系，这个点可能相当大。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，即如果我们将真空视为一种让光传播的乙醚，那么BEC就是信息传播的背景。在这个方案中，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，而不是真正的真空，而是它的类比，在非常低的温度下的BEC。然后我将提出一些实验，在这些实验中，两个在真空附近加速的可观测粒子将会纠缠在一起，也就是说，将显示EPR关联。这一实验的可行性不仅是对被认为是正确的物理理论的证明，而且是研究无法计算的方案的一种手段。加速产生纠缠是一个不能用解析方法解决的问题。这项实验的实现将为这一问题提供一个数值解决方案。这里需要注意的是，这个问题除了不是解析可解的之外，在常规计算机上也不能用数值方法进行检验。量子计算机可以检查这一结果，但不幸的是，这样的计算机并不存在。对只能用量子计算机进行数值检验的问题进行实验建模，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踏脚石。

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.