Study of Quantum Fields and entanglement using dilute quantum gases

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.