Quantum Coherence

量子现象的一个基本方面是描述粒子状态的量子波的非局域相干性，这被称为波粒二象性。由此产生的一个结果就是海森堡不确定性原理，根据这个原理，粒子的位置和动量或时间和能量的不确定性的乘积有一个最小值，这个最小值由普朗克常数给出。我们计划调查latteruncertainty原则与广义相对论引力场，使用我们早期的工作，获得这种不确定性关系，仅使用内在的测量系统正在调查。我们还将使用我们引入的新的非定域量，称为模变量，来研究波函数的非定域量子相干性。这将用于研究Aharonov-Bohm效应（由PI发现），这是波函数与电磁场的非局域相互作用。由于Aharonov-Bohm效应的散射的一些新的方面将被研究。后一项工作涉及到一系列问题，包括表面波和偏振光在光纤中的传播，光纤中可能存在各种杂质。波函数的量子相干性也为使用量子系统进行安全通信和构建量子计算机提供了可能性。用目前最先进的计算机所需时间超过宇宙寿命的计算，量子计算机将在不到一秒钟的时间内完成。我们将尝试使用PI发现的弱测量来获得更好的量子通信。我们还将尝试使用PI和co-PI发现的几何相位来构建量子计算机。

A fundamental aspect of quantum phenomena is the non-local coherence of thequantum wave that describes the state of a particle, which is called thewave-particle duality. A consequence of this is the Heisenberg uncertaintyprinciple according to which there is a minimum to the product of theuncertainties of the position and momentum or time and energy of the particlethat is given by the Planck's constant. We plan to investigate the latteruncertainty principle in relation to the general relativistic gravitationalfield, using our earlier work that obtains this uncertainty relation using onlymeasurements intrinsic to the system under investigation. We shall also use newnon-local quantities that we have introduced, called modular variables, to studythe non-local quantum coherence of the wave function. This will be used toinvestigate the Aharonov-Bohm effect (discovered by the PI), which is thenon-local interaction of the wave function with the electromagnetic field. Somenew aspects of scattering due to the Aharonov-Bohm effect will be studied. Thelatter work is relevant to a wide class of problems involving surface waves andpolarized light propagating in optical fibers, where various impurities may bepresent.The quantum coherence of the wave function also opens up the possibilities forsecure communication using quantum systems and the construction of a quantumcomputer. Computations which would take a present state-of-the-art computer morethan the life-time of the universe to do would be done in less than a second bya quantum computer. We shall try to use the weak measurement, discovered by thePI, to obtain better quantum communication. We shall also try to use the geometric phase discovered by the PI and a co-PI towards constructing a quantumcomputer.