Research On Eigenstates Of The Higher Powers Of Annihilation Operator And Non-Local Tests Of Quantum Mechanics

This thesis mainly includes the following two parts:(1) The squeezing effect is one of the most typical non-classical properties in a quantized light field, and has an important application prospect in optical communication and gravitationalwave detection. Since the implement of the squeezed light experimentally in 1985, much attention has been paid to non-classical optical fields. In order to study the non-classical effects of optical fields and their possible applications, various quantized optical states with non-classical effects should be beforehand prepared. In the framework of dynamical invariant theory, we introduce the annihilation operator a(t) and creation operator d+(t) for a time-dependent harmonic oscillator. The orthonormalized eigenstates of the operator aN(t) (N≥3) are constructed in terms of the eigenstates of the corresponding dynamical invariant, and the mathematical and quantum statistical properties are discussed in detail. The harmonic oscillator is a simple but typical idealized model in physics.It provides a suitable description of many practical problems, such as a quantized optical field, the vibrations of lattices, the motion of the particle in a Paul trap, etc. Specifically, a particle moving in a Paul trap with periodically varying frequency is treated as an example to demonstrate the dynamical squeezing effects in the eigenstates of a3 (t). It is shown that the eigenstates of a3(t)of the time-dependent harmonic oscillator are squeezed, while there is no squeezing effect in the time-independent system.(2) Many years ago, Einstein and Born argued on a basic concept, i.e., the so-called completeness, in quantum mechanics. With Bell inequalities, their debates for this basic principle of quantum mechanics were changed from the speculative nature to experimentally-testable quantitative modalities. Among many forms of the Bell inequalities, the CHSH one is the most convenient ones for experimental tests. In this part, we design an experimental system to test the violation of the CHSH inequality by taking into account certain specific measurement errors. Here, the desirable entangled photon pairs are also produced by a nonlinear optical parametric down-conversion process, and the detections of the entangled photon pairs are implemented by using the single-photon detectors with significantly low dark conuters.