In the last chapter, we considered the possibility that an object such as the pointer of an apparatus designed to measure H/V polarisation (see Figure 7.1) might in principle be forbidden from being in a quantum superposition if it was large enough. A microscopic system, such as a photon polarised at 45° to the horizontal, would then collapse into an h or a ν state as a consequence of such a measurement. To test this idea, we considered how we might detect a macroscopic object in such a superposition and we found that this was very difficult to do. The oscillating pointer of Figure 7.1 is very sensitive to random thermal disturbances and as a result is almost certainly going to swing in one direction or the other, rather than being in a superposition of both. Macroscopic superpositions have indeed been observed in SQUIDs (see the last section in Chapter 7), but only after great care has been taken to eliminate similar thermal effects. In the context of the last chapter, the randomness associated with thermal motion was considered as a nuisance to be eliminated, but might it instead be just what we are looking for? Perhaps it is not that thermal effects prevent us observing quantum superpositions, but rather that such states are impossible in principle when thermal disturbances are present. This could provide another way out of the measurement problem.
In the last chapter, we considered the possibility that an object such as the pointer of an apparatus designed to measure H/V polarisation (see Figure 7.1) might in principle be forbidden from being in a quantum superposition if it was large enough. A microscopic system, such as a photon polarised at 45 ° to the horizontal, would then collapse into an h or a v state as a consequence of such a measurement. To test this idea, we considered how we might detect a macroscopic object in such a superposition and we found that this was very difficult in practice. The oscillating pointer of Figure 7.1 is very sensitive to random thermal disturbances and as a result is almost certainly going to swing in one direction or the other, rather than being in a superposition of both. Macroscopic superpositions have indeed been observed in SQUIDs (see the last section in Chapter 7), but only after great care has been taken to eliminate similar thermal effects. In the context of the last chapter, the randomness associated with thermal motion was considered as a nuisance to be eliminated, but might it instead be just what we are looking for? Perhaps it is not that thermal effects prevent us observing quantum superpositions, but rather that such states are impossible in principle when thermal disturbances are present. This could provide another way out of the measurement problem.
The objective of this thesis is to investigate two fundamental problems of quantum optics: macroscopically distinguishable quantum superposition states and quantum chaos. After a brief introduction, Chapter II and Chapter III investigate the problem of superposition states. A method for generating the macroscopically distinguishable superposition states via single two-level atom dispersion was proposed by Savage et a/.[Opt.Lett. 15, 628(1990)]. In chapter II, an extension of this model to a three-level atom is investigated and the result shows that the superposition state can be obtained from the three-level model sytem in the dispersive limit. In chapter III, S ’ the effect of the atomic linewidth is considered. If the atomic linewidth is included, there will be two contradictory conditions for the generation of distinguishable superpositon states. This shows that the atomic linewidth prevents the formation of macroscopically distinguishable superpositon states by the proposed method. From chapter IV to chapter VI, we investigate the transition from a dissipative quantum system to a classically chaotic system. Specifically, wre apply the method of quantum trajectories to the case of optical second harmonic generation. In chapter V, the Q function is obtained numerically by this method and found to agree with the results obtained by solving the master equation. In chapter VI, the field amplitudes and mean photon number associated with a single quantum trajectory are investigated. The results show that the trajectory becomes more classical and the configuration of the classical strange attractor is approached as the field strength is increased. This is because the mean values of operator products factorize into products of mean values in the classical limit.