Generally speaking, a phase transition is a discontinuous change of certain properties of a system upon changing some external condition.

In quantum mechanics, it is well known that a Hermitian operator guarantees a real eigenvalue spectrum, but the reverse is not necessarily true. If an operator is PT symmetric, its eigenvalues are real in PT symmetric phase and are imaginary in broken PT symmetric phase. Such a PT symmetric system is hard to realize in quantum system, but it is relatively easy to realize in optics by system with carefully designed regions with different refractive indices. However, the experimental observation reported by recent literature often relies on analyzing successive interference patterns [1] and thus the observation is not real time, or relies on mea...[ Read more ]

Generally speaking, a phase transition is a discontinuous change of certain properties of a system upon changing some external condition.

In quantum mechanics, it is well known that a Hermitian operator guarantees a real eigenvalue spectrum, but the reverse is not necessarily true. If an operator is PT symmetric, its eigenvalues are real in PT symmetric phase and are imaginary in broken PT symmetric phase. Such a PT symmetric system is hard to realize in quantum system, but it is relatively easy to realize in optics by system with carefully designed regions with different refractive indices. However, the experimental observation reported by recent literature often relies on analyzing successive interference patterns [1] and thus the observation is not real time, or relies on measuring complex transmission coefficients [2] which are difficult to measure at optical frequency. Also, the PT symmetric systems proposed in other literature are often very complicated to realize in experiment.

In this thesis, we propose to use a simple and passive waveplate to observe phase transition due to PT symmetry breaking. By arranging unit cells consisting of two orthogonal dipole oscillators with different loss on a waveplate and by varying their relative distance, translational symmetry is retained but PT symmetry breaking is manifested by a sudden jump of cross-polarization intensity pattern with its angle representing the phase of the system. Neither interference with a reference beam nor measurements of complex transmission coefficients are required. Also, the observation is real time. An experimental feasible design which requires only one type of metal is proposed. It is found that the waveplate must be compact with low order of rotational symmetry and the observation frequency must be very close to the resonance frequency of the oscillators in order to observe a sharp phase transition, otherwise the angle is not quantized which corresponds to a detuned PT symmetric system.