Abstract
It is a typical assumption that closed quantum systems must have real eigenvalues and hence, be Hermitian. However, Parity-Time (PT) symmetric systems are systems that, despite being non-Hermitian, can have real eigenvalues. They have a number of properties and applications that have been demonstrated using a variety of classical systems. To date, while several quantum simulations of PT-symmetric systems have been performed, they all require postselection and no applications of physical quantum PT-symmetric systems have been shown or demonstrated.Here, we first look at simulating PT-symmetric and non-Hermitian systems using postselection by embedding the non-Hermitian system into a larger Hermitian system, including using Halmos' dilation to simulate two coupled PT-symmetric systems that are the time-reverse of each other using single photons input into a unitary interferometer.
With the realisation that there is a link between symplectic transformations inherent in nonlinear optical systems and PT-symmetry, we then consider a nonunitary interferometer created using nonlinear optics in the form of squeezing that can perform postselection-free simulations of N-mode non-Hermitian systems and emulate this simulating a small 2-dimensional PT-symmetric system.
Finally, we look at coupled microring resonators, which necessarily requires both squeezing and loss terms to function as a single photon source. In considering this from the viewpoint of PT-symmetry and creating an Exceptional Point, we theoretically show that this system can create single photons with a purity above 99% at an enhanced efficiency compared with a single ring.
As a result of considering these systems, we will demonstrate that non-Hermitian and PT-symmetric dynamics can be naturally created using Hermitian systems.
| Date of Award | 22 Mar 2022 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Anthony Laing (Supervisor) & Yogesh Joglekar (Supervisor) |